Physics 15b Lab 2: Current, Ohm’s Law, Resistance, EMF
In Chapters 1-3 of Purcell, the potentials and fields associated with stationary
charges were studied. Chapter 3 allowed charges to move freely in conductors, but the
resulting potentials and electrical fields were only evaluated after the charges stopped
moving. Chapters 1-3 were the subject of the previous lab. Chapter four, which considers
moving charges, is the basis for this lab.
Conductivity as a macroscopic property of materials that depends upon the
number of free charge carriers in a material and on the collisions experienced by the
charge carriers as they move through the material. The resistivity and conductivity of
various materials is presented in table 4.1. The number of free charge carriers in a metal
is fixed. The number of free charge carriers in a semi conductor can be increased by
doping, or by increasing the temperature of the material. The number of free charge
carriers in a neutral gas can be increased by ionizing gas atoms, a process that is used in
Geiger counters and neon signs. http://en.wikipedia.org/wiki/Neon_lamp. This lab will
consider the temperature dependence of conductivity, as well as the effect of doping,
temperature, and ionization on the number of free charge carriers.
Just as the concept of capacitance underlies circuit element known as the
capacitor, the concept of conductivity underlies the circuit element known as the resistor.
The current, I, flowing through a resistor with resistance R is a linear function of the
voltage, V, across the resistor where I=V/R. Many important systems have current to
voltage relationships that are highly non-linear. Sparks and arcs are particularly dramatic
manifestations of non-linear current to voltage relationships. This lab will consider
systems with non-linear current to voltage relationships, where the non-linearities have
different origins.
Not only can current be a non-linear function of voltage, but the magnitude of the
current can also depend on the sign of the voltage; therefore, the I/V for a positive
voltage may be different from I/V for the corresponding negative voltage. To study such
effects, you will measure the response of a system when charge is sent through the
system in one direction and then the response when charge is sent through the same
system in the opposite direction. If space is uniform, changing the sign of the voltage
applied across a circuit element is the same as keeping the sign of the voltage the same,
but reversing the direction of the device. As shown below, if the device is uniform
reversing the device has no effect on the experiment at all. If the device is uniform,
leaving the device fixed, but reversing the voltage results in a current that is also
reversed; however, the ratio of I to V for the reverse voltage is exactly the same as for the
case where the voltage went in the forward direction as long as the rest of the space is
symmetric. In contrast, if the device is not uniform, then changing the sign of the voltage
can make a physical difference. Purcell often stresses the role of symmetry in limiting
what is physically possible (e.g. symmetry requires that the electric field of a spherical
object have only a radial component), and much of modern physics studies and exploits
different sorts of symmetries. Checking whether the response of a circuit to a voltage
Vo>0 differs from its response to –Vo is a very simple example of a measurement that
probes symmetry by reversing the direction of a potential and measuring the response of
the system to the reversed potential.
The current is not always a unique function of the voltage: in some cases, the
same voltage can produce different currents. A system is hysteretic if its response to a
stimulus depends on the history of the system, not just the present value of the stimulus.
Biological systems can be hysteretic. Systems that experience avalanches are also
hysteretic. Memories require hysteresis, and ferromagnetic systems are used in magnetic
memories precisely because of their strong hysteretic properties. Thermostatic
temperature control systems and battery rechargers are hysteretic, and their energy
efficiency depends on how hysteretic they are. The hysteresis in battery charging is an
important issue that has limited the successful exploitation of solar energy. Hysteresis can
destabilize systems: factors affecting global warming show destabilizing affects.
Hysteresis is also exploited to stabilize systems by making them less sensitive to noise. In
this lab you will consider at least one hysteretic system.
Current, voltage, energy, and power are not only interesting as basic science
topics, they also play a significant role in public policy: energy generation and use are
becoming subjects of vigorous debates for a number of reasons including national
security and climate change. The relationships between current, voltage, energy, and
power impose significant constraints on how much electrical energy efficiency can be
achieved. Lighting consumes a large fraction of the electrical energy in the United States.
At present, a large fraction of our lighting comes from incandescent light bulbs that are
very energy inefficient. Australia is already banning incandescent light bulbs. Two
alternatives are fluorescents lights and light emitting diodes LEDs. LED’s consist of an
n doped semiconductor next to a p doped semiconductor, where a voltage source does
work to move charge up the potential hill generated by the internal electric field of the
LED. That potential energy is released in the form of light. The use of compact
fluorescent light bulbs and LED’s is being heavily promoted. It has been suggested that
if all of the incandescent light bulbs in the US were switched to LEDs, the US could
lower its electrical energy consumption by approximately 30%. In this lab, you will
consider how the current to voltage relationships for conductors, semiconductors, and
plasmas determine the efficiency with which incandescent light bulbs, LEDs, and
fluorescent light bulbs convert electrical energy to light. You will also consider some of
the spectral and temporal properties of the light that is produced, as well as the power
conversion efficiency.
A consequence of the definition of temperature is that
where ν is the frequency, T is the temperature in degrees Kelvin, h is Planck’s constant,
and c is the speed of light. This distribution is illustrated in an applet. Figures from the
applet are shown on the left below, where the red curve shows the intensity as a function
of wavelength with a rainbow in the back showing the positions of various colors of
visible light. The corresponding temperatures are shown in pink. The vertical scale is the
same on all of the graphs, so the decrease in intensity with temperature can be clearly
seen. The figure below shows the measured intensity of the light emitted from the sun,
where the yellow corresponds to the spectrum measured at the top of the atmosphere and
the red corresponds to a measurement made at sea level. The black lines shows the
blackbody spectrum for a temperature of 5250 C.
.
http://en.wikipedia.org/wiki/Solar_radiation
People like light that has approximately the same color distribution as sunlight and are
less happy when there are significant deviations. Light is emitted by an incandescent light
bulb when its filament is made sufficiently hot that it emits visible light with a spectrum
similar to sunlight, so people like incandescent illumination; however, the process is very
energy inefficient. In fluorescent lights, charged particles that are accelerated by an
electrical potential collide with atoms, so the electrical potential is doing work to
accelerate the charge particles. The collisions between the charged particles and the
atoms leave in an excited state. The atoms emit light when they decay from the excited
state to which they were transferred by the collisions. The emitted light is in the UV, so a
third step is required to convert it to visible. The white lining inside a fluorescent light
absorbs the UV and reemits it at a variety of frequencies; therefore, the light emitted from
a fluorescent bulb consists of many narrow lines distributed over the visible spectrum.
Thus, the conversion of electrical energy to light is a three step process; however,
fluorescent lighting generates much less wasted heat than incandescent lighting. LED’s
use electrical energy to do work that increases the potential energy of charges. Light is
emitted when the charges suddenly give up the potential energy that they gained from the
electrical work. In this process, the electrical energy does work directly on the charges
that emit the light rather than accelerating charges that then excite atoms as in fluorescent
lights. The energy efficiency of LEDs is significantly higher than for fluorescent lights.
Pre-lab Questions:
1. Consider an Ohmic system (V=IR), where V=VoCos[wt]. Plot V as a function of time
for t between from 0 to 2 (2 Pi)/w. Plot I as a function of time for t between from 0 to 2(2
Pi)/w. What is the ratio of I(t) to V(t) ? Make an x y graph, consisting of a series of
points with an x value given by V(t) and a y value given by I(t) Hint: This is just I vs V
since y= I(t) =V(t)/R=x/R.
Bonus: Consider a system with V=VoCos[wt] and I= (Vo/R) Sin[wt] as determined by a
system that takes data for t between from 0 to 2 (2 Pi)/w. This is a system where the
current is proportional to the voltage, but there is a phase lag between them. Such
systems will be discussed in detail in Chapter 8 of Purcell and one example is given in a
bonus experiment in this lab.
2. Consider an electric heater with a metallic heating element. When the heater is first
turned on, the heating element is cold and the resistance of the heater is Rcold. If a
constant voltage V is applied across the heater, what is the current that flows through the
cold heating element? If the voltage across the heater remains fixed, does the current
increase, decrease or stay the same as the heater warms up? Is I(V) a function (that is,
given a value of V is the value of I uniquely determined by V)? If you quickly turn off
the heater and then turn it on again, is the current just after the heater is turned on larger,
smaller, or the same as the current flowing when you first turned on the cold heater.
Bonus: Give an example of a system with hysteresis that is not a magnetic memory.
3. To understand a PN diode, it is useful to think about a fish tank with a central divider,
where the left side is full of red water and the right side with blue water. This is
illustrated on the left below. If the divider is removed, the red water will begin to diffuse
from right to left and the blue water will move from left to right. This is how cream
mixes into coffee if the coffee is not stirred. The net result is a mixed region, as shown
on the right. In the PN diode case, it is the positive charges from the P doped region that
move into the N doped region and the electrons from the N doped region that move into
the P doped region. The free charge carriers in the N doped region are electrons. The
free charge carriers in the P doped region are called holes.
A cartoon of the process is shown in this applet
http://jas.eng.buffalo.edu/education/pn/pnformation2/pnformation2.html (Note the menu
at the right side offers a heading called “introduction” that explains the applet).
Both the N and P regions were originally electrically neutral; therefore, diffusive motion
of the charges results in the N doped region acquiring a net positive charge and the P
doped region a net negative charge. These net charges produce an electric field that
opposes the diffusive motion. The system rapidly approaches equilibrium, and the
average charge distribution becomes time independent. The resulting free charge carrier
density as a function of position, net charge distribution as a function of position, electric
field as a function of position, and potential as a function of position are shown in the
image below from Wikipedia. http://en.wikipedia.org/wiki/P-n_junction The area
labeled “space charge zone” corresponds to the depletion zone because the density of free
charge carriers in that region is depleted in comparison with the density in the neutral
regions. There is almost no free charge in the depletion zone; therefore, when the size of
the depletion zone is large the two sides of the diode behave as if there were no
conducting path connecting them. In this case, the diode could be approximated by a
single pole single throw switch in the open position where no charge can pass through the
switch.
So far, we have considered the charge distribution and electric field in the diode when
there is no potential difference applied across the diode. If one applies a voltage across
the diode, the charge distribution inside the diode changes. If a sufficiently large positive
voltage is applied across the diode, the depletion zone disappears and free charge can
easily move through the diode. In this case, the diode could be described as a closed
single pole single throw switch in series with a battery and a small internal resistance, as
illustrated below. In the illustration ,the top line shows the internal structure, the line
below it shows the circuit symbol for the diode in the same orientation, and the two final
lines show the approximate equivalent circuits, where one applies when the voltage
across the diode is less then Vthreshold and the other applies when the voltage is greater then
Vthreshold.
Illustrate the size of the depletion zone, and include arrows illustrating the magnitude
and direction of the electric field in the depletion zone and the direction of the current
flow in the depletion zone for a PN diode for four applied voltage differences: 1. Vo=0,
Vo=0.6 V, Vo=-2.
Sketch I vs V for a Si diode for voltages from -1 V to 1 V. Label the regions
corresponding to a reverse bias, a small forward bias, and a large forward bias.
Bonus: Sketch V/I(V) as a function of V. If the diode were an ohmic device with
resistance R, this plot would be a constant with a value equal to the resistance R. The
plot for the diode is not constant, so the diode is not ohmic; however, the value of V/I(V)
could be interpreted as a voltage dependent resistance.
Bonus: The Shockley equation for the current in a diode as a function of V, the voltage
across the diode, is approximately given by I= isat (Exp[V/VT]-1), where VT= k T/e is
the ratio of the thermal energy a a temperature T to the charge of the electron. Note: k is
Boltzmann’s constant= 1.38x10-23 j/K and Vthresh is the threshold voltage for the
material. Isat varies widely from 10-8 to 10-14 amps, but choose 10-12 as a value. Plot I vs
V for a diode at room temperature (T=300 K) for voltages from -1 V to 1 V.
The following websites offer useful information for this problem. You can cut and paste
images from a website to answer questions, but you must provide explanations of the
images. http://electronics.howstuffworks.com/led.htm/printable
http://en.wikipedia.org/wiki/Diode
http://jas.eng.buffalo.edu/education/pn/biasedPN2/BiasedPN2.html
http://www-g.eng.cam.ac.uk/mmg/teaching/linearcircuits/diode.html ; (Note at V=0
question marks appear next to the depletion region diffusion current and drift current. If
you click on a question mark, an additional explanation appears and the red rectangles
highlight the representations of that quantity in the applet. Also note that the charge
flows shown by the dots are for electrons, which are negative charge carriers)
http://jas.eng.buffalo.edu/education/pn/biasedPN/index.html
Bonus: Why does the drift current independent of voltage for voltages less than -1 V?
Bonus: Why are diodes capacitive? Hint:
http://jas.eng.buffalo.edu/education/pn/cv/index.html
4. For a voltage as a function of time given by 170 Cos [2 pi 60 t], what is the RMS
value of the voltage? For a system that delivers electrical power with an RMS voltage of
VRMS, explain why the average power consumed by a device with resistance R that is
connected to this power source is simply VRMS R. What the potential difference between
ground and neutral at a breaker box?
5. What is the Thevenin equivalent resistance of a series combination of R=100 Ohms
and R=1010 Ohms? If the voltage difference across the series combination is V, what is
the current flowing through the series combination. If there is a voltage difference V
across the series combination of 100 Ohms and 1010Ohms, what is the approximate
voltage difference across each of the two resistors? If there is voltage V across a series
combination of R=100 Ohms and R=0.01 Ohms what is the voltage difference across
each resistor?
6. Consider a device with a voltage dependent resistance such that R= 1010 Ohms if the
potential difference across the device is less than 0.6 V, and R=0.01 Ohms if the voltage
is more than 0.6 V. Let the voltage difference across the device be V=2 Cos[wt]. Plot
the voltage across the device as a function of time. Draw vertical lines at the times when
the V=0.6 V. Shade the areas of the graph where V>0.6 V. Plot the resistance as a
function of time on the same graph. What is the current flowing through a resistor with
R= 1010 Ohms if the voltage difference across is 2V? What is the current flowing through
a resistor with R= 0.01 Ohms if the voltage difference across is 2V? Plot I(t), the current
flowing in the circuit as a function of time for t between from 0 to 2 (2 Pi)/w.
Bonus: Consider a device with a voltage dependent resistance such that R= 1010 Ohms if
the potential difference across the device is less than 0.6 V, and R=0 Ohms if the voltage
is more than 0.6 V. Let the device be connected in series with a 100 Ohm resistor. The
voltage difference across the series combination is V=2 Cos[wt]. Plot this voltage
difference as a function of time. Draw the Thevenin equivalent resistance of the series
combination as a function of time on the same graph. Plot I(t), the current flowing in the
circuit as a function of time for t between from 0 to 2 (2 Pi)/w. Plot the voltage across the
100 Ohm resistor as a function of time.
Bonus: Consider a diode in series with a 100 Ohm resistor. Use the equivalent diode
model given in problem 3 to plot V(t) for the signal generator output, the diode and the
resistor on the same plot. Plot I(t) for the circuit. Plot I vs the voltage across the resistor
for voltages from 0 to 1. Plot I vs the voltage across the diode for voltages from -1 to 1 V.
Bonus: Consider a power system that must deliver a fixed power P. This power must be
transmitted over an electrical cable characterized by a resistance R. Express the energy
lost in transmitting electricity through the system in terms of P, R, and the voltage V at
which the power is delivered. Note, the US is pushing for higher power line transmission
voltages and high temperatures superconductors to reduce energy losses in power
transmission.
Bonus: Consider the circuit below. At times t<0, let the switch be connected to the left
side, so that the capacitor is charged by the battery, as shown in the diagram on the left
below. Assume that the system has reached equilibrium by t=0. At t=0 flip the switch so
it is connected on the right, as shown in the diagram on the right below. What is the
voltage across the capacitor as a function of time for t>0?
7. What is the origin of the difference between the yellow and red curves in the solar
radiation graph above that was copied from Wikipedia and included in the introduction to
this lab? What is the origin of the narrow spikes of reduced intensity in the red curve?
8. Draw the electrical schematic drawing corresponding to the breadboard circuit shown
above. Assume both resistors have the same resistance R and that the power supply has a
potential difference V.
Bonus: Assume that you want to measure the current that flows in a device as a function
of the voltage applied across the device. This is called an IV curve. A circuit for such a
measurement is shown in the figure on the left above, but to make the measurement you
need some way to the measure the voltage across the device and the current flowing
through the device. The diagram in the center shows an appropriate circuit, where the A
in the circle represents and ammeter and the V in the circle represents a voltmeter.
Unfortunately, adding them perturbs the circuit. The new circuit is shown on the right
above where R1 is the resistance of the ammeter and R3 is the resistance of the voltmeter.
The perturbation does not significantly affect the experiment if R1<<R2 <<R3. Let R1=
alpha R2 and R3= R2/beta, where alpha and beta << 1. Show that the IV curve for R2
can be approximated by I1/V3= (V1/R1)/V3, where to first order in alpha and beta the
ratio of the measured IV to the true IV is (1+beta), independent of alpha. (Hint: Apply
Kirchoff’s Laws with R1 and R3 expressed in terms of R2)
Circuit schematics will be used extensively in this lab, so a table of circuit symbols is
provided below.
Lab Goals
1. Study the influence of voltage, electric fields, and collisions on charge
propagation and explore the limitations of Ohm’s Law
2. Study the influence of charge carrier density on conductivity.
3. Study energy transfer and power consumption in electrical systems.
4. Study charge propagation in semi-conducting materials, including diodes formed
by combining an n-type semiconductor with a p-type semiconductor.
5. Study parity detection and hysteresis in simple systems
6. Learn how to assemble temporary circuits
7. Discover some effects of apparatus choice on data acquisition and measurement
8. Study effects of combining resistors and capacitors
9. Practice with the correspondence between circuit schematics and actual circuits
10. Learn about the form in which electrical power is distributed in the United States
11. Study the mechanisms underlying the generation of light from electrical power,
including the detailed emission properties and energy efficiency of different
electrically driven light sources.
1. Relationships between Voltage and Current
Goals: Determine the current to voltage relationships for a 150 Ohm resistor, an
LED, and light bulb. Understand the basic mechanisms that govern IV
relationships, and consider symmetry and hysteresis as they apply to light
emitting devices. Study the power consumption of the devices. Measure the
relative energy efficiency of the LED and the light bulb.
a. Materials: 150 Ohm resistor; 100 Ohm Resistor ; 1 BNC T ;1 BNC to
banana;4 BNC cables;4 micrograbber to BNC; function generator; multimeter
Measure the IV (current to voltage) curve for a 150 Ohm resistor using the
function generator as a voltage source for a voltage range of +-5V. You could use
a source with a voltage that is constant as a function of time, but this is very
tedious. You can use the signal generator to produce a voltage that changes
slowly with time. If the change is slow enough, the circuit will be in equilibrium,
so you can apply the results from Chapter 4 to the IV relationships. Thus, you
can measure the IV curve by changing V with time and measuring the resulting
current as a function of time.
Apparatus Assembly Directions
1. Setup the scope to monitor the signal generator
a. Connect the BNC T shown on the left above to the output of the signal
generator that is highlighted by the light blue arrow in the image in the center
above.
i. The T is used to convert a single BNC jack to two jacks, so that two
BNC cables can be connected to the same output as shown in the
image on the right above.
b. Make sure that none of the buttons highlighted by the purple rectangles
depressed. If any are, press on the button and it should pop out.
2. Setup the signal generator to produce a 5 V amplitude triangle wave at 20 Hz
a. Turn on the signal generator on by pressing the button highlighted by the
purple arrow.
b. Connect the output of the signal generator to CH1 on the scope using a BNC
cable connected to one side of the BNC T on the output of the signal generator.
c. Choose the triangle wave output by depressing the button indicated by the
pink arrow.
d. Use the signal on the scope to adjust the signal generator to produce a triangle
wave with a 5 Volt amplitude and a 20 Hz frequency. The amplitude is
controlled by the knob highlighted by the yellow circle. Get the 20 Hz
frequency by pressing the 100 Hz frequency choice button ( indicated by the
dark green arrow) and tuning the coarse frequency adjustment
knob(highlighted by the red circle) until the frequency display reads 20 Hz. If
the displayed frequency changes by more than 1 Hz after you have let go of
the knob for more than 10 seconds, then ask for assistance.
3. Connect the circuit
a. Place the 150 Ohm resistor in the breadboard
b. Connect the Logger Pro current sensor in series with the resistor, as shown in
the schematic and image above
c. Connect a second BNC cable to the BNC T on the output of the signal
generator. The picture on the left above shows the signal generator with the
BNC T connected, and two cables coming out from the sides of the T.
d. Connect a jack/micrograbber combination to the end of this BNC cable, and
then use the micrograbbers to connect the voltage source in parallel with the
series combination of the resistor and the current sensor, as shown in the
schematic and image above.
e. Connect a Logger Pro voltage sensor in parallel with the resistor. Use the
voltage probe with the wires permanently attached to the alligator clips. Place
each of the wires in the voltage sensor alligator clips into a hole in the same
column as each of the two resistor lead wires as shown in the image above.
4. Setup Logger Pro to acquire data
a. Make sure the spectrometer is NOT connected to the USB port on the
computer. If it is connected, it will make data acquisition extremely slow.
b. Make sure that the LabPro Box is connected to the USB input on the computer.
c. Connect the LoggerPro probes to the LabProb Box.
i. Connect the LoggerPro voltage probe with the alligator clips that are
permanently clamped around wires to the input of channel 3 on the
LabPro Box.
ii. Connect the voltage probe with the unmodified alligator clips to the
input of channel 1 on the LabPro Box.
iii. Connect the current sensor to the input of channel 2 on the LabPro
Box.
d. Start IV Template.cmbl. This is a LoggerPro program that will assist you in
taking data. This program should be on the desk top, but if it is not you can
download it from the 15b website. A screen shot of the program is shown
below. The image on the left includes annotation on the significance of each
window. The image on the right shows typical data, including a linear fit to
the IV curve.
Meaning of the program display
e. The upper left box shows the voltages as a function of time. For section 1a
you are using only 1 voltage probe, and its output should be on channel 3. The
output channel 3 is plotted in green, and the output of channel 1 is plotted in
red. The voltage for channel 1 should always be zero for section1a.
f. The lower left box shows the current as a function of time. This should
appear in column 2.
g. The box in the center of the top row shows a plot of the current flowing
through the resistor, IR, as a function of the voltage across the resistor, VR.
h. The superimposed dialog plot gives the linear fit parameters for IR vs VR.
i. The other plots are not used in section 1a.
5. Tune the signal generator to the setting for data acquisition and begin data
acquisition
a. Set the signal generator to 0.2 Hz by depressing the 1 Hz frequency button
highlighted by the bright green arrow. Do not change the frequency
adjustment knobs. The frequency display sometimes shows odd values at
these low frequencies, but the signal generator output should be at 0.2 Hz.
b. Start data acquisition.
c. Measure the IV curve for a 0.20 Hz triangle wave. The data should resemble
the window on the upper right.
6. Troubleshooting: Skip this if everything is working.
i. If the scaling on the graphs is bad
1. You may want to rescale some of the curves so that they
occupy most of the space in the graph, making them easier to
read. Try autoscaling first. To get autoscale right click on the
window and choose autoscale. If LoggerPro makes bad
choices using autoscale, rescale the plot
ii. If the current is not appearing on CH2 or the voltage across the
resistor is not appearing on Ch3, then do the following.
1. Quit LoggerPro
2. Correct the connections to the LabPro Box so the current is on
CH2 and the voltage across the resistor is on channel 3. The
other voltage probe should be connected to CH1, but not
measuring anything. Restart IV Template.cmbl. If the data
acquisition still not working, please ask for immediate
assistance.
Is the resistor ohmic? Calculate the effective resistance as a function of
voltage. Hint: If you click on the IV curve, then choose “Analyze” from the
toolbar, a dropdown menu will appear. Choose linear fit, and a LoggerPro
will calculate the slope and intercept of the line and print the values in the
window. How does the measured resistance compare with the nominal
resistance? Is the device symmetric? Is it hysteretic? Note: you would get the
same results for a 20 Hz triangle wave.
Bonus: Repeat with a 20 Hz triangle wave.
b. Materials: Light Bulb, signal generator;scope;BNC T ; BNC to banana;
micrograbber/BNC jacks and BNC cables; photodiode;multimeter
Apparatus Assembly Directions
1. Setup to apparatus to monitor the IV curve
a. Replace the 150 Ohm resistor with the light bulb by removing the resistor and
placing the light bulb leads in the same breadboard holes that were occupied by
the resistor. An image of the light bulb is shown above on the left. The new circuit
diagram is shown in the center of the figure above.
2. Setup the light collection
a. Connect the photodiode to the LoggerPro voltage probe by clipping the
alligator connectors to the leads of the photodiode. A photograph of the
photodiode is shown at the far right.
b. Place the photodiode so that the black surface is facing the light bulb. The
photograph is actually of the back of the diode.
c. Hold the photodiode just above the surface of the light bulb and keep it there
during data collection.
3. Tune the signal generator to the setting for data acquisition and begin data
acquisition
a. Make sure the signal generator is set 0.2 Hz and start data acquisition.
b. Start IV Template.cmbl. A screen show is shown below. The image on the
left includes annotation on the significance of each window. The image on
the right shows typical data, with directional arrows drawn in to indicate
which curve corresponds to x axis values that are decreasing the time and
which corresponds to x axis values that are increasing with time.
Meaning of the program display
1. The upper left box shows the voltages as a function of time.
a. The green line shows the voltage across the light bulb
b. The red line shows the voltage from the photodiode. This signal is
proportional to the intensity emitted by the light bulb.
2. The lower left box shows the current as a function of time.
3. The box in the center of the top row show a plot of the current flowing
through the light bulb, Ibulb, as a function of the voltage across the light bulb,
Vbulb. as a function of voltage
4. The upper right box shows the intensity emitted by the bulb as a function of
the voltage difference across the bulb
5. The central box in the lower row shows the intensity emitted by the bulb as a
function of the current flowing through the bulb,Ibulb.
6. The lower right hand box shows the intensity emitted by the bulb as a function
of the product VR and IR.
c. Troubleshooting: Skip this if everything is working.
i. If the diode voltage becomes increasingly negative as the light
intensity increases and you would prefer the voltage to become more
positive, reverse the connection between the voltage probe and the
leads to the photodiode. This should make the voltage increase with
increasing intensity.
Measure the IV curve for a 0.20 Hz triangle wave while measuring the voltage
on the photodiode at the same time. The voltage on the photodiode is
proportional to the intensity falling on it, so the voltage is proportional to the
emitted intensity. Is the light bulb ohmic? Is the device symmetric? Is it
hysteretic? What is the voltage across the light bulb when it begins emitting
light? What is the voltage across the light bulb when it stops emitting light?
For currents where the bulb is emitting light, what is the slope of the intensity
vs current curve when the current is increasing with time? Is the slope as a
function of current for the case where the current is decreasing with time
higher or lower than the case when the current is increasing with time?
Explain your result. How many light pulses does the light bulb emit during
one voltage cycle? Is the intensity a linear function of electrical power? For
voltages where the light bulb does emit light does the ratio of emitted intensity
to electrical power increase or decrease with increasing power? Repeat the
measurement with a 20 Hz triangle wave by pressing the 100 Hz frequency
selection button on the signal generator. Explain any differences between the
20 Hz measurement and the 0.2 Hz measurement.
c. Materials: LED (Light Emitting Diode); 100 Ohm resistor;tunable voltage
source; current and voltage monitors; photodiode;1 BNC T ;;4 BNC cables;4
micrograbber to BNC;multimeter
Apparatus Assembly Directions
1. Setup to apparatus to monitor the IV curve for a resistor in an RC circuit
a. Replace the light bulb with the LED by removing the resistor and placing the light
bulb leads in the same breadboard holes that were occupied by the resistor. A schematic
and illustration of the new circuit are shown in the next two images.
2. Setup the light collection
a.Place the photodiode so that the black surface is facing the top of the LED.
LED emission is quite direction, so plcing it on top is important.
b. Hold the photodiode just above the surface of the light bulb and keep it there
during data collection.
3. Tune the signal generator to the setting for data acquisition and begin data
acquisition
d. Make sure the signal generator is set 0.2 Hz and start data acquisition using IV
Template.cmbl.
Measure the IV curve for a 0.20 Hz triangle wave while measuring the voltage
on the photodiode at the same time. Is it ohmic? Is the device symmetric? Is
it hysteretic? What is the voltage across the LED when it begins emitting
light? What is the current across the LED when it begins emitting light? How
many light pulses does the LED emit during one voltage cycle? For voltages
where the LED emits light, does the ratio of the emitted intensity to the
electrical power consumed increase or decrease with increasing power? For
voltages where the LED emits light, is there a range of current values for
which the intensity is a linear function of current? Look at the signal
generator output on the scope. Remove the BNC cable that is connected to
the circuit from the BNC Does the signal generator output change when you
disconnect the circuit? Why?
Bonus: Diodes are often modeled as a series combination of an ideal
diode (R=0 for V>0, R= Infinity for V<0), a battery with a voltage
difference equal to the threshold voltage of the diode, and a series resistor.
Find the values of the series resistance and the battery for the diode in this
experiment.
Bonus: Plot Log[I] vs V for the LED. How well does it fit the Shockley
mode? Fit the Shockley model parameters.
Bonus: Repeat the experiment with a 1k series resistor. Explain the
difference between this result and your original result.
Bonus: The emitted is almost intensity a linear function of current just
above threshold because almost every charge that crosses the junction
transfers from the conduction band to the valence band by emitting light.
At higher voltages, this process becomes less efficient. Offer some
possible mechanisms for this decreased efficiency.
d. Bonus: Overall Questions about the resistor, LED, and flashlight bulb. Please
skip these if you are running short of time.
a. In devices with a potential difference V across them that results in
current flow, does the change in kinetic energy of the electron entering
and leaving the device correspond to eV? If not, why not. Does this
violate conservation of energy?
b. Did the motion of the electrons through the device result in an energy
change in the device? If not, where did the energy go. Please answer
separately for each device with a discussion of results for different
voltages for a given device if applicable.
c. Is there any device to which a voltage can be applied without resulting
in power consumption? If so, over what range of voltages results in no
energy consumption?
d. Double Bonus: Design an experiment to detect an external electric
field. Given the parameters of your experiment, how small a field
could you detect?
2. What comes out of the wall?
Goal: Learn about the form in which electrical power is delivered to consumers
in the US.
a. Materials: light source box; scope probe; scope; multimeter; wet paper towel
Electricity is delivered in the form of an alternating current (AC) signal where
the voltage and current vary sinusoidally with time. Different countries have
different standards. AC voltmeters read the RMS values of the current and
voltage. Ask someone on the laboratory staff to use an AC Voltmeter to
measure the voltage difference between the hot, ground, and neutral outputs of
a standard duplex wall plug, such as the one shown below. A detailed
discussion of power generation and delivery in the US is given in a
supplemental information section. What is the measured voltage difference
between hot and ground? What is the measured voltage difference between
hot and neutral? What is the measured voltage difference between neutral and
ground?
Bonus: Measure the resistance across your body by holding the Ohmeter
leads in your hands. Compare to the resistance across one hand. Compare
with the resistance across your body when your hands are wet. Compare with
the resistance when your hands are wet with salt water. How much current
would flow through those three resistive paths if a 110V AC potential was
connected to those points on your body. How does this compare with 5 mA,
the “safe current?”
b. Materials: Scope; light box, BNC cables, scope probe
The two images above illustrate the connections to the lightbox. For this
section of the lab, you will just use the lightbox to monitor the AC voltage
coming out of a wall socket. The lightbox just makes this experiment safer.
Apparatus Assembly Directions
1. Setup the scope to monitor the AC voltage coming from the wall using the light
box
a. Monitor the voltage difference between hot and ground on Ch1
i. Attach the scope probe to the light box as shown in the image on the
right above
1. Attach the scope probe micrograbber to the wire loop inside
the box behind the slot. The slot in the lightbox has a wire
loop to which the micrograbber on the scope probe can be
attached.
a. The wire behind the slot is connected to the hot output
of the wall socket; therefore, the central pin of the
BNC for the scope probe is attached to the hot voltage
coming from the wall.
2. Attach the alligator clip on the scope probe to the ground
terminal on the outside of the lightbox.
a. The outside of the BNC is not connected to the ground
coming from the wall.
ii. Connect the BNC output of the scope probe to the input of CH1 on
the scope.
b. Monitor the voltage difference between neutral and ground on Ch2
i. Connect the BNC jack on the light box that is labeled neutral to
channel 2.
a. This jack is connected so its center pin is at the neutral
potential, and the outside of the BNC is at ground.
c. Adjust the scope settings so that several cycles of the 60 Hz frequency are
visible on the scope.
2. Finish setting up the light box a and begin data acquisition
a. Plug the cord on the light box directly into the wall socket
b. Adjust the voltage scale on the scope so that you can clearly read the signals
on CH1 and Ch2.
Channel 1 shows the difference between hot and ground. How well is CH1
described by V = 170 Sin (2 π 60 t)? How do the measured peak to peak values
compare with voltage reading on the AC voltmeter when it was connected between
hot and ground? Channel 2 shows the voltage difference between neutral and ground.
Is it zero? How can there be a voltage difference between neutral and ground if the
two are connected at the breaker box?
3. Efficiency of the conversion of Electrical Power to Light
Goal: Understand the basic mechanisms that transfer electrical energy to optical
energy in light sources. Compare the energy efficiency of different electrically
powered light sources. Study the properties of the light emitted by the different
sources.
Divide the class so that at least one group does each of the light sources: 1.
incandescent light bulb; 2. compact fluorescent light bulb; 3. LED spotlight. Each
group will do the same experiments, but with the different bulbs
a. Materials: light emitter and lightbox;variac; photodiode; spectrometer;
temperature sensor; ruler; scope;scope probe;BNC cables, Labview
A schematic of the light box and its connections to the scope are shown in
the schematic diagram in the left hand section of the image above. The
other two images in the figure show photographs of the wiring inside the
box. In the central image, each of the wires is highlighted and labeled,
where red is hot, white is neutral, green is ground, and yellow is V3. In the
right hand image, the wires are visible. Wires at the hot voltage are shown
in red and wires at the neutral voltage are shown in gray.
Apparatus Assembly Directions
1. Setup the scope to monitor voltage across and current flowing through a light
emitter, as well as the intensity emitted.
a. CH1 already displays the potential difference between hot and ground as
monitored by the scope probe. This connection is still correct, so no change
is required.
b. CH2 already displays the potential difference between neutral and ground.
This connection is still correct, so no change is required.
c. CH3 will monitor the voltage across the 1 Ohm resistor that is connected in
series with the light emitter.
i. Connect the BNC jack labeled 1 Ohm to the input of CH3 on the
scope using a BNC cable. How is this voltage related to the
current flowing through the light emitter?
d. CH4 will monitor emitted light by the device, which is proportional to
measuring the voltage generated across the leads of the photodiode.
i. Connect a micrograbber to BNC to the leads of the photodiode
ii. Connect the jack on the micrograbber to BNC connector to a BNC
cable that is in turn attached to the input of channel 4, so CH4
displays the emitted intensity as a function of time.
iii. Hang the photodiode so that it can measure the light emitted by the
light source without your having to hold it. It is convenient to hang
the photodiode from a chemistry stand where the diode is
approximately 1 cm from the light source. Be careful to avoid
saturating the photodiode.
e. Make sure all 4 channels are displayed on the scope.
2. Setup the variac to control the voltage difference between hot and neutral.
a. Connect the plug from the lightbox to the outlet on a variac, and connect the
variac to a wall plug. An image of a variac is shown above. The wheel on
the top of the variac controls the RMS amplitude of the AC voltage coming
out of the variac. You will use the variac to control the RMS voltage
suppled to your light box, which in turn controls the voltage across the light
emitter.
b. Set the knob so that the line points to 0 volts
c. Turn on the variac by flipping the power switch.
3. Begin data acquisition
a. Start the Labview program entitled 15b_lighting.vi. It will not acquire data
if all 4 channels are not displayed on the scope. A screen shot is shown
below.
Meaning of the items in the program display.
i. The green curve on the left shows the RMS current IRMS flowing through the light
emitter as function of VRMS, the voltage across the light emitter. IRMS= (CH3CH2/1 Ohm) and VRMS is CH1-CH3.
ii. The lavender curve on the right shows the emitted intensity vs the RMS power.
b. Begin slowly and smoothly turning the knob on the variac and continue
turning until the knob points to 120 V. DO NOT TURN THE VOLTAGE
ABOVE 120V!!! As you turn the knob, you change the voltage supplied to
the lightbox. The plots on the program should changes as you turn the knob.
When you reach 120 V, the program should display an IV curve for voltages
from 0 to 120 V. It should also display intensity as a function of electrical
power for voltages from 0 to 120 V. Turn the voltage slowly and smoothly
back down to 0 V and click on the stop button on the program.
Does your device emit light for all input voltages? If not, at what voltage does the
device turn on? For voltages where the device emits light, does the intensity increase
significantly with voltage? For voltages where the device emits light, does the ratio
emitted intensity to electrical power increase or decrease with increasing power. Sketch
the relative efficiency of the conversion of electrical power to optical power as a
function of applied voltage. Is it linear? Explain your result
Apparatus Assembly Directions
1. Setup the spectrometer to measure the intensity as a function of frequency for
the light emitted by the light sources as a function of the voltage across the light
emitter.
a. Disconnect LabPro from the USB connection on the computer. If it remains
connected, the spectrometer will not work.
b. Place the spectrometer so the hole is facing the light source.
2. Finish the setup the spectrometer to and begin data acquisition
a. Start the program called light spectrum that should be on the desktop. This
program operates the spectrometer for you and displays the resulting data, as
shown in the screen shot below.
Meaning of the program display
a. The line shows the intensity as a function of wavelength. The rainbow in the
back shows the color that corresponds to each wavelength.
b. Several different spectra can be obtained
The equation above gives the relationship between the temperature of an object and its
emission spectrum. The pink curves in the image below the screen shot show the
intensity as a function of wavelength for four different temperatures, where again the
rainbow shows the color corresponding to that wavelength. As you can see, cooler
objects emit light that is redder and less intense than hotter objects. You can use the
graphs to estimate temperatures of the light emitters studied in this section.
For comparison, the emission spectrum for the sun is shown in the figures on the
left. The top left figure shows the distribution for a temperature approximately equal to
the temperature at the surface of the sun. The wavelength scale is much larger, so the
rainbow only occupies a small fraction of the figure. The bottom figure has the same
wavelength scale and shows the measured intensity as a function of wavelength for
sunlight, where the black curve shows the predicted curve for an object with a
temperature of 5250 C. Notice only about 1/3 of the light emitted by the sun falls within
the visible wavelengths.
Data Taking Steps
1. Turn the Variac to 40 V. Leave the voltage constant.
2. If the light emitter is emitting light, take a spectrum at 40 V. Otherwise skip to step 4.
3. Click on the stop button when you are satisfied with the spectrum.
4. Turn the variac up to 60 V. Leave the voltage constant.
5. If the light emitter is emitting light, take a spectrum at 60 V. Otherwise skip to step 7.
6. Hit the collect button again and choose the option to keep collecting in the same
graph.
7. Click on the stop button when you are satisfied with the spectrum. Both spectra
should be displayed at the same time.
8. Turn the variac up to 110 V. Leave the voltage constant.
9. Hit the collect button again and choose the option to keep collecting in the same
graph.
10. Click on the stop button when you are satisfied with the spectrum. All 3 spectra
should be displayed at the same time.
Does the spectrum of your source change with voltage? How does your
measured spectrum the solar spectrum shown above? Is the emitted spectrum
well described by a black body at some temperature T? If so, what
temperature? If not, what is the origin of the light and what determines its
color? Are there any narrow features in the emission spectrum? If so, what is
their origin.
Bonus: Use the curve fit option to fit the spectrum to a Gaussian.
Bonus: For the maximum voltage, measure the photo-detector current as a
function of distance from the bulb. Note Solid state temperature sensors
exploit the temperature dependence of conductivity.
Bonus: 1. measure the angular dependence; 2. calculate the actual total power
conversion from electrical power to optical power. Hint: the conversion
efficiency of a photodiode is approximately 50 microamps per mW/cm2.
b. Present and explain the results.
4. Bonus: Charging and Discharging a Capacitor
Goal: Study the current and voltage as a function of time for an RC circuit, as
well as parallel and series combinations
a. Materials: function generator, oscilloscope, breadboard, micrograbber/BNC
connectors, BNC cables,two 0.1 microFarad capacitor, 10k Ohm resistor,1
kOhm resistor
In the previous lab, you measured the decay of the RC circuit formed by a 10
microFarad capacitor and the resistor inside the LoggerPro voltage probe and
found that the voltage across the capacitor decayed exponentially with time;
however, since RC circuits had not yet been covered in class, we did not
discuss it as an RC effect. In that lab, you charged and discharged the
capacitor using a battery and a single pole double throw switch. In this lab,
you will use the square wave from a function generator to change the voltage
across the capacitor from +5 V to -5 V . If the frequency of the square wave is
slow enough, the RC will have time to reach equilibrium before the square
wave changes voltage, so you will be making a DC measurement using
something that is really an AC source.
Apparatus Assembly Directions
1. Setup the signal generator to produce a 5 V amplitude triangle wave at 20 Hz
a. Change the signal generator frequency to 20 Hz by pressing the 100 Hz
frequency button.
b. Change the signal generator output to a square wave. If the signal on the
scope is not a nice clean square wave, then ask a staff member for assistance.
It probably means that the input impedance of the scope is set to 50 Ohms
and should be changed to 1 MegaOhm.
2. Connect the RC Circuit
a. Use the breadboard to connect a 10 k resistor in series with a 0.1 microfarad
ceramic capacitor. Such a ceramic capacitor with axial leads is shown on the
left above.
b. Connect the output voltage of the signal generator in parallel with the series
combination, as shown in the images above. Make sure the positive voltage
(red micrograbber) is connected to the capacitor and the ground (black
micrograbber) is connected to the resistor. Note: Channel 1 already displays
the voltage across the RC series combination since it is the same as the
output of the signal generator.
3. Setup the scope to measure the voltage difference across and current flowing
through the RC circuit
a. Channel 1 already displays the total voltage difference across the series
combination
b. Channel 2 will monitor the voltage across the resistor. Connect the
micrograbbers from a micrograbber to BNC jack in parallel with the resistor,
where the black micrograbber is connected to the same end as the black
micrograbber from the signal generator. Use a BNC cable to connect this
BNC jack to CH2 on the scope so that CH2 displays the voltage across the
resistor. How is this related to the current flowing through the resistor?
How is this related to the current flowing through the capacitor?
c. The math function will display the voltage across the capacitor. Press the red
button highlighted by the red rectangle that is superimposed on the image of
the scope that is shown on the left below. Choose “-“ from the function
menu so that the red display shows Ch1-Ch2 as shown in the image on the
right below. If the menu comes up in FFT mode, press the bottom left menu
button that is highlighted by the light green box, and the scope should return
to the correct menu. If the channels are wrong, press the menu buttons just
to the right of the box showing the channel for the math operation and keep
pressing the button until your desired channel appears. Why is Ch1-Ch2
equal to the voltage across the capacitor
d. Adjust the voltage sensitivities on CH1, CH2, and MATH so that they are
the same.
e. Adjust the scope settings so that approximately 1 period of the square wave
square wave is displayed. Do the voltages across the resistor and
capacitor approach equilibrium during one half cycle of the square
wave? Why does this approximate a measurement where the RC is
charged and discharged using a switch and a battery?
4. Tune the signal generator to the setting for data acquisition and begin data
acquisition
a. Readjust the timescale so that the display for CH1 and CH2 on the scope
resembles the image below.
b. Troubleshooting: Skip this if everything is working.
i. If you cannot get your display to resemble the image shown above,
ask for assistance. Instructions are included below should you wish
to try on your own.
1. If you keep getting a voltage spike that is negative, then the
edge trigger menu is set to trigger on a negative slope rather
than a positive slope.
a. Option 1
i. Hit autoset. This will fix the edge trigger
problem, but mess up all of your other settings
ii. Fix the voltage and time scales to get the
image above
b. Option 2
i. Enter the trigger menu by pushing the button
that is highlighted by the yellow rectangle in
the image of the scope two figures above.
ii. Choose normal from the right hand menu.
iii. Choose slope from the bottom menu. A new
right hand menu should appear, featuring a
positive slope and a negative slope.
iv. Pick the icon for positive slope.
c. Start the Labview program called 15B_RC.vi.
d. Acquire a signal from the scope by pressing the white arrow in the upper left
hand corner of the screen. This launches a process where Labview queries
the scope and obtains the voltages as a function of time for each channel. An
annotated screen shot is shown in the image on the left below.
Meaning of the program display
a. The upper left window shows the scope trace where CH1 is yellow and CH2
is blue, just as they are on the scope. CH1 is displaying the signal generator
voltage, VS, and CH2 is the voltage across the resistor, VR.
i. The small box on the left allows you to average your data. Each
point becomes the average of the N time points, where N is the
number in the box. If N=1, there is no averaging. If the noise
changes rapidly during the time that the signal is effectively constant,
then averaging over time removes a lot of noise.
b. The lower left hand window also shows CH2 vs time.
i. The small box at the left allows you to choose a linear or log plot,
where 1 gives a log plot and 0 gives a linear plot.
ii. The red line shows a linear fit to the plot with a value for the slope
displayed in the window just above the graph.
iii. It is possible to restrict the data shown in this window to a only a
portion of the time displayed in the upper left window. The portion is
selected using the cursors.
c. The upper right hand window is the IV curve for the capacitor
Is the current a linear function of the voltage across the resistor? Is the current a
linear function of the voltage across the capacitor? Immediately before the
square wave voltage changes from +5 V to -5 V, what is the current flowing in the
circuit, and what are the voltages across the resistor and the capacitor?
Immediately after the square wave switches, what is the current flowing in the
circuit, and what are the voltages across the resistor and the capacitor? Is the
absolute magnitude of either of the voltages larger than 5V? Is the voltage linear
on a semi-log scale? What is the decay rate for the resistor voltage, and is it
consistent with what you would expect? The white box at the right of the window
shows the time points that are averaged to make the plot. Choose 1 and take data.
Choose 10 and take data again. Did the signal change? If so, how? The signal to
noise improves if the averaging number increased, but if you make it too large the
data becomes distorted. Why?
Bonus: Add the second 0.1 microFarad capacitor in parallel with the original 0.1
microFarad capacitor. Draw a schematic of this circuit. Repeat the voltage vs
time measurement. Is the new RC time constant what you would predict? Explain.
Look at the time dependence of the resistor voltage when the resistor is in series
with a series combination of the two 0.1 microFarad capacitors. Draw a schematic
of this circuit. Repeat the voltage vs time measurement. Is the new RC time
constant what you would predict? Explain.
Bonus: Compare with the case where the 1 k Ohm resistor and the 10 k Ohm
resistor are in series with the 0.1 microFarad capacitor. Draw a schematic of this
circuit. Repeat the voltage vs time measurement. Is the new RC time constant
what you would predict? Explain. Consider the case where the 1 k Ohm resistor
and the 10 k Ohm resistor are in parallel with each other and the parallel
combination is in series with the 0.1 microFarad capacitor. For both cases draw a
schematic of this circuit. For both cases, repeat the voltage vs time measurement.
Is the new RC time constant what you would predict? Explain. What does the
result of these last to measurements suggest about making approximations in
circuit diagrams to simplify analysis before applying Kirchoff’s Laws?
Bonus: change the frequency of the square wave from 1 Hz to 1 MHz. Over what
frequency range is the RC response to the square wave effectively a response to a
DC voltage?
Bonus: Look at the voltage for a parallel combination of the 0.1 microFarad
capacitor and the 100 Ohm resistor where the parallel combination is in series
with the 1 kOhm resistor. Look at the voltage for a parallel combination of the 0.1
microFarad capacitor and the 100 Ohm resistor without an additional resistor in
series.
Double Bonus: Look at the IV relationship for the capacitor when the circuit is
driven by a sine wave.
Triple Bonus: Measure the IV using Loggerpro and explain why it produces the
wrong voltage responses.
Challenge Problems:
1. Design a voltage rectifier that takes an AC input and converts it to an output that
contains only positive voltages. Such a device is called a half wave rectifier. Use
4 diodes, a resistor, and a capacitor to construct a full wave rectifier that takes an
AC input and produces an output voltage that is approximately equal to the
absolute value of the input voltage.
2. Design a voltage doubler or tripler that starts with a 60 Hz 5V signal from the
signal generator.
3. Use a combination of diodes and capacitors to create a DC voltage larger than the
peak AC voltage.
4. Design a clock/timer using a comparator
5. Send and receive an optical Morse Code SOS transferred over the longest distance
6. Measure the IV curve for a transistor as a function of gate voltage for a NPN
transistor. Also, plot collector current as a function of base current. The ratio is
called beta. The figure below shows the symbols for both npn and pnp resistors,
as well as a schematic showing the physical connections to the 3904 npn. The
figure at the right is a circuit hint. Explain your result and predict the result for a
PNP transistor. Check your prediction. Bonus: Change the base resistor to 10k
and try again. Design a voltage amplifier. Observe change when the transistor is
cooled to liquid nitrogen temperatures or heated with a hair dryer.
7. Theory Challenge: In the lab you considered the IV relationships for three devices
and their departures from simple Ohmic predictions. Though Chapter 1 of Purcell
mentions that charge is quantized, this fact is ignored in most of 15b; however, it
does play an important role in nanoscale devices. An example is the Coulomb
blockade. It can be described theoretically as two conductors separated by a small
non-conducting gap. Classical mechanics predicts that no charge can flow across
the device, but quantum mechanics allows charge to tunnel from one side to the
other. The quantum mechanics predicts that the tunneling current should be
proportional to the voltage, that is it should follow Ohm’s law; however, a small
gap between conductors is also a capacitor. If the two conductors are initially
uncharged, the current due to the applied voltage will begin to build up a charge
on the plates. What is the potential change due to each particle with charge e that
tunnels across the gap? Does this increase or decrease the potential applied by the
voltage source? Sketch the IV curve for this device when the tunneling current is
taken into account. How could this effect be used to make a quantum transistor?
What dimensions would be required for one single electron to control the charge
flow at room temperature?
Supplemental Information
Breadboards
Breadboards are used to quickly create model circuits without creating the mass of wires
that would be required to connect everything with alligator clips or micrograbbers. An
image of a breadboard is shown on the left below. They consist of a series of holes into
which the leads from circuit elements can be inserted. Leads are the wires that stick out
of circuit elements and allow them to be connected. The holes are connected on the back
of the breadboard as shown in the diagram on the right below, where the light blue lines
indicate holes that are electrically connected. The holes between the red and blue ones at
the top and the bottom of the breadboard are connected horizontally. They are usually
used to distribute the voltage from the power supply to the circuit. The two central
regions are electrically connected in columns. They are used to connect circuit elements
to each other. The photograph in the center below shows the back of the breadboard with
part of the protective insulation peeled off. The metal strips that connect the central
columns and the edge rows are clearly visible.
An image of a circuit and the equivalent schematic are shown below as an example.
Spectrometer Use Instructions
Use a USB cable to connect the Vernier Spectrometer to the computer. (Note: Do
not connect the spectrometer to a USB hub.) The Spectrometer is powered by your
computer through the USB cable.
2. Start the Logger Pro 3.4.5 software.
3. Select Connect Interface → Spectrometer → Scan for Spectrometers from the
Experiment menu.
4. To calibrate the Spectrometer, choose Calibrate → Spectrometer from the
Experiment menu. The calibration dialog box will display the message: “Waiting
…seconds for lamp to warm up.” (see Figure 1) The minimum warm up time is
one minute. NOTE: For best results, allow the spectrometer to warm up for
at least three minutes. Follow the instructions in the dialog box to complete the
calibration. Click OK.
Figure
5. Choose Change Units → Spectrometer → Intensity from the Experiment menu.
Intensity is a relative measure.
6. Aim hole in the spectrometer at the light source. Click . Observe the
graph of intensity vs. wavelength. Click to end data collection. Note: If
the spectrum maxes out with flat tops to peaks, reduce the integration time.
The screen will then display intensity as a function of wavelength, where the graph is
overlayed on a rainbow that displays the color corresponding to that wavelength.
Symmetries in Physics
In the discussion above, we compared the IV curves for a positive voltage across a device
and compared that to the result for a negative voltage. If the device is uniform, then the
ratio of I to V for the two systems should be identical. If the device has different
properties at one end than at the other, then the two results may not be identical. This
system is essentially one dimensional; therefore, if the device is invariant under
translation along the current carrying direction (shown in the figure below as the device
having the same purple property everywhere), it is also invariant under reflection about
its center. In this case, the result of all four physical measurements shown must be
exactly the same. In contrast, if the device has two different sides with different
properties, then it is not invariant under translation or reflection. Such a device is shown
below with red and blue sides where the two sides have physically distinct properties.
Measurements where one sets up two sets of experiments that should be identical if a
symmetry exists, but may yield different results if the symmetry does not exist have and
continue to play a vital role in our understanding of the basic properties of the universe.
http://www-project.slac.stanford.edu/e158/parityviolation.html
http://ccreweb.org/documents/parity/parity.html
Symmetry is one of the most important concepts in physics. Emily Noether
showed that conservation laws in physics are linked symmetries in the mathematical
formulation. Conservation of energy, momentum, and angular momentum are
associated with invariance as a function of translation in time, position, and angle
respectively. There are many other more subtle symmetries in physics. Until 1957,
inversion, or mirror, symmetry was expected of nature. It came as some surprise that
parity, P, symmetry is broken by the radioactive decay beta decay: electrons from the
beta decay are preferentially emitted in the direction opposite that of the aligned
angular momentum of the nucleus process a discovery made by C.S. Wu and her
collaborators. When it is possible to distinguish these two cases in a mirror, parity is
not conserved. As a result, the world we live in is distinguishable from its mirror
image. At present there is no proof that the combination of CPT (charge,parity, and
time) is not conserved, that is the universe looks the same if CPT are ALL reversed.
Evidence for CPT symmetry violations are eagerly sought
http://www.physics.indiana.edu/~kostelec/faq.html
http://www.atomic.princeton.edu/romalis/CPT
Great care must be taken to determine that observed changes are due to variables
controlled by the experimentalist. Sometimes experimental conditions that are assumed to
be identical are not because some important variable has been ignored. For example,
Jerry Gabrielse research group at Harvard suddenly got different results when the subway
connection from Harvard Square to Alewife opened. They were still doing exactly the
same experiments, but the magnetic fields associated with the running of the subway
changed the conditions in their lab. Sometimes, the phase of the moon even matters.
http://news-service.stanford.edu/news/2000/march29/linac-329.html
http://accelconf.web.cern.ch/accelconf/e00/PAPERS/MOP5A04.pdf
http://www.agu.org/pubs/crossref/2003.../2001JB000569.shtml A crucial aspect of
experimental physics is sorting out what factors determine the outcome of your
experiment.
Resistor Color Code
Additional Capacitor Information
In this lab you are using ceramic capacitors. You used electrolytic capacitors in the
previous lab. Ceramic capacitors typically have smaller capacitance, but are more ideal
than electrolytic capacitors: electrolytic capacitors leak more and show inductive
behavior at high frequencies. Also, unlike electrolytic capacitors, ceramic capacitors are
not polar. Voltage and capacitance ranges for different types of capacitors are shown
below, and additional discussion of capacitor types and applications is available.
http://www.electrosuisse.ch/display.cfm?id=113982
Diodes
In a vacuum diode, the motion of the charges is particularly simple since there are no
collisions, as discussed in section 4.2. Vacuum diodes are still used in some specialty
applications such as ion gauges where the very rare collisions between ions allow low
pressures to be measured ; however, in most cases they have been replaced by semiconductor diodes consisting of a P doped semi-conductor (positive free carriers) adjacent
to an N doped semiconductor (negative free charge carriers). An excellent applet shows
the current to voltage relationship for a diode . Semiconductors are discussed in section
4.9 of Purcell.
Photodiodes
Photodiodes produces a current that is proportional to the light intensity hitting the diode,
so when a voltmeter is connected to its leads, the current will flow through the resistor in
the voltmeter resulting in a voltage difference that appears at the voltmeter output. A
photodiode is basically an LED operating in reverse: the internal electric field of a PN
junction is used to separate an electron hole pair created by a photon hitting the diode.
The same principle is used in solar cells to generate electricity from sunlight
US Electrical Power Distribution System
The power generated by power stations has voltage that changes periodically as a
function of time. In the United States at a wall outlet, the voltage as a function of time is
approximately V = 170 Sin (2 π 60 t) a sine wave with a frequency of 60 cycles/second
with a root mean square(RMS) voltage of 120 V, corresponding to an amplitude of 170 V
and a peak to peak excursion of 340 V. The root means square value of an AC voltage is
equal to the amplitude of the voltage divided by the square root of 2. AC has at least
three advantages over DC in a power distribution grid:
1. Large electrical generators generate AC naturally, so conversion to DC would
involve an extra step.
2. Transformers can either increase or decrease the voltage. In power supply
systems a chain of transformers changes the voltage in steps from 155,000 to
765,000 V at the power plant to 110 V at the wall plug. Transformers must have
alternating current to operate
3. It is easy to convert AC to DC but expensive to convert DC to AC, so if you were
going to pick one or the other AC would be the better choice.
Electrical Power Delivery in the US
All power companies use an alternating current transmission scheme with long range
transmission voltages sometimes in excess of 100,000 volts, with long distance transmission at
voltages from 155,000 to 765,000. The Three wires leave the power station, where there is a
phase delay of 120 degrees between each of the three wires, as shown below.
V1=Vo sin[ 2π 60t] V2=Vo sin[ 2π 60t -2 π/3] V3=Vo sin[ 2π 60t -4 π/3]
Three phase systems are frequently used in to power large electric motors, but most residences
get only 1 phase power.
Local Distribution
Power is brought down from the high voltage transmission towers to substation transformers.
Substation transformers lower the voltage for local distribution via power poles. The power pole
line can come all the way to your home or be converted to an underground distribution system for
the final leg to your house. Only one phase is required for residential applications, so at some
point there is a tap that attaches to only one of the three phases. Another transformer steps the
one phase voltage down to the two 120 volt circuits, plus a neutral wire, to your house. A photo
of a typical pole transformer that converts 7200V to 120V is shown below, with an electrical
schematic of the transformer shown at right. Some systems now use14,400 V instead of 7200.
Transformers are treated in Purcell in Chapter 7. New federal regulations require that the energy
efficiency of pole transformers increase by 2010. One increased efficiency is provided by
changing from changing the internal wiring form Aluminum to Copper because copper has a
higher conductivity.
The one phase voltage is shown at the top of the pole, with the ground wire even with the
top of the transformer. The 7200 V is the difference between the one phase voltage and
the ground. This is fed into one side of a transformer. The other side is a center tap
transformer with three outputs. The three output wires leave the transformer and enter
your house, as shown in the diagram on the right above. The voltages as a function of
time are shown below for a total time interval of 0.1 seconds. The blue corresponds to
the far left wire, the green corresponds to the central wire, and the red corresponds to the
far right wire. The red and the blue are 180 degrees out of phase, so the three voltages are
Vblue =170 sin[ 2π 60t] , Vgreen =0 , V red=170 sin[ 2π 60t+π]
Notice that the green is the sum the red and the blue. Most residential power applications
use a connection between one of the hot wires (either red or blue) and the green wire. This gives
110 V RMS 60 cycle power. Some appliances, such as electric dryers use 240 V RMS. This is
obtained by using the difference between the hot wires, shown by the purple line below, where
the other lines are the same as those shown above.
.
Power Meter
The power meter measures the power entering your house. A photo of a typical power meter is
shown above. The power meter is in line with the power feed from your nearest transformer. The
Watt is the unit of electrical energy. One kiloWatt-hour is equivalent to the use of 1000 Watts of
electricity (ten 100-Wattbulbs) for one hour. A kiloWatt-hour varies with location. Hawii is the
most expensive at 21.48 cents/kW-hour. Massachusetts is third most expensive at 15.13 cents.
Idaho is cheapest at 4.91 cents. The US average is 8.77 cents.
http://www.eia.doe.gov/fuelelectric.html A nice map of price by state is given at
http://www.eia.doe.gov/fuelelectric.html
Load Centers
A load center is positioned between a breaker box and the power meter. They are located near the
power meter and therefore are frequently found in your garage. The load center has one big
breaker for each of the 120 volt circuits from the power meter. A typical main breaker in a load
center is 150 amperes (amps)
Breaker Boxes
The diagram below shows the pole transformer picture above producing the two 120 V AC
signals plus the neutral voltage, where the red, light green, and blue correspond to the colors in
the voltage plots above. The dark green shows the connection to the ground. The neutral and the
ground are attached at the breaker box, so they represent the same voltage.
The red and blue power feeds are connected to two power buses located behind the circuit
breakers. The upper breaker highlighted in blue corresponds to a 110V circuit. The black wire
that comes down from the breaker corresponds to the black wire shown at the bottom in the three
wire set that goes out to the wall outlet. The white wire going to the wall outlet is attached to the
neutral, and the beige wire is attached to the ground. The lower left hand breakers in the diagram
above (pink 30-amp ganged breakers) correspond to the 240 V circuit that goes out to the dryer in
the picture above. The top breaker in this pair, with the black wire leading to it, is connected to
one 120 volt bus attached to the blue wire shown coming into the top of the box from the pole
transformer. The bottom breaker in this pair, with the red wire leading to it, is connected to the
other 120 volt bus that is attached to the red wire coming from the pole transformer into the box.
The white wire is connected to the neutral, and beige wire is connected to the ground. The
difference of voltages on the red and black wires is 220V rms. The difference between the black
and the white is 110V RMS, as is the difference between the red and the white.
House Wiring
Now let's take a look at the wall outlet circuit that starts with the black wire leading down from
the top left 20-amp breaker in the breaker box image above. This is a single 120 volt circuit that
will service 2 or 3 wall outlets. If we follow this wall outlet circuit out to a duplex wall outlet, it
will be wired as follows:
http:// www.cornerhardware.com/howto/images/ht052_1.jpg
Note that the vertical slot to the left is longer than the one to the right, to distinguish the hot wire
from the neutral wire. If the outlet is wired properly, the white wire is connected to the longer
neutral slot to the left and the hot black wire is connected to the short slot to the right. The
semicircular connection below the slots is connected directly to the ground outside the house. It
is not connected to the neutral except at the breaker box. The wiring for a 220V four plug
receptacle is shown at right. Again, the semicircular slot corresponds to ground. In this case,
BOTH of the side slots are hot and connected to the two out of phase 110V bus bars, so the
difference between them is 220V. The lower L shaped connector is the neutral. The outer case of
an appliance should always connected to the safety ground, so it doesn't make much difference
what happens to the other wires. If the neutral wire shorts to the case nothing happens. If a hot
wire shorts to the case, a short circuit is presented to the breaker and it should open. The safety
ground prevents YOU from being the path for a circuit from a hot wire shorted to the case to
ground.
Much of the information and many of the pictures in this document were adapted from
http://www.the-appliance-clinic.com/electwiring.html and
http://science.howstuffworks.com/power.htm/printable
Electricity Generation and Distribution to the Local Network
The physics underlying electrical power generation is covered in Chapter 7 of Purcell, but the
material below gives an overview of the energy sources that are used to produce electrical power,
and the physical infrastructure used to transfer the power from the power stations to users. The
discussion above began with the long distance transmission lines, but there are two earlier stages :
the generation of the power at the power plant and the increase in voltage that occurs before the
long distance transfer begins. All the steps are shown below in a diagram from How Stuff Works,
where I have added the voltage levels that are typical at each stage. The second image below is
from Encarta. It shows the actual values of different long haul distribution lines, as well as
showing the few High Voltage Direct Current lines that now exist. High voltage direct current
is becoming more attractive for reasons including: improved electronics allow better
conversion between AC and DC; the feasibility of linking AC power grids whose phases
are not synchronized; reduced losses in comparison to AC in very long haul applications
where the capacitance of the wires becomes important; http://en.wikipedia.org/wiki/Highvoltage_direct_current
It may at first seem odd that such high voltages are used for power transmission, and that there is
an effort to keep increasing the voltages not only for long distance transmission, but also for
transmission from power substations to pole transformers. The answer is that increasing the
voltage reduces the energy lost as the power is transmitted. Transmitting electricity at high
voltage reduces the fraction of energy lost to heating. Consider an electrical power
delivery system that must deliver a power P=IV where I is the current and V is the
voltage. Let a metal power line be characterized by a resistance R. (In chapter 8 of
Purcell complex reactance will be introduced, allowing one to include AC signal losses
due to the capacitance of the cable, but the basic scaling laws of power efficiency vs
voltage are the same). The energy lost in the transmission line is then I2R=(P/V)2 R.
Thus the power loss decreases inversely with the square of the voltage and proportional
to the resistance, driving one to try to increase energy efficiency by increasing line
voltage. This process cannot go on without limit, At voltages larger than 2,000 kV
corona discharge losses are so large that they can offset the lower resistance loss in the
line conductors. A nice video of a corona discharge is available. Transmission and
distribution losses in the USA were estimated at 7.2% in 1995 , and in the UK at 7.4% in
1998.
As discussed above, low electrical resistance in cables can also improve energy
efficiency; however, the installation and maintenance costs have favored higher
conductivity materials. Thus aluminum is often used in transmission lines, though its
conductivity is small than copper because its cost is lower as is its conductivity to weight
ratio The issue of long term energy efficiency due to improved conductivity vs short term
installation cost is a significant issue, not only for long distance power transmission, but
also for local energy use. As noted above, new pole transformers are required to use Cu
rather than Al to improve efficiency. In the1970’s houses were wired with Al wire rather
than Cu wire to save money in new construction. Unfortunately, there are many safety
problems associated with Al wiring, and the practice has been discontinued.
In order to produce electrical power, the power station must consume another form of energy. In
the US this is dominantly the burning of hydrocarbons, dominated by coal. A diagram of the
primary energy sources for US power plants are shown in the map below from the US
department of energy. Once the power is generated, it needs to be distributed. Power distribution
in the US is divided into regional authorities, some of which include Canada and Mexico. The
regional power authorities are shown in the pack at right, which also shows the power control
centers and connections that are used to redistribute power around the US to provide continuous
power despite changes in supply and demand.
http://www.nerc.com/regional/NERC_Regions_BA.jpg
A grid works very well as a power distribution system because it allows a lot of sharing.
If a power company needs to take a power plant or a transmission tower off line for
maintenance, the other parts of the grid can pick up the slack.
The thing that is so amazing about the power grid is that it cannot store any power
anywhere in the system. At any moment, you have millions of customers consuming
megawatts of power. At that same moment you have dozens of power plants producing
exactly the right amount of power to satisfy all of that demand. And you have all the
transmission and distribution lines sending the power from the power plants to the
consumers.
This system works great, and it can be highly reliable for years at a time. However, there
can be times, particularly when there is high demand, that the interconnected nature of
the grid makes the entire system vulnerable to collapse. Here's how that happens:
Let's say that the grid is running pretty close to its maximum capacity. Something causes
a power plant to suddenly trip off line. The "something" might be anything from a serious
lightning strike to a bearing failure and subsequent fire in a generator. When that plant
disconnects from the grid, the other plants connected to it have to spin up to meet the
demand. If they are all near their maximum capacity, then they cannot handle the extra
load. To prevent themselves from overloading and failing, they will disconnect from the
grid as well. That only makes the problem worse, and dozens of plants eventually
disconnect. That leaves millions of people without power.
The same thing can happen if a big transmission line fails. In 1996 there was a major
blackout in the western U.S. and Canada because the wires of a major transmission line
sagged into some trees and shorted out. When that transmission line failed, all of its load
shifted to neighboring transmission lines. They then overloaded and failed, and the
overload cascaded through the grid.
In nearly every major blackout, the situation is the same. One piece of the system fails,
then the pieces near it cannot handle the increased load caused by the failure, so they fail.
The multiple failures make the problem worse and worse and a large area ends up in the
dark. One solution to the problem would be to build significant amounts of excess
capacity -- extra power plants, extra transmission lines, etc. By having extra capacity, it
would be able to pick up the load at the moment that something else failed. That
approach would work, but it would increase our power bills.
http://people.howstuffworks.com/blackout.htm
http://www.aip.org/tip/INPHFA/vol-9/iss-5/p8.html
The blackout provided an opportunity to measure the pollutants emitted by powerplants since
there was no emission during the blackout. The reduction in emissions was both rapid and
significant.
Electrical power is only one component of our energy use. The chart below shows the original
sources for US energy, the final form in which it is used is shown below. Notice that almost 60%
of the energy is actually lost.