Name:
Lab Partner(s):
Date lab performed:
Dr. Julie J. Nazareth
Physics: 133L
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 (
)
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
Capacitors in
Parallel
Cpcalc =
Capacitors in
Series
Cscalc =
Calculations: Using equation 11, calculate the 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 and your experimental values. SHOW THE CALCULATIONS for C1 (the
one marked 22 F), 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 11. 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 F)
V ps

C1exp  C 
 1 
V

C1 % diff. = [(C1exp - 22 F)/(22 F)] x 100% =
Calculating the “known” capacitance for series and parallel capacitors
Cpcalc = C1exp + C2exp =
Cscalc 
C1 expC 2 exp
C1 exp  C 2 exp
Lab: Capacitors

Updated 10/25/14
Data & Reporting score:
Part C: Measurement of internal resistance, R
Table 2: Time for a RC circuit to fall to ½ maximum voltage
Maximum
Discharge Voltage, Vmax
Trial
(
)
1
One half
maximum voltage,
½Vmax (
)
Internal
Resistance of
Voltmeter,
Rint (
)
Time for
V = ½ Vmax, Capacitance,
t1/2 (
)
C (µF)
10
2
22
3
47
Average internal resistance of voltmeter, Rave (
):

Calculations: Using equation 14, calculate the 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 DECIMAL ANSWER WITH
UNITS. [Remember: micro-Farads, F = 10-6 F, Farads.] Using all three Rint values, determine
a sample uncertainty for the internal resistance of the voltmeter. Make sure you round properly
when recording the result with the best estimate in Table 2.
t
Trial 1: Rint  1 / 2 
C ln 2
Without numbers, substitute/cancel units to SHOW how seconds/Farads equals Ohms (s/F = ).
Some of the following definitions/relationships may be helpful. You won’t need to use them all.
Electrical charge: Coulombs = C
Electrical Field Strength: N/C
Voltage (volts): V = J/C
Resistance (Ohms):  = V/A
Capacitance (Farads): F = C/V
Electrical current (Amperes): A = C/s
Part D: Measurement of a time constant
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
Time, t (s)
0
natural log
voltage, ln V
Voltage, V (volts)
2.00
1.75
1.50
1.25
1.00
0.75
Time, t (s)
natural log
voltage, ln V
Lab: Capacitors
Updated 10/25/14
2.50
0.50
2.25
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.
Then, use the slope of the graph to determine the experimental time constant (do this in your
calculator only). Record both 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 12 directly from your data twice, once using your experimental
time constant, exp, and the other time, using the “theoretical” time constant, theo. Use the time
you recorded in Table 3 for 3.50 volts. SHOW BOTH CALCULATIONS. Don’t forget units!
Time from Table 3 at 3.50 volts: t = ________________ seconds
Vmax = 4.00 volts (if you followed directions)
Verify eq. 12 using τexp
V(t) = Vmax e-t/exp =
Verify eq. 12 using τthep
V(t) = Vmax e-t/theo =
Questions: Answer the following questions completely and be specific. [Questions modified
from Phy 123L/Phy 133L lab manual, Capacitors Experiment]
1. Which time constant, τexp or τtheo is the most accurate? Consider the voltages you calculated
when verifying equation 12. [Hint: Which value is closer to 3.50 volts?] Make sure you
state your reason or reasons for choosing that particular time constant.
Lab: Capacitors
Updated 10/25/14
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 parallel, instead of just one.
(Resistance = R) Be precise/specific and show your work or state your reasoning to receive
credit. [Note: saying it increases or decreases is not precise enough.]
3. 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 precise/specific and show your work or state your reasoning to receive
credit. [Note: saying it increases or decreases is not precise enough.]
Bonus question (Extra credit will be granted only for correct answers, not for effort)
EC1. Use variables to find what percentage of the initial potential remains after one time
constant has passed (t = )? Do NOT use your data to calculate this. (Show your work or state
your reasoning.)
Don’t forget to write your conclusion paragraph! If you feel that you need more than one
paragraph to discuss the various parts of this lab, that’s ok – it’s a long, multipart lab.
Before writing your conclusion paragraph(s) you might want to consider the following “hint”
questions. I have phrased the following “hints” as individual questions to focus your critical
thinking skills and point out the major results of your experiment that should be discussed in
your conclusion paragraph(s). Once you have answered the “hint” questions in your head, you
can then work on turning those answers in your head to a coherent, connected paragraph where
sentences transition from one idea to the next.
Lab: Capacitors
Updated 10/25/14







Without plagiarizing the lab manual or another student, what is the purpose(s) of this lab?
(This is the introductory sentence of your conclusion paragraph.)
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?
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 mistakes.] Note: It is
OK to have verified one equation, but not the other – just discuss them separately.
What is the internal resistance of the voltmeter in Ohms, with uncertainty? (Part C)
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 of 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 one or both
time constants? [If the values are very different, see the instructor right away!]
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 12
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.]
Which time constant, τexp or τtheo is the most accurate? You should have answered this in
question 1 in detail. For your conclusion paragraph, just state which is most accurate
with a very brief explanation of why you chose that particular time constant.
Now, write out your conclusion paragraph(s) on lined paper or type it. To turn the “hint”
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 10/25/14