Series/Parallel Capacitors in RC DC Circuits
OBJECTIVE:
By using the known value of the resistance and the experimentally measured value of capacitance, determine the effective
capacitance of two capacitors connected in series and in parallel.
THEORY:
The charge q on a capacitor’s plate is proportional to the potential difference V across the capacitor. We express this with
the equation
V =
q
,
C
where C is a proportionality constant known as the capacitance. C is measured in the unit of the farad, F, (1 farad = 1
coulomb/volt).
If a capacitor of capacitance C (in farads), initially charged to a potential V0 (volts) is connected across a resistor R (in
ohms) and is then discharged, a time-dependent current will flow according to Ohm’s law. This situation is shown by an
RC (resistor-capacitor) circuit when the switch is closed.
As the current flows, the charge q is depleted, reducing the potential across the capacitor, which in turn reduces the
current. This process creates an exponentially decreasing voltage, modeled by
V (t ) = V0 e
−
t
RC
Eq. 1
The rate of the decrease is determined by the product RC, known as the time constant, τ, of the circuit. A large time
constant means that the capacitor will discharge slowly.
τ = RC
Eq. 2
Equation 1 can be rewritten as:
V(t) = V e(-t/τ) Eq. 3
For capacitors in series, the theoretical equivalent capacitance is given by:
1
⎛1⎞
= Σ⎜ ⎟
Ceq
⎝C ⎠
Eq. 4
And for capacitors in parallel, the theoretical equivalent capacitance is given by:
Ceq = Σ(C )
Eq. 5
PROCEDURE
1. Connect the circuit as shown in Figure 1 with a single
capacitor. Be sure to observe the polarity of the
capacitors. Notice that the capacitor and resistor are
connected in series.
2. Connect the voltage probe across the capacitor, with the
red (positive lead) to the positive side of the capacitor.
Connect the black (negative lead) to the other side of the
capacitors. Turn on the computer click on the physics lab
folder and click on the RCDC icon.
3. Turn the power supply on and adjust to zero. Zero the probe (the Zero button is to the left of the Collect
button). Now adjust the voltage to 5 volts and allow a minute for the capacitor to charge.
4. Click the Collect button to begin data collection. As soon as the graphing starts, throw the switch to the
off position (do this quickly) to discharge the capacitor. Your data should show a decreasing function.
Repeat if your data does not look similar to Figure A.
5. Click on Experiment and then Store Latest Run. Double Click on the table where it says Run 1 and
change it to the trial name that is being performed. (Example C1 for CAP 1 and SERIES FOR SERIES)
6. Click and drag over the decreasing portion of your graph (if there is a plateau, do not include it). Fit an
appropriate equation to your data: A*exp(-Ct) + B. Compare this to equation 1. Note that this C does
not equal capacitance. Turn the power supply to zero. For this data set write the voltage at one
second on the data table.
7. Repeat steps 1 through 6 for the second capacitor. Be
sure to store the Run.
8. Set up the circuit in Fig. 2. Connect the positive
terminal of the voltage probe to the positive side of C1
and the negative terminal to the negative side of C2.
Repeat steps 3 through 6 for this series connection.
Store the Run.
9. Set up the circuit in Fig. 3. Connect the voltage probe in
parallel with C1. Repeat steps 3 through 6. Store the
Run.
10. Save this graph on a flash drive and print it out. Show graph to receive Lab Instructors initials
Series/Parallel Capacitors in RC DC Circuits Lab Sheet 1
Given by Lab Instructor after graph is shown.
C1 Actual Capacitance____________
C2 Actual Capacitance____________
DATA TABLE : INCLUDE UNITS
Voltage at 1 second
Trial
1 C1
2 C2
3 SERIES
4 PARALLEL
CALCULATIONS: SHOW ALL WORK RECORD ANSWERS ON RESULTS TABLE
1. Use the equation for the Curve Fit and equations 1 and 2 to calculate the time constant, τ for each trial
The equation in the Auto Fit box is in the form: y = A*exp(-Ct) + B. This is equivalent to y = Ae-Ct + B
which corresponds to V (t ) = V0 e
−
t
RC
, where y = V(t), A = V0, B = 0, and
C. (The “C” on the left side of the equation is the C from the Auto Fit box)
2. Use the values of τ from question 1 and the given value of R (22.0 kΩ) to calculate the experimental
value of C1 (Capacitance).
3. Calculate the experimental value of C2.
Series/Parallel Capacitors in RC DC Circuits Lab Sheet 2
4. Use Equation 4 (Series) and Equation 5 (Parallel), and the values obtained for C1 and C2 in question 1
through 3, to calculate the experimental capacitance, Cs, for the series circuit and the experimental
capacitance, Cp, for the parallel circuit
5. Calculate Cs for the series connection using given values. This is the accepted value for Cs
6. Calculate Cp for the parallel connection using given values. This is the accepted value for Cp
7. Compare the accepted values of Ceq obtained in steps 4 and 5 to the experimental values obtained in
question 6.
RESULTS TABLE: INCLUDE UNITS
Experimental Actual Value
value
C1
C2
Series
Parallel
Percent Error
CONCLUSION:
TURN IN: RCDC LAB SHEET 1 AND 2, 1 GRAPH
τ