Orange Coast College
Physics 280
The Oscilloscope and Resistance
Part I. Adding Voltage Signals
Goal: Learn to add and subtract (invert) voltage signals.
The oscilloscope may be used to display two voltage signals simultaneously: one voltage signal
is sent to channel 1 and the other voltage signal may be sent to channel 2. The sum of the two
signals, and the difference between the two signals can also be displayed. In the sum (+) mode
the displayed signal is the sum of the input signals to channels 1 and 2. In the difference (-) mode
the displayed signal is the difference of the signals to channels 1 and 2. Another way to display
the difference between the signals sent to channels 1 and 2 is to “invert” (display the negative of)
the voltage signal to channel 2, and then adding the two signals. In this case, the sum mode
displays the difference between the voltage signals sent to channel 1 and channel 2. This allows
the oscilloscope to be used in a differential mode.
Connect the main “output” of the function generator to the channel 1 input of the oscilloscope,
and the pulse (“sync out”) output of the function generator to the channel 2 input. Set the
function generator frequency to about 1 kHz and select a square wave. Set both (channels 1 and
2) vertical sensitivity controls of the oscilloscope to the same number of Volts/Div of 5 V. Also
set the Sec/Div horizontal sensitivity control to 250 µs, and the trigger source to channel 1.
Adjust the amplitude of the function generator output, if necessary, to give similar signal
amplitudes in both channels 1 and 2 of the oscilloscope. Set the “channel 1 menu” of the
oscilloscope to AC coupling, BW limit to Off, Volts/Div to Coarse, Probe to 1X, and Invert to
Off. Set the “channel 2 menu” of the oscilloscope to AC coupling, BW limit to Off, Volts/Div to
Coarse, Probe to 1X, and Invert to Off. Carefully sketch the observed trace.
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Now set the “Invert” mode of the channel 2 menu of the oscilloscope to On. Adjust the trigger
level on channel 1 if necessary so you see a stable trace on the oscilloscope screen. Carefully
sketch the trace.
Now press the “math menu” button of the oscilloscope a few times until you see that the
“Operation” is set to “+” so that the oscilloscope adds the two voltage signals (ch1 + ch2), and
again sketch the trace with all the three signals: channel 1, channel 2, and their sum. Convince
yourself that you are now displaying the difference of the voltage signals being sent to channels
1 and 2 (because you inverted the signal going to channel 2).
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Part II. Differential Mode Measurements
Goal: Learn how to measure voltage signals between points neither of which corresponds to a
circuit ground.
Use your two resistors (about 1 kΩ and 1.7 kΩ) and the function generator to assemble the
circuit (shown in the figure 1 below) on your “breadboard”. Set the function generator to a sine
wave with a frequency of about 1 kHz, and peak-to-peak voltage amplitude of 5 volts, as
measured with the oscilloscope. Then use a BNC-to-alligator clip cable to connect the main
output of the function generator as indicated in the circuit below.
Fig 1
Now connect the channel 1 and channel 2 oscilloscope inputs to circuit points A, B, and C in the
proper way (see figure 2 below) to permit a differential measurement of the voltage ΔVAB = VA VB. That is, we wish to measure the voltage VA - VB corresponding to the electric potential
difference between points A and B neither of which corresponds to a circuit ground!
Fig 2
Because of the ground location in the circuit, the differential input mode of the oscilloscope must
be used to display the electric potential difference between points A and B. Make sure the
vertical settings are correct for such a measurement: vertical sensitivities equal (2 Volts/Div
works well with these numbers), “add”, and “invert for channel 2” modes. {In the circuit you
have assembled, the ground (black) connections to all of your instruments should be
connected to the same point on your circuit, denoted the ground point.}
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Record the peak-to-peak amplitude of the voltages ΔVAC = VA – VC displayed on channel 1, and
the peak-to-peak amplitude of the voltage ΔVBC = VB – VC displayed on channel 2:
ΔVAC = VA – VC = _________________________________
ΔVBC = VB – VC = __________________________________
Record the peak-to-peak amplitude of the voltage ΔVAB = VA – VB by using the oscilloscope in a
differential mode (invert channel 2 and add the signals to channels 1 and 2):
ΔVAB = VA – VB = __________________________________
Now calculate the difference of the two measured values of ΔVAC and ΔVBC {note this difference
of measured values equals ΔVAC - ΔVBC = (VA – VC) – (VB – VC) = VA – VB which is precisely
ΔVAB } and compare with your measured value of ΔVAB = VA - VB when you used the
oscilloscope in differential mode.
ΔVAC - ΔVBC
(volts)
(channel 1 – channel 2)
ΔVAB
(volts)
(differential mode)
Calculate the % difference between the two measured values of ΔVAB :
% difference = _________________________
Part III. Resistance
Goal: Practice reading resistor codes and measuring resistances.
Carbon-composition resistors are usually found in electronic devices. They are of low wattage.
They are made in 1/8-W, ¼-W, ½-W, 1-W, and 2-W sizes. Carbon composition resistors are
usually marked according to their ohmic value with a color code. The colors are placed on the
resistors in rings or bands. Read from left to right. The band closest to one end is placed to the
left so you can read it from left to right. The first band gives the first number according to the
color code. The second band gives the next number. The third band represents the power of 10
multiplier. If there is no fourth band, the resistor has a tolerance rating of ± 20%. If the fourth
band is silver, the resistor has a tolerance of ± 10%. If the fourth band is gold, the resistor has a
tolerance of ± 5%. For example a red-violet-green corresponds to 27x105 Ω = 2.7MΩ with a
tolerance of ± 20% of 2.7 MΩ so that R = (2.7 ± 0.54) MΩ.
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A digital multimeter (DMM) is an instrument that can be used to measure voltage, current, and
electrical resistance for both AC and DC applications. In this lab you will use the “BK Precision”
model 2706A. The resistance accuracy data for the BK precision DMM is found in the following
table:
Range
200 Ω
2 kΩ
20 kΩ
200 kΩ
2 MΩ
20 MΩ
Accuracy
± 1 %
± 0.8 %
± 0.8 %
± 0.8 %
± 0.8 %
±3%
For example: suppose you use the DMM to measure the resistance of a resistor and the value
comes out to be 10.54 kΩ when the DMM is set on the 20 kΩ range. What is the uncertainty in
the measured value of the resistance? We consult the table above and see that for the 20 kΩ
range the meter’s accuracy is ± 0.8% of the reading so that the uncertainty is ( ± 0.8 %) (10.54
kΩ) = ( ± 0.008) (10.54 kΩ ) = 0.08432 kΩ . Hence, we should write the measured value of the
resistance, including the uncertainty, as R = (10.54 ± 0.08) kΩ. Normally it is not necessary to
calculate the uncertainties for meter readings, but you should know how to do it.
For the carbon-composition resistors provided by the instructor, read the color code using the
table above and record the expected resistance values. Then measure the resistance values using
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the DMM and record the values in the table below. Determine the uncertainty of each resistor
reading made with the DMM. Are the resistor’s measured values within tolerance?
band colors
Coded resistance value
(kΩ)
Measured resistance value
(kΩ)
Part IV. Series and Parallel Resistance Combinations
Goal: Predict and measure resistances of resistor combinations.
Choose two of your resistors (one with a resistance of about 120 kΩ and the other with a
resistance of about 330 kΩ):
R1 = ________________________
R2 = ________________________
Resistors in series
Theory
Using the measured values for their resistances in part 3 above, calculate the expected equivalent
resistance (from theory: Req = R1 + R2 ) when the two resistors are connected in series.
Req = ________________________
Experiment
Now use the DMM to measure the resistance of the two resistors connected in series using the
circuit board to connect the resistors, and compare with your prediction by calculating the %
error.
Req = ________________________
% error = _____________________
Resistors in parallel
Theory
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! !
Now calculate the expected equivalent resistance (from theory: !!" = ! !!!! ) when the two
resistors are connected in parallel.
!
!
Req = ________________________
Experiment
Now use the DMM to measure the resistance of the two resistors connected in parallel using the
circuit board to connect the resistors, and compare with your prediction by calculating the %
error.
Req = ________________________
% error = _____________________
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