AP PHYSICS C
RC CIRCUIT LAB
NAME ____________________
Objective: This lab will help us prove the exponential relationship between the charge on
a capacitor and the time it takes to discharge itself in an RC circuit! The challenge is to
experimentally derive the value of the mystery resistor!
Materials:
 1 power supply
 6 wires
 1 capacitor
 1 stopwatch



1 resistor
1 switch
1 multi-meter
Procedure:
1. Clip a wire into each of the terminals of the power supply. The colors red and
black are used to represent the positive and negative terminals, respectively.
*Most electronic conventions use black color to represent negative or “ground.” This
helps identify and organize complex wiring and prevent damage and/or injury.
“Ground” is the reference point in an electrical circuit from which other voltages are
measured, or is a common return path for electric current. All charges eventually
want to get to ground, at which point a power source can reenergize the charges back
to a higher electric potential. Just like all falling objects will eventually hit the
ground unless work is done to raise their height.
2. Make sure your power supply is at 3.3 or 4.5 Volts MAX. Your capacitors have a
5 Volt limit. Applying a potential difference greater than 5 will lead to serious
injury, and more importantly, my capacitor will be ruined!
3. Make sure negative lead off the capacitor is hooked up to the negative terminal
from the power supply. The two black stripes on the capacitor designate the
negative terminal. Ask if you are unsure about this step.
Charging your capacitor:
4. Wire your group’s mystery resistor (the mystery resistor has an identifying
number for you to record) to the positive terminal of the capacitor. These and
most other resistors are not polar elements and can be hooked up at either end.
Notice that the resistor can be placed behind or after the capacitor without affecting
the behavior of the circuit. We just want to make sure the negative terminal of the
capacitor is always lined up with the negative terminal of the power supply.
5. Wire the free end of the resistor to the positive terminal of the power supply. If
your power supply is on, your capacitor will begin charging up. Check to see if it
is with your multi-meter. Have the voltmeter set to 20 DCV (direct current
Volts).
Remember to wire the multi-meter (voltmeter) in PARALLEL when measuring
VOLTAGE. Wire the multi-meter (ammeter) in SERIES when measuring CURRENT
(procedure #11). Use the diagrams as a visual aid.
6. When your capacitor is charged up to a sufficient voltage, unplug the wires
coming off your power supply while making sure not to cross the leads.
Discharging your capacitor:
7. Wire both ends of your open circuit to the switch (leave the switch open).
8. Divide up tasks to record data. One person should read the voltmeter as it
discharges. One person will be the timer and signal the reader to call out voltage
AP PHYSICS C
RC CIRCUIT LAB
NAME ____________________
readings at timed intervals (5 second intervals is good). One person will copy the
voltage readings into a table as they are being called out. The last person’s task is
to make sure the circuit is wired correctly and flip the switch to the closed
position to start.
9. Close the switch and record the trial’s voltage vs. time.
10. Do steps 4-9 three times to get data from three trials. If the capacitor’s discharge
rate is noticeably slow, there is a good chance that a wire connection is loose or
there is a source of high resistance in the circuit. Reconnect wires and try
scratching off some of the oxidation on the resistor leads.
11. Charge up your capacitor one more time for one more trial. This time, you want
to measure the current, I, versus time. The important thing to remember is to
place the multi-meter is SERIES with the circuit to measure CURRENT. If you
try to measure current in parallel, you create a short circuit through the ammeter,
and you will blow the fuse.
Make sure your ammeter (measuring amps, the unit of measurement of current [1A=1
Coulomb/second]) is turned to 20m in the DCA range (direct current Amps).
Calculations and Analysis:
1. To analyze your data, you will need to make a curve fit around the Voltage vs.
Time data points. Look up the procedure on how to make curve fits with the
analysis tool of your choice (calculator or spreadsheet). The analysis done by a
calculator or an Excel spreadsheet yields an equation of the form y = abx. Record
the value of b, as this is related to the general exponential equation as follows:
y = abx = ae-kx
So the value of b is simply e-k, where e is the base of the natural logarithms and k
is the decay constant. Setting those two equal, gives the following
b = e-k
ln|b| = -k
k = -ln|b|
2. Solve for k, the decay constant.
3. The mathematical equation that describes the voltage on a discharging capacitor is
V (t )  V0 e
t
 RC
. Note that the constant k that we calculated should be equal to the
reciprocal of the RC product. Solve for R, the mystery resistance in Ohms.
4. Look up the actual resistor value for your resistor from your teacher. How does this
difference compare to the tolerances for the resistor? Are there any systematic errors
(data that is always skewed to one side)?
5. Now set up the Current vs. Time graph:
6. Describe the graph in general in your analysis. What is happening in the circuit
over time? Is the change constant, or does the rate change over time? Compare the
shapes and meanings of the two graphs you obtained while the capacitor was
discharging.
AP PHYSICS C
RC CIRCUIT LAB
NAME ____________________
Charging
-
Discharging
Switch
+
Power Supply
+
Voltmeter
V
Resistor
A
Ammeter
MORE ANALYSIS
1. If we examine the general equation for exponential decay, we could substitute the
value Vo/2 for V(t), and solve for the time it takes for the voltage to drop to half
its former value.
V(t) = Vo/2 = Vo e-t/RC
1/2 = e-t/RC
ln (1/2) = -t/RC
t1/2 = -RC ln (1/2) = 0.693 RC
2. Now go to your data for the capacitor voltage during discharge. Pick a value for
voltage near the highest one and record the voltage and time in the following
table. Then scroll down until you get to a voltage that’s half of that. Record these
new values. Repeat, going down in halves.
Voltage
Time
t1/2
3. Subtract the first time from the second, the second from the third, etc. to yield the
half-voltage time. When finished, calculate the average half-voltage time.
4. What you have just done is to demonstrate that capacitors discharge in a
mathematical pattern that is identical to the half-lives that radioactive materials
demonstrate. Namely, that in equal times, half of the original decays away, then in
an additional equal time, half of that decays. And right there on your lab bench!
5. Compare the average time your capacitor took to drop to half its voltage value
with the theoretical 0.693 RC. How does the percentage difference compare to the
tolerances of the resistor?
AP PHYSICS C
RC CIRCUIT LAB
NAME ____________________
*You may use this sheet to scribble values on, but be sure to record lab neatly in your lab
book. Include the problem, hypothesis, materials, procedure, data, calculations, analysis,
and conclusions. This is a major lab that does not require a formal lab write-up, but extra
points will be given for a word-processed write-up.
Sample Data Table Trial x
Time (s)
Voltage (V)
0
5
10
15
20
25
30
35
45
50
55
60
Sample Data Table Trial x
Time (s)
Voltage (V)
0
5
10
15
20
25
30
35
45
50
55
60
Sample Data Table Trial x
Time (s)
Current (mA)
Sample Data Table Trial x
Time (s)
Voltage (V)
0
5
10
15
20
25
30
35
45
50
55
60
0
5
10
15
20
25
30
35
45
50
55
60