E1.1
Lab E1: Introduction to Circuits
The purpose of this lab is to introduce you to some basic instrumentation used in
electrical circuits. You will learn to use a DC power supply, a digital multimeter which
can measure current, resistance and voltage. An oscilloscope can measure both DC and AC
voltages, where DC means constant in time, and AC means time-varying, usually
sinusoidal.
The DC power supply has three output terminals: plus (red), minus (black), and
ground (green). The internal circuitry of the power supply holds the (+) terminal at some
voltage higher than the (-) terminal, and this voltage difference can be adjusted with the
voltage knob and read on the voltage meter. The ground terminal (green) is always at 0
volts. The internal circuitry does not know or care whether the (-) or (+) terminals are at
zero volts; it only knows the difference between the (+) and (-) outputs. To make the (-)
terminal output voltage be 0 volts, the ground terminal and the (-) terminal must be
connected. In that case the (+) terminal is a positive voltage (>0). If the ground and (+)
terminals are connected, then the (+) terminal is at zero volts and the (-) terminal becomes
a negative voltage. When neither the (+) or (-) terminals are connected to ground, then the
supply is said to be floating, and you cannot easily tell the absolute voltage of either.
Although the DC power supply used in this lab is a voltage source, it has both
voltage and current adjust knobs. The current knob is used if you wish to limit the current
to some maximum value (for safety or other reasons). The voltage knob adjusts the
voltage, unless the voltage is so high that the current output exceeds the limit set by the
current knob, in which case turning up the voltage knob further will have no effect. For
this lab, you can leave the current-limit knob turned up fully(fully CW).
DC POWER SUPPLY
voltage
current
Digital Multimeter (DMM)
voltage knob
DC
A
V
Ω
F
current-limit knob
20A µA/mA COM
AC
VΩ
The hand-held digital multimeter is a wonderful little device which can be used to
measure voltage and current (DC or AC), resistance, and capacitance. When making any
measurement, there are always 2 wires to the DMM. One of the two wires always goes to
the COM (common) terminal. To measure voltage or resistance, the second wire lead is
attached to the VΩ input. To measure current, the second wire is attached to one of the two
current inputs. For currents up to 2 A, use the µA/mA input, for currents in the range 2 -
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E1.2
20A, use the 20A input. In this lab, all our measurements will be DC, so the DC/AC
switch (upper right) should always be in the DC position. The DMM has an alarm; it sings
if you have wires plugged into positions which conflict with the central knob’s position.
(For instance, if you have the wires in COM and VΩ, but have the center knob in the amps
quadrant.)
DMM
resistor
When measuring a resistance with a DMM, you must
disconnect the source of the resistance (be it single resistor or
some combination of resistors) from any other devices, such as
power supplies. Never try to measure the resistance of a resistor
while it is in a circuit.
The oscilloscope is a device which displays a graph of voltage vs. time (voltage on
the vertical axis, time on the horizontal axis). If the voltage is DC, that is, constant in time,
then the oscilloscope display is a horizontal line, whose vertical position indicates the
voltage. Your TA will introduce you to the use of the oscilloscope. The oscilloscope
screen has 1 cm divisions on both axes. There is a volts per division (volts/div) knob,
which sets the vertical (volts) scale and a seconds per division (sec/div) knob which sets
the horizontal (time) scale. There are knobs for setting the vertical and horizontal position
of the display. Under the volts/div knob is a 3-position switch which reads (AC - ground DC). In the ground position, the input to the oscilloscope is grounded (set to 0 volts), and
the display becomes a horizontal line whose position (which can be adjusted with the
vertical position knob) is the zero volts position. For instance, one could set the middle
line of the screen to be 0 volts. Then positions above the middle would be positive
voltages, and positions below the middle would be negative voltages. When the switch is
in the DC position, the signal is input to the oscilloscope unaltered. When the switch is in
the AC position, an internal capacitor is in series with the input to the oscilloscope, and the
DC component of the signal is removed. There is small knob in the center of both the
volts/div and time/div knobs, called the CAL or calibration knob. This should always be in
the fully CW position in order for the volt/div and sec/div scale settings to be correct.
Electrical connections to the oscilloscope are made through a special kind of
connector called a BNC connector. The BNC connector is used with coaxial cables (coax,
for short). Coax cables have a central wire carrying the signal voltage and an outer
cylindrical conductor which is usually grounded (0 volts). The outer conductor on the
BNC connector on an oscilloscope is always grounded, and it is important to remember
that the outer wire of a coax cable is always at zero volts when it is connected to an
oscilloscope. There are special adapter connectors for attaching coax cables to bananaplug type connectors. The ground side of a double banana plug always has a little plastic
tab, indicating which banana plug is at ground.
Fall 2004
E1.3
coaxial cable
BNC connector
Oscilloscope Front Panel
POSITION
POSITION
CH.1 VOLTS/DIV CH.2 VOLTS/DIV
CAL
AC
GND
CAL
DC
AC
GND
POSITION
SEC/DIV
CAL
DC
BNC connectors
Part I. IV characteristic of a light bulb.
We will measure voltage vs. current of a light bulb filament, and use these data to
compute the resistance of the filament. The relation between voltage, current, and
resistance is Ohm's Law: V = IR . Ohm’s Law can always be used to compute the
V
resistance R =
; but only in the special case of an ohmic resistor is voltage proportional
I
to the current so that the resistance is independent of current or voltage. A plot of V vs. I
for an ohmic resistor is a straight line which passes through the origin and whose slope is
R.
V
The curve of V vs. I is called an IV
characteristic.
A light bulb filament is not ohmic;
its
V
vs.
I curve is not a straight line. As
slope = V/I = R
the filament current increases, the filament
gets hot and as it gets hotter, its resistance
I
increases, resulting in a very non-linear IV
characteristic.
IV curve for an
ohmic resistor
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E1.4
Before starting anything for the first part, use the digital multimeter (DMM)
to measure the resistance of the lightbulb. Then connect the power supply, the light
bulb, the digital multimeter (DMM) and the oscilloscope as shown below. We will use the
oscilloscope to read the voltage drop across the filament and the DMM to read the current
through the filament. Note that the ammeter is in series with the filament, while the
voltmeter is in parallel with the filament. An ideal ammeter has zero resistance so that it
does not impede the flow of the measured current. An ideal voltmeter has infinite
resistance so that it does not draw any current from the circuit it is probing. Our
oscilloscope has an input resistance of 1MΩ, high enough not to affect most circuits.
Schematic
ammeter (DMM)
A
Voltage
Source
(adjustable)
resistance
(filament)
voltmeter
V (oscilloscope)
ground
DC power supply
DMM
light bulb
-
gnd +
com
oscilloscope
volt/div
Physical Layout
sec/div
gnd tab
coax cable
Double-check your wiring before turning on the DC power supply. Start with the
voltage knob turned all the way down (fully CCW) and the current limit knob turned up
(fully CW).
Setting the Oscilloscope and taking measurements:
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E1.5
1. On Channel one, set the AC/DC/Ground switch to zero and turn the Volts/Div knob
to 50 mV. (This sets the scale on the screen to 50 mV per box, not per small tic
mark.)
2. Set the DMM to 2000mA on the dial and leave it there. Do not change this setting,
it will create more resistance in your circuit which results in inconsistent data.
3. Use the vertical position knob and move the trace to the bottom gridline on the
oscilloscope screen. (This gridline is now set to zero volts for the entire
experiment.)
4. Now set the AC/DC/Ground switch to the DC setting to begin making
measurements.
5. Slowly increase the voltage on the power supply so the oscilloscope trace rises to
the very next gridline. Once you reach this gridline the voltage is at 50 mV. Record
your voltage and current.
6. After recording your measurements increase the voltage to the next gridline and
record the voltage and current measurements.
7. Once the oscilloscope trace reaches the top of the screen, change the Volts/Div
knob to the 100 mV or 200 mV settings and continue to increase the voltage,
recording your measurements as you go.
8. Each time the oscilloscope trace reaches the top of the screen, increase the
Volts/Div knob to change the scale on the oscilloscope. Doing this changes the
scale between the gridlines but will not change the position of the zero volts line.
9. Continue increasing the voltage until you reach 20 measurements. You should be
able to make 20 measurements before you get to a maximum of 10 volts. The low
voltage measurements are very important because they really allow you to see the
non-Ohmic characteristics of the light bulb filament.
For each of your measured IV points, compute resistance R = V/I and power
P = IV . [Don’t do this by hand! Use Mathematica to compute all the points at once. You
know.... after entering your values for V and I , then define R = V/I , etc.] Make plots of V
vs. I, R vs. I, and P vs. I. From your data, determine the resistance of the light bulb
filament when it is cold and when it is very hot. These will be the first and last data points
of your Voltage and Current measurements. What is the maximum power dissipated in the
light bulb? Is the DMM measurement you made of the filament consistent with your data?
Part 2. Measurement of the frequency of a periodic signal
At each lab position there is a photodiode attached to a BNC connector. A
photodiode produces a small voltage when exposed to light. You will also be given a box
with a neon flash tube (neon light) that produces a periodic light signal with some
frequency f. Point the photodiode into the box so a periodic signal shows up on the
oscilloscope channel two. You should see a periodic signal on the oscilloscope screen.
Play with the volts/div knob and the sec/div knob to see how these knobs change the
display. Also, observe what happens as you cover the photodiode with your hand.
Measure the period T of the signal (period = time for one complete cycle of a periodic
signal). The best way to do this is to adjust the sec/div knob to get several complete cycles
Fall 2004
E1.6
on the screen. Measure the time for the several cycles and divide by the number of cycles
to get the period. From the period, compute the frequency f (f=1/T).
Line voltage, which is the voltage coming out of a wall socket, is an AC voltage
with a frequency of 60 Hz, and amplitude of 120V rms. How does the frequency of the
device compare to 60Hz? Can you explain why?
Fall 2004
E1.7
PHYS1140 Lab E1: Part 3 Construction of a Circuit
For this section, you need only fill out the accompanying data sheet. No other write-up
needed.
At your lab station, you will find 3 carbon resistors, mounted in double-banana mounts.
Measure and record on the data sheet, the resistances of the 3 resistors with your DMM.
Build the following circuit, using the 3 resistors and the DC power supply (which acts like
a battery). Set the voltage Vo to about 10 V and measure Vo with the DMM. You can put
the three resistors in any order in the circuit, just be sure to record which is which.
Measure the voltages across each of the
three resistors. (V1 = voltage across R1,
etc)
Compute the currents through each of the
three resistors, and record answers in mA
(I1 = current thru R1, etc.)
R1
R2
Vo
Verify Kirchhoff’s voltage law (the loop law) and Kirchhoff’s current law (the junction
law). Include in your discussion, a statement of each law. Is there any discrepancy? If so,
explain.
Compute the total resistance seen by the battery (the power supply), using your earlier
measurements of R1, R2, R3. Then with the ohmmeter, measure the total resistance.
Compute Ibat the current through the battery. Does this agree with your earlier
measurements?
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R3
E1.8
NAME____________________________
DATE_______________________
PARTNER’S NAME(S)_______________________________________
Record all results with a reasonable number of sig.figs!
Vo = _______________________
R1 = ________________
R2 = ________________
R3 = ________________
V1 = ________________
V2 = ________________
V3 = ________________
I1 = ________________
I2 = ________________
I3 = ________________
How is I1 computed?
Check that Kirchhoff’s voltage law (loop law) is obeyed:
Check that Kirchhoff’s current law (junction law) is obeyed:
Compute Rtotal (show how you computed it):
Rtotal (computed) =_____________________
Rtotal (measured) =_____________________
Compute Ibat (show how you computed it):
Ibat = __________________
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(OVER)
E1.9
What do you expect to happen to I1 when the resistor R3 is removed from the circuit?
Explain in writing, show your TA, and then check your prediction experimentally with
your circuit.
PREDICTION (no credit unless you show your TA before checking experimentally):
Experimental Result:
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E1.10
Guiding Questions:
1. The resistance of all metals increases with temperature. At low temperatures (room
temperature and below), the resistance is nearly independent of temperature. But at higher
temperatures, the resistance R is roughly proportional to the temperature, R ∝ T , where T
is the temperature in Kelvin. A light bulb filament is made of tungsten metal. Knowing
these things, make a qualitative sketch of the resistance of a light bulb filament as a
function of current. On the same graph, plot R vs. I for an ohmic resistor. (Qualitative
sketch only; no numbers!)
2. Describe a coaxial cable with a picture. Which conductor on a coaxial cable is usually
the ground (0 volts)?
3. How would you hook up a DC power supply to produce a negative voltage output?
Draw a picture to make your answer clear.
4. Make a simple sketch showing how you would hook wires between an ohmmeter and
two resistors R1 and R2 in order to measure the resistance of the two resistors in series.
5. What are the formulas for the total resistance of two resistors R1 and R2 in series and in
parallel? (Look up the answer in your physics text, if you do not know.) Consider two
resistors with resistances R1 = 100Ω and R2 = 200Ω. Compute the resistance of these two
resistors in series and in parallel. Show your work!
6. Suppose you connected two resistors in parallel to a DC power supply so that there is a
voltage across the two resistors R1 and R2. Now suppose you wish to measure the current
coming out of the power supply, using the DMM. Make a sketch showing how you would
connect the power supply, the two resistors, and the DMM to make the desired
measurement.
7. Suppose that you have the same circuit as in problem 6, except that now you wish to use
the DMM to measure the voltage across the two resistors, rather than the current. Make a
sketch showing how you would connect the DMM to the circuit to make the desired
measurement.
8. True or False: It is perfectly safe to stick your tongue into a light bulb socket that is
plugged into the wall.
9. True or False: the resistance of an ohmic resistor depends on the current in the resistor
during the measurement.
10. True or False: the voltage in the wall sockets in your home is 240 Volts, DC.
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E1.11
Pre-lab assignment for E1: Introduction to Circuits.
This prelab is designed to focus your attention on what is important in the lab before you
start the experiment and give you a “leg up” on writing your report. Use this template
when you write your report.
1. Carefully read the lab instructions for E1
2. Using Mathematica, set up a template for your lab report. This will include:
I.
II.
Header information such as title, author, lab partner, and lab section: (to
do this, In Mathematica, go to “File”, “Print Settings”, “Header and
Footer” from this dialog box you can enter all of the required
information.) Mathematica automatically enters the file name in the
right side of the header. Leave this alone.
Section Headings including “Title”, “Summary of Experiment”, “Data
and Calculations”, “Discussion of Uncertainty”, and specific section
headings for each part of the experiment. (All of the Physics 1140 lab
manuals include multiple parts.)
3. Write a Summary of the experiment. What are you going to measure and what
data will you collect to make the measurement? (For example, in part one of
M1, you will measure the length of a pendulum along with the period of the
pendulum to determine the acceleration due to gravity.)
4. For each part of the lab do the following:
A.) In your Mathematica document, make a theory plot of Voltage vs. Current
for a circuit that has a resistor of 850 ohms. Use Ohms Law for inspiration
in making this graph.
B.) For Part 2, write a one sentence prediction of what the graph would look
like if you plotted the voltage from the photodiode vs time.
C.) Suppose you have a circuit with a 10V power supply and two 100ohm
resistors. If the resistors are in series with each other, what is the voltage
drop across each resistor? What is the Current through each resistor? Now
if the resistors are in parallel, what is the voltage drop across each resistor
and what is the current through each resistor?
I.
II.
III.
Fall 2004
Plot your theory or expectation as a line. (In Mathematica, you should
define a function and plot it using the command “Plot”) Reference the
Mathematica tutorial to do this.
Label your axes, in English (not just symbols) and with units.
Include a brief caption (namely, a text statement of what the plot
shows.)
E1.12
IV.
Set the x and y range of the plot to be close to what you expect for your
data. For example: in M1 your longest length pendulum should be no
more than 130 cm in length.
5. Write a Discussion of Uncertainty. What are the major sources of uncertainty in
the experiment and how will you account for them?
6. Turn in a printout of your Mathematica document that includes 2-5 above. This
document should be no more than 2 pages long.
Fall 2004