Physics 182 - Fall 2014 - Experiment #5
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Experiment #5, Ohm’s Law
1 Purpose
To investigate the Current-Voltage, I-V, characteristics of a carbon resistor at room temperature
and at liquid nitrogen temperature, a tungsten filament in an incandescent bulb and a
semiconductor diode.
2 Introduction
An electrical circuit is any continuous path or array of paths along which current may flow. A
circuit usually contains a battery or other sources of EMF to create the current. In addition, it
may contain anything from a single wire to a complicated collection of wires, resistor, and other
circuit elements. As for example, in a flashlight the path from one terminal of a flashlight battery
through the lamp and back to the other terminal of the battery is a simple circuit. A string of
Christmas tree lights plugged into a wall socket forms part of a circuit or it may be considered a
circuit by itself.
2.1 Current-Voltage (I-V) Characteristics of Circuit Elements: Ohm's Law
Part A. If both positive and negative electric potential
differences V (voltage) are applied across a carbon resistor
(maintained at a constant temperature) and the current I that
flows is measured, we find that I is proportional to V and the
resistance R is a constant. When I versus V is plotted, as
shown in Figure 1, a straight line graph is obtained. The
resistance is the same for all data points and is therefore
independent on the direction (positive and negative) and
magnitude of the current used. Materials which obey this
linear relationship are referred to as ohmic conductors. This
straight line is symmetric with respect to the origin: R(V, I)
= R(-V, -I). Note that if the current’s magnitude is increased
too much, the circuit element may start to heat up and loose its linear ohmic I-V characteristics.
Ohm’s law is given as V = IR. We define the resistance as R = V/I ohms. For an ohmic
conductor, at a given temperature, R is a constant independent of I and V and is equal to the
inverse of the linear slope of the I versus V graph for that conductor (Figure 1):
R=
That is, R =
∆
∆
Part B. Tungsten is a metallic conductor, yet the I-V characteristics of a light bulb with a
tungsten filament exhibit a nonlinear (Figure 2) behavior because the temperature of the filament
varies from around 20oC to around 3000oC. The temperature increases as the power (P = VI in
units of Watts) increases. The temperature of a hot filament can be accurately determined from
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its electrical resistance. The resistance of the tungsten filament is not constant, but is dependent
on the magnitudes of I and V, the power. The light bulb has point symmetry which displays 180
degree rotational symmetry with respect to the origin. That is, the current-voltage curve is origin
symmetric, as the magnitude of the current flowing for a given applied voltage value is the same
regardless of voltage polarity (positive or negative sign). The currents for 5 volts and -5 volts are
approximately the same, however, the current changes
direction (sign) when the voltage polarity changes. In Figure
2, resistance and power are approximately the same at each
symmetric point, R(V, I) = R(-V, -I), but changes at each
symmetric point as both are dependent on I and V, the
power. In terms of power, at each symmetric point, P(V, I) =
P(-V, -I). The magnitude of the power changes the
temperature. The resistance in Figure 2 depends on the
magnitude to the current and not its direction. Note that for
tungsten, higher power means a higher temperature and a
higher resistance. For the device in Figure 1, power is not
significantly changing the temperature for the range of
values of I and V used. Resistance for tungsten is:
R=
Again, it should be noted that at each symmetric point in Figure 2, R(V, I) and R(-V, -I), both the
temperature and the resistance are approximately the same. In addition, I is proportional to V at
these points. The light bulb is therefore ohmic at symmetric points but is not ohmic for the range
of data used when the power (I and V) is changed during the experiment.
Part C. Many conductors are not ohmic devices. Figure 3
illustrates the I-V plot for a solid state diode. The plot is
not symmetric and is not a straight line even though the
temperature remains constant. The resistance for this
device depends on the voltage and R is not a constant at a
given temperature. As indicted by Figure 3, the current for
this device is almost zero when the polarity of the voltage
is reversed. Such devices are said to have asymmetric
current-voltage characteristic curves corresponding to their
asymmetric electrical structure. (A diode is a two terminal
electronic device with an asymmetric current versus
voltage curve). Here too, resistance is:
R=
It should be realized that the relationship V = IR, which is Ohm’s law, is not by itself a statement
that a device is ohmic. A conductor is said to be ohmic if I is proportional to V and R is a
constant at a given temperature and is independent on the direction of the current. The
relationship R = V/I remains as the definition of the resistance of a circuit element whether or not
it is an ohmic device.
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3 Experimental Apparatus and Procedure
3.1 Apparatus
1. DC power supply and connecting cables.
2. Agilent 34405A digital volt-ohmmeter (to be used for voltage and resistance measurements).
3. Fluke 75 digital multi-meter (to be used for all current measurements).
4. Carbon resistor, six volt electric light bulb and a solid state diode.
3.2 Procedure. Measurements are entered into the data section of the Lab Report.
Determination of the I-V characteristics of various electrical elements
In the following studies, you will assemble the circuit shown in Figure 4 to measure the current
through the circuit element as a function of the applied voltage across the element. The
milliammeter (Fluke 75) must be connected in series with the circuit element, while the
voltmeter (Agilent 34405A) must be in parallel, i.e., across the ends of the circuit element.
Make sure you associate a plus + (positive high potential) or minus - (negative low potential)
sign to each voltage and current measurement. The correct range on the voltmeter will determine
the amount of digits after the decimal point.
3.2.1 Carbon Resistor at Room Temperature Part A 1.
1. Measure the resistance of the 1kΩ resistor using the
Agilent 34405A. The correct range on the meter will
determine the amount of digits after the decimal point.
Then assemble the circuit in Figure 4 using the 1kΩ
carbon resistor at the end of the long wire. 1 kilo-ohm
(kΩ) = 1000 ohms (Ω)
2. Set function and range switches on the digital
voltmeter (Agilent 34405A) to DCV and 10 Volts. The
correct range on the voltmeter will determine the
amount of digits after the decimal point.
3. Set the milliammeter (Fluke 75) function switch to
mA. Make sure the meter is set to measure DC current.
Figure 4
4. Set the knob on the power supply to zero volts (all the way counterclockwise) and plug in (if
not already) the power supply and digital meter to 110 volt AC outlet. Turn on the digital
meter and then have the TA instructor check out your circuit before turning on the electrical
equipment.
5. Measure and record the current through the resistor as a function of the voltage V across it
while increasing V from 1 to 7 volts in steps of 1 volt. Before proceeding to the next step,
set the power supply output back to zero volts.
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6. Reverse the direction of the applied voltage across the circuit element by reversing the leads
on the power supply. Again measure and record the current through the resistor for applied
voltages across the resistor in 1 volt increments between -1 and -7 volts (arbitrarily
designated as the negative polarity of applied voltage).
7. Lower the power supply output to zero volt and reverse the leads on the power supply to
return to the designated positive polarity of applied voltage.
3.2.2 Temperature dependence on resistance of carbon resistor in liquid nitrogen. Part A 2.
Place the 1kΩ carbon resistor in liquid nitrogen, and measure the resistance of the 1kΩ resistor
using the Agilent 34405A. Repeat steps 5, 6 and 7 described above to obtain the current-voltage
characteristic “curve” for the resistor in liquid nitrogen (T = -195.8C). Carbon is a semimetal,
and its resistance will increase when the temperature decreases. There is an energy gap between
the valence and conduction bands and the probability of an electron going from valence to
conduction is temperature dependent.
3.2.3 Six-volt Electric Light Bulb Part B.
Disconnect the 1kΩ resistor from the circuit and connect a sixvolt electric light bulb in its place (Figure 5). Measure the
current-voltage characteristics between .5 to 5 volts (plus and
minus polarity) in 0.5 volt steps following the procedure
above (steps 5, 6, and 7). Continue to read this section first
before starting your measurements to see how the above steps
will be modified. As you increase the voltage, the tungsten
will increase in temperature. As the temperature does increase,
first do .5 volts, then -.5 volts. Next will be -1 volts followed
by 1 volts. Use this staggered method of increasing the volt
for your light bulb measurements. Do not exceed 5 V
otherwise you will blow a fuse.
3.2.4 Diode: Asymmetric Circuit Element Part C.
The diode is said to be a "rectifying" circuit element since it
conducts current in only one direction and for only one
polarity of applied voltage. It can thus be used to produce
direct current from alternating current.
Disconnect the electric light bulb and assemble the circuit of
Figure 6 using a diode as the element to be studied. Note that
in Figure 6 that a 1kΩ resistor is placed in series with the
diode to limit the current through the diode. Be careful. The
voltmeter is connected only across the diode.
Measure the current-voltage relationship between 0.10 to
25.00 mA (see data table). Reverse the polarity on the power
supply and measure the current-voltage relationship in the
Figure 6
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range 0 to -12 V in steps of -3V.
4 Calculations, Analysis and Graphs for Lab Report
4.1 Analysis of current-voltage data on ohmic and non-ohmic circuit elements
4.1.1 Graphical Analysis for Lab Report
Plot three graphs, using the 18 x 25 cm graph paper, of the current (ordinate y axis) as a function
of the voltage (abscissa x axis) for the current-voltage data obtained for each circuit element. The
data for the 1 k resistor at room and liquid nitrogen temperatures (Parts 3.2.1 and 3.2.2) may be
plotted together on the same graph. They are both straight line graphs with different slopes.
You should do three graphs for this experiment: resistor, light bulb and diode.
The graph of the diode should include positive data only for I = 0.00 mA to 25.00 mA. Use the
total graph sheet for this positive data. Use the 25 x 18 cm graph paper for the three graphs in
your submitted work. If a graph is not linear, just enter the data points as a curve is hard to
draw.
4.1.2 Computations for Lab Report
1. Use your I vs. V data and linear regression on your calculator to calculate the electrical
resistance of the carbon 1kΩ resistor at room and liquid nitrogen temperatures. R = 1/(slope
I-V graph). Use your graph to determine the linear data to enter into your calculator. Your
linear regression calculations should include the coefficient of determination R2.
2. Calculate the resistance when the voltage across the light bulb is both plus and minus .5 and 5
volts. You should have four calculations.
3. Calculate the power when the voltage across the light bulb is both plus and minus .5 and 5
volts. You should have four calculations.
4. Calculate the resistance of the diode when the current is at both 2.00 mA and 12.00 mA.
5 Questions
1. Explain in a few sentences if the carbon resistor in 3.2.1 and 3.2.2 is an ohmic device.
Explain why.
2. Does the resistance of the resistor in question 1 increase or decrease when it is cooled by
liquid nitrogen? Why does this resistance change?
3. Compare your measured value of the resistance, RLN2, of the carbon resistor at liquid nitrogen
temperature to the calculated resistance, RCal, given by the following expression. This
comparison should be given as a percent error. Use the calculated value below as the
accepted value.
RCal = RRoom [1 + a(TLN2 – TRoom)]
a = -0.5 x 10-3/oC (Negative temperature coefficient, as carbon is a semimetal.)
RRoom = Measured resistance at room temperature, TRoom. TLN2 and TRoom from data sheet.
This expression approximates the temperature dependence of the resistance in the carbon
resistor. Expect a large percentage when you do the percent error. This should be a positive
number as the absolute value | | is used.
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% error = (| R LN2 – RCal | / | RCal |)*(100%)
4. a. Does the resistance of the electric light bulb depend on the direction of current flow
through it? Explain.
b. Does the resistance of the electric light bulb increase, decrease or remain constant as the
power, VI, is increased? Consult your data table.
c. Does the temperature of the light bulb filament increase, decrease or remain constant as
the power, VI, to the bulb is increased? (Associate a higher VI with an increase in
temperature.)
5. Does the diode conduct symmetrically when the current flows in the forward (positive
voltage) and the reverse (negative voltage) direction? Is the diode an ohmic device? Explain.
6 Discussion
In this open response section of the lab report you have the opportunity to demonstrate that you
have gained a comprehensive understanding of all aspects of the experiment. In your own
analysis, what were the key elements of the experimental measurement? Are the results intuitive
or do they appear in any way to be inconsistent with physical observations in daily life? Are
there intrinsic aspects of either the experimental design or the way it was implemented that could
introduce systematic errors or fail to account for relevant physical phenomena? A detailed
discussion should include analysis of any experimental errors, instrumentation problems or
mishaps that occurred, and how these may have impacted the results. Be thoughtful and think
critically about these considerations. If an experiment was challenging, a discussion of exactly
what made it challenging, and possibly, how it could be conducted differently, should be
included. Or, if an experimental measurement went completely smoothly, this should also be
discussed. Also this section may include discussion of how the insights from one particular
experiment are related or complementary to other experiments conducted in the course.
Remember that your discussion should be a thoughtful scientific analysis, not a discussion of
how you enjoyed or did not enjoy the lab.
7 Conclusions
The report should end with a clear conclusion statement. This is the “bottom-line” experimental
result summarizing the main quantitative results of the experiment and the extent to which they
are in agreement with theoretical predication and/or an established reference value. When the
experiment results in a measurement of a constant (e.g., the acceleration due to gravity at the
earth’s surface), compare it with its established handbook values for the Boston area. Use percent
error to quantify this comparison. To make this comparison meaningful, you should include the
impact of the experimental error (random, systematic and any individual investigator mistakes)
on your results. This includes errors in plotting and reading linear graphs when determining their
slope and intercept.
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Instrumentation
1. The DC Voltmeter measures the voltage difference between two points
to which its terminals are connected. The voltmeter is always connected
in parallel to the part of the circuit across which the potential
difference is to be measured (Figure A1). In this experiment the Agilent
34405A multi-meter is used to measure voltage differences and the
resistance of the carbon resistor.
2. The DC Milliammeter measures the electric current between any
two points to which its terminals are connected. To measure the
current in any part of the circuit, the circuit must be broken at that
point and the ammeter must be inserted in the gap with loose ends
connected to its terminals, i.e., the meter is connected in series
with that part of the circuit where the current is to be measured
(Figure A2). The Fluke 75 battery powered multi-meter is used to
measure the current in milliamperes in this experiment.
3. Connecting wire leads. Assumed to be made of a good conducting material, e.g., a metal such as copper,
and of a large enough cross-section to have negligible resistance and voltage drop across them.
4. The DC Power supply is a device used to supply a
constant source of EMF between its output terminals.
The electric current flows internally in the power
supply from the minus to the plus terminal. In the
external circuit it flows from the plus to the minus
terminal (Figure A3). The voltmeter on the actual
power supply is not accurate and should not be used to
determine the output voltage. The Agilent 34405A
multi-meter is used to measure voltages.
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Ohm's Law Data Sheet
Data goes into the data section of the Lab Report. Keep it neat and organized.
I-V Characteristics
3.2.1 and 3.2.2 Carbon Resistor at Room and Liquid Nitrogen Temperatures Part A.
Room Temperature = TRoom = __________oC
Estimated error in reading thermometer. ErrorT =  T = _______ oC
Liquid Nitrogen Temperature = TLN2 = -195.8oC
Table 1: Measurements of voltage and current from +1V to +7V and -1V to -7V in steps of 1 volt both
at room temperature and at liquid nitrogen temperature. Be sure to enter + or - for both
voltage and current.
Room Temperature 3.2.1 Part A 1.
RRoom = __________ kΩ at room temperature (Direct Measurement Using Agilent 34405A)
Voltage
V
volt
Current
I
mA
Voltage
V
volt
Current
I
mA
0.00
0.00
0.00
0.00
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Liquid Nitrogen Temperature 3.2.2 Part A 2.
RLN2 = __________ kΩ at LN2 temperature (Direct Measurement Using Agilent 34405A)
Voltage
V
volt
Current
I
mA
Voltage
V
volt
Current
I
mA
0.00
0.00
0.00
0.00
3.2.3 SIX VOLT LIGHT BULB Part B.
Measurements of voltage and current from +.5V to +5V and from -.5V to -5V in steps of ±0.5V.
Voltage
V
volt
Current
I
mA
Resistance
V/I
ohms
Power
VI
mW
Voltage
V
volt
Current
I
mA
Resistance
V/I
ohms
Power
VI
mW
0.00
0.00
-
0.00
0.00
0.00
-
0.00
a.
b.
d.
c.
e.
f.
h.
g.
i.
j.
l.
k.
m.
n.
p.
o.
q.
r.
t.
s.
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3.2.4 DIODE Part C.
Measurements of voltage corresponding to the current from 0.10 to 25.00 mA and measurement of the current
in the voltage range 0 to -12V.
Voltage
V
volt
Current
I
mA
Voltage
V
volt
0.10
0.00
0.25
-3.00
0.50
-6.00
1.00
-9.00
2.00
-12.00
Current
I
mA
3.00
5.00
8.00
12.00
18.00
25.00
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