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Lab-in-a-Box
Experiment 14: A Series RC Circuit
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Procedure
Analysis:
1. Calculate the time constant of the RC network shown in Figure 4 assuming the trim pot is adjusted to
provide the maximum resistance in the circuit.
1
OFFTIME = 500uS
ONTIME = 500uS
DSTM1
2
CLK
R1
1K
C1
0.1u
R2
10
3
A
B
0
Figure 4: Circuit diagram for RC time constant determination.
2. Using your choice of scientific graphing software (e.g., Excel or MATLAB), plot a graph of vC(t)
given by Eqs (2) and (3) versus t for the time constant calculated in step 1 and the clock signal shown
in Figure 4. Also show the clock signal on the same graph. Do not plot the data points for either
curve; show only a line connecting the data points. Be sure to compute a sufficient number of data
points to obtain a smooth curve. Your graph should show three full clock periods and should appear
similar to Figure 2(a) in the text. Procedures for plotting such graphs are given in the references in the
text.
3. Using Eqs (5) and (6), plot a graph of iC(t) versus t for the time constant calculated in step 1. Also
show the clock signal on the same graph. Do not plot the data points for either curve; show only a line
connecting the data points. Be sure to compute a sufficient number of data points to obtain a smooth
curve. Your graph should show three full clock periods and should appear similar to Figure 2(b) in
the text.
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4. Using Eqs (7) and (8), plot a graph similar to that prepared in step 2 for a circuit time constant of 500
μs. Your graph should show at least three full clock periods and should be similar to Figure 3(a) in
the text.
5. Using Eqs (7) and (8), derive expressions for the steady-state capacitor current for a network time
constant of 500 μs. Plot a graph similar to that prepared in step 3. Your graph should show at least
three full clock periods.
Modeling:
6. Model the circuit shown in Figure 4 in PSpice for a network time constant of 100 μs. Plot graphs of
the capacitor voltage and current similar to those created in steps 2 and 3. Verify that the PSpice
waveforms match those plotted in steps 2 and 3. Include screen shots of your waveforms in your
report.
7. Model the circuit shown in Figure 4 in PSpice for a network time constant of 500 μs. Plot graphs of
the capacitor voltage and current similar to those created in steps 4 and 5. Verify that the PSpice
waveforms match those plotted in steps 4 and 5. Include screen shots of your waveforms in your
report.
RC Network Measurements (100 μs time constant):
8. Using your digital multimeter, measure the capacitance of the 0.1 μF capacitor.
9. Adjust the resistance of the 1 kΩ trim pot so that the time constant of the circuit will be 100 μs. If the
trim pot will not produce sufficient resistance, you may add a small resistor in series with it to
increase the total resistance.
10. Build the circuit shown in Figure 4, being careful not to change the trim pot setting. Be sure to use the
same terminals of the trim pot as were measured in step 9.
11. Adjust the digital clock to produce a 1 kHz, 5 V square wave.
12. Connect the oscilloscope Channel 1 input via the ×10 attenuator to node A. Trigger the scope on this
channel. This signal is the capacitor voltage and should look similar to Figure 2(a) in the text.
Remember that you must attenuate the voltage because the voltage across the capacitor is too large
for the “Line” input of the iMic sound.
13. Connect the oscilloscope Channel 2 input via the ×1 attenuator to node B. This signal, when divided
by the value of the shunt resistor, is the displacement current of the capacitor and should look similar
to Figure 2(b) in the text.
14. Using the oscilloscope cursors, tabulate five data points on the rising waveform of the voltage across
the capacitor and five data points on the falling waveform as seen on Channel 1.
15. Similarly, tabulate five data points on the falling edge of the positive current pulse and five data
points on the rising edge of the negative current pulse as measured at node B.
16. Make screen shots of the oscilloscope output and include them in your report.
17. Plot the capacitor voltage data acquired in step 14 on the graph created in step 2. Note that you will
have to adjust your data points vertically by 2.5V depending on the true output of your digital clock
in order to compensate for the ac coupling of the scope. Plot the data points, but do not connect them
with lines. Include this plot in your report. Comment on the agreement between the observed and the
expected results.
18. Plot the data for the falling voltage curve acquired in step 14 on a semi-logarithmic graph and
determine the network time constant from the least squares slope of this graph [see Eq (3)].
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19. Calculate the percent deviation of the experimental time constant from the 100 μs expected value.
Explain any significant deviation.
20. Calculate the current in the branch from the data acquired in step 15 and plot it on the graph created
in step 3. Plot the data points, but do not connect them with lines. Include this plot in our report.
Comment on the agreement between the observed and the expected results.
RC Network Measurements (500 μs time constant):
21. Measure the resistance of the 4.7 kΩ resistor with your DMM.
22. Rewire the circuit to include the 4.7 kΩ resistor in series with the capacitor and the trim pot.
23. Remove the 1 kΩ trim pot from the circuit and adjust its resistance so that the circuit RC time
constant will be 500 μs. Be sure to use the measured values for the capacitance and the series resistor
as were measured in steps 8 and 21 in your calculations.
24. Replace the trim pot in the circuit, being careful to use the same terminals as were measured in step
23. The circuit should now be wired similar to that of step 10.
25. Using the oscilloscope cursors, tabulate five data points on the rising waveform of the voltage across
the capacitor and five data points on the falling waveform as was done in step 14.
26. Similarly, tabulate five data points on the falling edge of the positive current pulse and five data
points on the rising edge of the negative current pulse.
27. Make a printout of the oscilloscope screen and include it in your report.
28. Plot the data acquired in step 25 on the graph plotted in step 4. Plot the data points, but do not connect
them with lines. Include this plot in your report. Comment on the agreement between the observed
and the expected results.
29. Plot the data for the falling voltage curve acquired in step 25 on a semi-logarithmic graph and
determine the network time constant from the slope of this graph [see Eq (8)].
30. Calculate the percent deviation of the experimental time constant from the 500 μs expected value.
Explain any significant deviation.
31. Calculate the current in the branch from the data acquired in step 26 and plot it on the graph plotted in
step 5. Plot the data points, but do not connect them with lines. Include this plot in your report.
Comment on the agreement between the observed and the expected results.
Extra Credit Question:
32. Extra credit will be awarded to students who can provide a complete and correct derivation of Eqs (7)
and (8). The derivation should start with Eq (1).
Last Revision Rev 3.1: 10/29/2006
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