Phy132/222 Experiment
RC Circuits
(revised5/27/08)
Name: _______________________________
Date: _____________
Lab Partners: ________________________________________
Introduction: As discussed in class, capacitors can be used to store energy. The RC circuit we will be
discussing today is commonly used in disposable cameras (and even pacemakers). For example, you have
probably used a disposable camera with a flash. Flash bulbs output a large amount of energy in a short span
of time. A capacitor is necessary because a battery cannot output enough energy in a fraction of a second to
provide the light needed to illuminate a dark room. In this lab we will explore a series of questions involving
capacitors. How long does it take to charge a capacitor? How does the voltage vary across a capacitor with
time? How does the current vary with time?
Time Constant [τ]:
The time constant lives up to its name. It is a measure of the time it takes to charge or discharge a capacitor.
You can calculate the time constant by multiplying the resistance value of your resistor in ohms by the
capacitance value of your capacitor in farads. The time constant has units of seconds.
τ [s] = RC
For our purposes it takes about 5 time constants before a capacitor is fully charged or discharged. So if τ =
10 s, it will take approximately 50 s to fully charge or discharge that particular capacitor. Your instructor will
show you why this is the case during an in class lecture. Just keep this simple rule of thumb in mind while
performing the lab. You will need to use this rule of thumb to choose your own resistor/capacitor
combination before you begin. Once you have chosen your resistor/capacitor combination, measure the
resistance with an ohmmeter and the capacitance with a capacitance meter and record in your data table.
Your instructor will show you how to use the capacitance meter properly.
Part I: Charging RC Circuit.
Choose a capacitor and a resistor from the bins. Be sure to choose a combination that gives you a reasonable
time constant. If you choose a combination with a time constant of 120 seconds you will be waiting around
10 minutes or more for the capacitor to charge with a correspondingly large amount of data points. If you
choose a combination with a time constant of 5 seconds, it will be charged before your reflexes have time to
record any data.
Set up the circuit shown below. Remember to set up all the circuit elements before you hook up any wires. In
this lab we get to take advantage of the DPDT (double pull double throw) switch. Notice the circuit consists
of two loops. One loop (the one with the battery) will be used to charge the capacitor. The other loop
(without the battery) will be used to discharge the capacitor. Connect a Voltmeter to the capacitor, and an
Ammeter between the resistor and the capacitor.
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DPDT
C
R
V
Figure 2 RC Circuit Diagram
Close the switch on the loop containing the battery simultaneously with starting your stop watch. Measure
the voltage across the capacitor and the current in the circuit every 5 seconds. If you run out of rows in your
data table feel free to attach additional sheets of paper with your data. When the voltage across the capacitor
stops changing, somewhere near 6.0 V, open the switch. When the switch is open it should be in the middle
position. If you flip it in the other direction you will immediately begin to discharge the capacitor. DO NOT
do thus unless you have not reset your stopwatch to zero and are ready to start collecting data.
Using Logger Pro, plot the voltage as a function of time and the current as a function of time for the charging
circuit, then find the curve that best fits this set of data. Be sure to scroll down past the linear and quadratic
fits to try some other functions. (Hint: How about an exponential or ln curve fit?)
Part II: Discharging RC Circuit.
Now throw the switch to the other side so that the loop WITHOUT the battery is closed while
simultaneously starting your stop watch. Record the voltage across the capacitor and the current in the circuit
every 5 seconds. If you run out of rows in your data table feel free to attach additional sheets of paper with
your data.
Using Logger Pro, plot the voltage as a function of time and the current as a function of time for the
discharging circuit, then find the curve that best fits this set of data. Be sure to label your graphs as the
discharging circuit to distinguish them from the previous two graphs.
Proceed to the Questions section.
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Data
R
C
Part I: Charging Circuit
time [ ]
Vc [ ]
I[ ]
3
Part II: Discharging Circuit
time [ ]
Vc [ ]
I[ ]
4
Questions
1.
Which curve fit the best fit for your data?
Equation for Voltage V. Time from the charging circuit.
Equation for Voltage V. Time from the discharging circuit.
2.
Use the equation above and what you have learned in class about RC circuit relationships after
performing the lab to determine the time constant for your RC circuit from the graphs you plotted.
Explain how you found the time constant. (Do not use τ = RC from your measured R and C values.)
Compare these two values. (% Error or % Difference?)
τcharging
τdischarging
3.
Determine the potential difference across the capacitor after three time constants if (a) you are charging
the capacitor from zero voltage, and (b) discharging the capacitor from the fully charged state.
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3.
In theory , it takes an infinite amount of time for a capacitor to discharge. In reality, how many time
constants will it take a discharging capacitor to reach 1% of its initial voltage?
4.
(PHY 222) An exponential curve can be transformed into a straight line so that the time constant can be
read directly from the slope. Take the exponential function for the charging circuit, transform it into a
linear relationship, and re-plot your data so that you can determine the time constant from a linear
curve fit.
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