Phys 202 Lab 6 - RC Circuits Lab

Lab 6 – RC Circuits Physics 202
Objective
To study RC circuits, measuring charging and discharging times in order to confirm the RC time constant, 𝝉.
Background
RC Circuit
RC circuits are circuits containing resistors and capacitors where the current and voltage varies with time.
Charging a Capacitor
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∆𝑉! (𝑡) = ∆𝑉" (1 − 𝑒 %) 𝑄(𝑡) = 𝑄" ,1 − 𝑒 %- 𝐼 = 𝐼' 𝑒 # &% 𝜏 = 𝑅𝐶
Discharging a Capacitor
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∆𝑉! = ∆𝑉' 𝑒 # &% 𝑄 = 𝑄' 𝑒 # &% 𝐼 = 𝐼' 𝑒 # &% 𝜏 = 𝑅𝐶
Materials and Equipment

¨ AC/DC Electronics Board ¨ D-cell battery (1.5V)
¨ Wire leads ¨ Digital Multimeter (DMM) and cables
¨ Resistors, 22 kΩ and 220 kΩ ¨ Capacitors, 100 μF and 330 μF
¨ Stopwatch ¨ Capacitance Meter
Safety
Follow all standard laboratory safety procedures when dealing with voltage and current. To avoid shock never hold
the conductive part of the positive and negative terminals of a battery or capacitor at the same time. Always assume
that capacitors are charged and discharge them before handling. Because of the possible toxic nature of the solder
on the board, wash your hands after this lab.
Set up
For this lab, students will work in groups of two using the electronics board. Each group must write up their own lab
report and submit.
Physics 202
Experiment 1 – RC Circuits – single capacitor

Measure the charging and discharging time for various resistor/capacitors combinations. Compare to the
RC time constant for each combination.
1. Draw the table below in your lab report and use it to record the resistances, capacitances and charging and
discharging times. Record the actual measured resistances and capacitances.
Resistance Capacitance RC time constant, 𝝉 (secs) Charging time, 𝝉 (secs) Discharging time, 𝝉 (secs)
2. Select a 100 µF capacitor and a 22 kΩ resistor. Measure the resistance value of the resistor with the DMM set to
Ohms. Record the value in the table.
3. Measure the battery voltage with the DMM set to DC Volts. The battery voltage should be close to 1.5 Volts. If
it is not, replace it with one that does.
4. Confirm the value of the capacitor by having your instructor measure it with a capacitance meter. Record the
value in the table.
5. Construct the circuit below and draw the circuit diagram in your lab report.
6. Calculate the voltage at which a capacitor would be charged after one RC time constant (𝜏 ) by multiplying your
battery voltage by 0.632, and record in your lab report.
7. Calculate the voltage at which a capacitor would be discharged after one RC time constant (𝜏 ) by multiplying
your battery voltage by 0.368, and record in your lab report.
8. Connect the DMM between points C and B as shown on the circuit diagram above. Orient the DMM so the
black “ground” lead is on the side of the capacitor that connects to the negative terminal of the battery. Set the
DMM to the DC Volts setting.
9. Start with no voltage on the capacitor and the switch off. If there is remaining voltage on the capacitor, use a
piece of wire to “short” the two capacitor leads together, draining any remaining charge.
10. Close the switch by pushing and holding the red button down. Observe the voltage across the capacitor using
the DMM.
11. Open the switch by releasing the button, the capacitor should remain at its present voltage with a very slow
drop over time. This indicates that the charge you placed on the capacitor has no way to move back to
neutralize the excess charges on the two plates.
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Physics 202
12. Connect a wire between points A and C as shown on the circuit diagram above, allowing the charge to drain
back through the resistor. Observe the voltage readings on the DMM as the charge flows back.
13. Repeat steps 9 - 12 until you have a good feeling for the process of charging and discharging of a capacitor
through a resistor.
14. Repeat steps 9 - 11, this time recording the time taken to move from 0.0 volts to your target voltage for charging
as calculated in step 6. Record in the table under charging time, 𝝉.
15. Charge the capacitor to its maximum value which is the battery voltage.
16. Repeat steps 12, this time recording the time taken to move from the maximum voltage to the target voltage for
discharging as calculated in step 7. Record in the table under discharging time, 𝝉.
17. Replace the 100 μF capacitor with a 330 μF capacitor and have your instructor measure its capacitance. Record
its capacitance in the table.
18. Repeat steps 14-16, recording the charging and discharging times in the table.
19. Take the 220 kΩ resistor and measure the resistance with the DMM and record it in the table.
20. Replace the 330 μF capacitor with the original 100 μF capacitor and replace the resistor with the 220 kΩ
resistor in the circuit.
21. Repeat steps 14-16, recording your data in table.
Data Analysis/Conclusion
22. Calculate the RC time constants for each combination of capacitor and resistor and record in the table. Compare
to the charging and discharging times you measured. Are they similar? If not, what could have affected your
measurements?
23. What is the effect on charging and discharging times if the capacitance or resistance is increased?
Experiment 2 – RC Circuits – series and parallel capacitors
Measure the charging time for capacitors in series and in parallel. Compare to the RC time constant.
1. Draw the table below in your lab report and record the measured capacitor and resistor values, using the 22 kΩ
resistor and both capacitors.
Resistor Capacitor 1 Capacitor 2 Ceq RC time Constant, 𝝉 (secs) Charging time, 𝝉 (secs)
Series
Parallel
2. Configure a RC circuit using the 22 kΩ resistor and the 100μF capacitor in series with the 330μF capacitor.
Draw the circuit in your lab report.
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Physics 202
3. Place the voltmeter across the two capacitors.

4. Repeat the measurements in Experiment 1, steps 9-11, measuring the charging time for the series capacitors.
Record your results in the table.
5. Reconfigure your circuit placing the 100 μF and the 330 μF capacitors in parallel. Draw the circuit in your lab
report.
6. Place the voltmeter in parallel with the two capacitors.

7. Repeat the measurements in Experiment 1, steps 9-11, measuring the charging time for the parallel capacitors.
Record your results in the table.
Data Analysis/Conclusion
8. Calculate the series and parallel equivalent capacitance for each circuit and record it in the table under Ceq.
9. What is the effect on charging and discharging times if the capacitors are combined in series compared to in
parallel?
Grading
The project will be graded out of 100 points.

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Lab 6 – RC Circuits Physics 202

Materials and Equipment

Experiment 1 – RC Circuits – single capacitor

3. Place the voltmeter across the two capacitors.

6. Place the voltmeter in parallel with the two capacitors.

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