Name:
Lab Partner(s):
Date lab performed:
Dr. Julie J. Nazareth
Physics 123L
Section:
Capacitors
Parts A & B: Measurement of capacitance – single, series, and parallel combinations
Table 1: Voltage and capacitance for individual capacitors and capacitors in series and parallel
Power Supply Voltage, Vps (volts)
Average
Known
Measured
Measured
Experimental
Known
Capacitor,
Voltage,
Voltage,
Capacitance,
Capacitance,
Percent
C = 10 μF
Vm (
)
V(
)
Cexp (
)
(µF)
Difference
Capacitor, C1
C1 = 22
Capacitor, C2
C2 = 47
Cpcalc =
Capacitors in
Parallel
Cscalc =
Capacitors in
Series
Calculations: Using equation 3, calculate the experimental capacitance of the unknown capacitor
for C1, C2, C1 and C2 in parallel, and C1 and C2 in series. Calculate the percent difference
between the known capacitance values and your experimental values. SHOW THE
CALCULATIONS for C1 (the one marked 22 µF), Cpcalc, and Cscalc. THIS MEANS SHOW
WHAT NUMBERS YOU PUT INTO THE FORMULA, AS WELL AS THE DECIMAL
ANSWER WITH UNITS. Use the average measured voltage for V in equation 3. Also, use
your experimental capacitance values for C1 and C2 to determine the known (calculated)
capacitance for the capacitors in series and capacitors in parallel. Don’t forget units!
Experimental capacitance and percent difference for capacitor C1 (the one marked 22 µF)
Vp s 
C1e x p  C 
 1 
V

C1 % diff. = [(C1exp – 22 µF)/(22 µF)] x 100% =
Calculating the “known” capacitance for series and parallel capacitors
Cpcalc = C1exp + C2exp =
Cscalc 
C 1 e xpC 2 e xp
C 1 e xp  C 2 e xp
Lab: Capacitors

Updated 04/17/14
Data & Reporting score:
Part C: Measurement of internal resistance, R
Table 2: Time for a RC circuit to fall to ½ maximum voltage
One half
maximum
Time for
Maximum
voltage,
V=½
Discharge
Voltage,
½Vmax (
Vmax,
Capacitance,
Trial
Vmax (
)
)
t1/2 (
)
C (µF)
1
10
2
22
3
47
Average internal resistance of voltmeter, Rave (
):
Internal Resistance of
Voltmeter,
Rint (
)
±
Calculations: Using equation 6, calculate the in internal resistance of the voltmeter for the three
trials. SHOW THE CALCULATION for the first trial. THIS MEANS SHOW WHAT
NUMBERS YOU PUT INTO THE FORMULA, AS WELL AS THE DECIMAL ANSWER
WITH UNITS. [Remember: micro-Farads, μF = 10-6 F, Farads.] Using all three Rint values,
determine a sample uncertainty for the internal resistance of the voltmeter.
Trial 1: R i n t 
t1 / 2

C ln 2 
Without numbers, substitute/cancel units to SHOW how seconds/Farads equals Ohms (s/F = Ω).
Some of the following relationships may be helpful. You won’t need to use all of them.
Electrical charge (Coulombs): C = A s
Electric Field Strength: N/C
Voltage (volts): V = J/C
Resistance (Ohms): Ω = V/A
Capacitance (Farads): F = C/V
Electrical current (Amperes): A = C/s
Part D: Measurement of a time constant
***You must set the power supply so that the voltmeter reads exactly 4.0 volts before the switch
is opened and the capacitor begins to discharge. Use the 22 μF capacitor !!!!! ***
Table 3: Time for the voltage to fall to specified amounts for an RC circuit
Voltage, V (volts)
4.00
3.75
3.50
3.25
3.00
2.75
2.50
2.25
Time, t (s)
0
natural log
voltage, ln V
Voltage, V (volts)
2.00
1.75
1.50
1.25
1.00
0.75
0.50
Time, t (s)
natural log
voltage, ln V
Lab: Capacitors
Updated 04/17/14
Graph: Plot the natural logarithm of the voltage versus time (lnV(t) vs. t). Spread the data out use most of the sheet of graph paper. Draw a best-fit straight line to your data points and
calculate the slope. SHOW YOUR SLOPE CALCULATION ON YOUR GRAPH PAPER IN
AN UNUSED PORTION OF THE PAPER. Draw a small box around the points (not data
points) you used to calculate the slope. Don’t forget to title and label your plot appropriately.
Note: the natural log of the voltage, ln V(t), has no units, but the time, t, does. One graph per
lab group is allowed if the graph is completed, slope calculated and recorded on data sheets,
and the graph is signed off by the instructor by the end of the lab period.
Calculations: SHOW the calculation of the “theoretical” time constant, using the average
resistance from Table 2, including uncertainty, and the capacitor used in the Part D procedure.
Use the slope of the graph to determine the experimental time constant. Record the results in
Table 4. Don’t forget units!
τtheo = RaveC = (
±
)(
)=
±
Table 4: Comparing experimental and theoretical results for the time constant, τ
Slope
Experimental time constant,
Theoretical time constant,
(
)
τexp (
)
τtheo (
)
±
Calculations: Verify equation 4 directly from your data twice, once using your experimental
time constant, τexp, and the other time, using the “theoretical” time constant, τtheo. Use the time
you recorded in Table 3 for 3.50 volts. SHOW BOTH CALCULATIONS. Don’t forget your
units!
Time from Table 3 at 3.50 volts: t = ______________ seconds
Vmax = 4.00 volts (if you followed directions)
Verify eq. 4 using τexp
V(t) = Vmax e–t/ τexp =
Verify eq. 4 using τtheo
V(t) = Vmax e–t/ τtheo =
Questions: Answer the following questions on an attached sheet of paper (not the back of your
graph). These questions will replace the Conclusion/Summary paragraph for this lab.
1. Without plagiarizing the lab manual or another student, state the purpose(s) of this lab. (Write
the sentence(s) like it was the introductory sentence of a conclusion paragraph.)
2. In part A, how well did your experimental capacitance values match the given values? If the
values are more than 10-15% off from each other, who do you think is off – you or the
manufacturer – and why?
Lab: Capacitors
Updated 04/17/14
3. In part B, did you verify the equations for capacitors in series and capacitors in parallel? If
your answer is yes, then what about your data or results verifies this? If your answer is no,
what thing or things beyond your control may have affected your experiment(s)? [Things
beyond your control do NOT include mistakes. You fix things when you make mistakes.]
Note: It is OK to have verified one equation, but not the other – just discuss them separately.
4. How does the experimental time constant you got from the slope of your graph compare to
the theoretical time constant you calculated from the resistance and capacitance? Do the
values agree within the uncertainty from the “theoretical” time constant? If they do not agree
within uncertainty, are the values “close” (tell me your definition of “close”)? What things
beyond your control might have affected the determination of either or both of the time
constants? [If the values are quite different from each other, see the instructor right away!]
5. Did the voltage across the capacitor decay at the rate expected as the capacitor discharges
(i.e., did you directly verify equation 4 for either τexp or τtheo or both)? [If you don’t know
how to answer this question, think about the voltages you calculated using equation 4 and the
time you measured for 3.50 volts in part D? Were those voltages “pretty close” to 3.50
volts? From experience with this particular experiment, I would say “pretty close” is ± 0.10
volts.]
6. Which time constant, τexp or τtheo is the most accurate? Consider the voltages you calculated
when verifying equation 4. [Hint: Which value is closer to 3.50 volts]. Make sure you state
your reason or reasons for choosing that particular time constant.
There is no summary/conclusion paragraph for this lab report, because I have phrased it as
individual questions to lighten the load and to focus your critical thinking skills. In fact, other
than stating the internal resistance of the multimeter, questions 2-6 make you discuss all the
major results of the Capacitors lab in the correct order (insert internal resistance of multimeter
between questions 3 and 4). To turn the questions into a conclusion paragraph, you would
merely write the answers in paragraph form with transitions from one idea to the next. This
means that you CANNOT answer each question individually - you would NOT say “Yes, in part
A my experimental capacitance values match the given values.”) Instead, ideas need to flow
smoothly from one topic to the next. For example: “The Capacitors lab was done to learn about
the capacitance of several capacitors, to explore how the capacitance of the circuit changes when
you put capacitors in series or parallel, and to measure the time constant of a RC circuit created
by putting a voltmeter in series with a capacitor. In part A of the experiment, our experimental
capacitance values were fairly close to the values given for each capacitor, with the percent
differences ranging from 4% for the “22” μF capacitor to 16% for the “47” μF capacitor. As we
had very consistent measurements of the voltage for the “47” μF capacitor, and we were very
careful to discharge all of the capacitors between each experimental run, I think the manufacturer
may have marked the capacitor incorrectly. This possible mismarking of the “47 μF capacitor
didn’t affect our ability to verify the equations for capacitors in series or parallel. In part B, our
percent differences were less than 15%, supporting the series and parallel capacitor combination
equations. In part C, we used the time dependent decrease in voltage across a discharging
capacitor to determine the very large internal resistance of a Fluke 87 multimeter set to measure
voltage. We determined that the internal resistance was (11.7 ± 0.6)x106 Ohms. We then used
this result to calculate a theoretical time constant of ….”. Hopefully, you get the idea.
Lab: Capacitors
Updated 04/17/14
Extra credit questions (extra credit will be granted only for correct answers, not for effort):
1. Use algebra to figure out what would happen to the time constant of an RC circuit if you used
two identical capacitors of capacitance, C, connected in parallel, instead of just one.
(Resistance = R). Be specific/precise and show your work or state your reasoning to receive
credit. [Note: saying it increases or decreases is not precise enough.]
2. Use algebra to figure out what would happen to the time constant of an RC circuit if you used
two identical capacitors of capacitance, C, connected in series, instead of just one.
(Resistance = R). Be specific/precise and show your work or state your reasoning to receive
credit. [Note: saying it increases or decreases is not precise enough.]
3 Use variables to find what percentage of the initial potential remains after one time constant
has passed (t = τ)? (Do NOT use your data to calculate this.) Show your work to receive
credit.
Lab: Capacitors
Updated 04/17/14