Resistor-Capacitor Circuit Lab
AP Physics 2
Name___________________________
Introduction
In this experiment we will measure the charging and discharging behavior of a resistor capacitor
circuit. Resistors and capacitors are key elements in many electrical circuits. They are used in power
supplies to convert the alternating voltage of generated power into direct current voltage for circuit
applications. They are used in "spike removers" or "surge protectors" that safeguard computer
equipment from power surges. The list goes on. Understanding how resistors and capacitors work
separately and in combination is fundamental to a better understanding of common electrical
circuits.
Learning Objectives



To develop an understanding for the behavior of RC circuits
To understand the concept of a time constant and use it to find the capacitance.
To be able to analyze non-linear data
Theory
An RC circuit consists of a resistor and a capacitor wired in
series (see Fig. 1). In most common electronic devices, RC
circuits charge and discharge very quickly, requiring a fast
measuring device such as an oscilloscope. Some RC circuits,
like those in power supplies, have capacitors with very large
capacitances. These require much longer to charge and
discharge, making it possible to use a slower measuring
device. We will use Interface boxes attached to the lab PCs
and the appropriate data-monitoring program to make the
voltage measurements. We will then analyze the data using a
spreadsheet.
Capacitors are nonlinear devices: the rate at which they charge and discharge is a function of the
amount of charge on the capacitor. When charging, the larger the amount of charge on the
capacitor plates the slower it will increase its charge. When discharging, the more charge on the
capacitor, the faster the charge will decrease. The mathematical representation that describes the
charging behavior is:
t

Q(t )  Q (1  e )
(1)
max
Τ= RC
(2)
where Q(t) is the charge on the capacitor at any time, Qmax is the most charge the capacitor can hold,
and Τ is the "time constant" of the circuit, which governs how quickly the charging and discharging
occurs. Note that for this simple circuit, when the current is zero, Ohm's Law states that the voltage
across the resistor is zero. But the battery is still in the circuit, so its voltage must exist somewhere in
the circuit - it is all across the capacitor. This tells us that the maximum voltage across the capacitor is
is ∆V = Q/C and therefore, using Q = CV , we know that the maximum charge on the capacitor.
Since the voltage across the capacitor plates is directly proportional to the charge, we note that the
voltage across the capacitor as
a function of time is given by
t

V (t )   (1  e )
Charging
(3)
These expressions describe the charging behavior of the RC circuit. When the capacitor is
discharging, the voltage across the capacitor as a function of time is described by the relation
V (t )  V e
t

Discharging
(4)
0
Where V0 is the voltage when the capacitor begins discharging at t = 0. Using a LabQuest with a voltage
probe placed across the capacitor, we can capture voltage versus time curves for charging and
discharging. They will look something like
Figure 2. Graph showing typical charging and discharging voltage curves, for a
time constant is 60 seconds.
Procedure
Before assembling the RC circuit, use the ohmmeter to measure the resistances of the two resistors
you will use. Set the power supply voltage to be somewhere between 5 and 10 volts.
Read the capacitor label to find out the capacitance of the capacitor. This is an estimate of the
actual value. You will determine the actual capacitance as part of the experiment. Calculate what
the time constant should roughly be from your values of resistance and capacitance.
Assemble the following circuit with the smallest of your resistors. Note that because of the type of
capacitor we're using, you must have the longer lead connected to the resistor.
The 3-way switch will allow you to charge up the capacitor and discharge it without touching the
power supply (which causes some weird voltage spikes). The switch settings do the following things:

When the switch is in the down position, the upper wire is not really part of the circuit and
so you have a circuit that looks like Fig. 1-the capacitor will charge up over time.

When the switch is in the middle position, nothing is happening. If the capacitor is charged
up, it should remain charged up. But some charge will leak off the capacitor. We'll measure
this.

When the switch is in the up position, the battery is not in the circuit and charge is free to
leave the capacitor-the capacitor will discharge over time.
The switch should be wired like this (in the state shown, the top circuit is complete, discharging the
capacitor):
Test out the circuit
Hook up the Labquest and voltmeter probe to read the voltage across the capacitor and then use the
switch to charge up the capacitor. Watch the Labquest screen and verify that the voltage across the
capacitor is increasing, and the rough timescale. If the voltage does not ever reach near the power
supply voltage, you probably need to turn the capacitor around.
Now move the switch to the middle position. You should see the voltage across the capacitor slowly
decreasing as the charge leaks off.
Move the switch to the discharging position and watch how the voltage decreases. It should
discharge over the same timescale as it charged.
Calculate the Time Constant (Theoretical)
Fill in the table below for the circuit. You can get the Resistance of the resistor using the color code
and the Capacitance by reading it off the capacitor.
Trial
Resistor Value
Capacitor Value
Time constant (show work)
1
2
3
Take data
Now we're ready to take some data. Place the voltage probe connected to the LabQuest across the
capacitor and place the switch in upper position. Watch the voltage on the LabQuest screen until it
stops going down. This should not take more than two or three minutes. Now put the switch in the
middle position.
Under the Sensor menu, choose Zero to make sure the voltmeter is reading zero when it should be.
Also under the Sensor menu, choose Data Collection and set the Length to be about 2.5 times the
estimated time constant you calculated. Set the Sampling Rate to 2 per second.
Press the Collect button and move the switch into the charging position. Ideally, you want the
LabQuest to start taking data at the same time as you start charging the capacitor. When the
LabQuest is done taking data, export the data to a text file on the SD card as charging1.
Next, we'll discharge the capacitor. Try to start taking data and discharging the capacitor
simultaneously. Export that data to a second file o the SD card called Discharging 1.
Use Different Resistors
Replace the resistor in your circuit with the other, smaller resistor. Repeat the data collection above.
You'll have to change the Length of data collection to 2.5 times the new calculated time constant
and change the Sampling Rate to 2 per second. Save the Charging Data as Charging2 and the
Discharging data as Discharging2.
Finally put both resistors in the circuit in series and repeat. Save the Charging Data as Charging3 and
the Discharging data as Discharging3.
Turn off the LabQuest and then remove the SD Card. Bring it to your instructor and he will place the
data in a spreadsheet for you to graph.
Analysis
Plot your charging data as Voltage versus time (voltage on the y-axis). This should look like the black
curve from Fig. 2. We would like to be able to get the time constant from this data. The quick and
dirty way is to inspect the curve and find out when the voltage is 63.2% of the power supply emf.
Unfortunately, due to leakage of charge off the capacitor, the charging data is difficult to analyze.
Trial
Theoretical Value
(Τ = RC)
Data Value
(Time for 63.2% of max)
1
2
3
Now for your discharging data. We can analyze this data in a more rigorous way. To do so, we must
"linearize" the data -make it look like a straight line instead of an exponential curve. Note that
so if we take the natural log of the exponential term in equation (4) we'll end up with
, which we can then use to find
becomes
. With a little bit of algebra, equation (4)
(5)
where
is the voltage when you first started discharging the capacitor. Plotting
versus time should give a straight line with a slope of
. Add a trendline and get the slope.
Compare this
to the one you calculated from equation (2). Make sure to format the plot,
including the equation for the trendline and a caption.
With your value for , you can now find out what the capacitance of the capacitor is. Calculate that
and compare to the value stamped on the capacitor.
Trial
Theoretical
Value
(Τ = RC)
Data Value
(Slope of Trendline)
Capacitor Value
(Stamped)
Capacitor Value
(Calculated)
1
2
3
Turn in
1. This Handout.
2. Your 6 graphs:
a. Your 3 charging graphs, properly formatted, and with a figure caption, of course.
b. Your 3 discharging graphs, properly formatted with the trendline and equations, etc.
3. A conclusion, clearly stating and evaluating your results as asked above, along with any other
observations you can make about the results of the experiment.