Name:Dr. Julie J. Nazareth
Lab Partner(s):Physics 123L
Date lab performed: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)Known Capacitor,
C = 10 μF / Measured Voltage,
Vm ( ) / Average Measured Voltage,
V ( ) / Experimental Capacitance, Cexp ( ) / Known Capacitance, (µF) / Percent Difference
Capacitor, C1 / C1 = 22
Capacitor, C2 / C2 = 47
Capacitors in Parallel / Cpcalc =
Capacitors in Series / Cscalc =
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 Vin 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)
C1 % diff. = [(C1exp – 22 µF)/(22 µF)] x 100% =
Calculating the “known” capacitance for series and parallel capacitors
Cpcalc = C1exp + C2exp =
Cscalc
Part C: Measurement of internal resistance, R
Table 2: Time for a RC circuit to fall to ½ maximum voltage
Discharge Trial / Maximum Voltage, Vmax ( ) / One half maximum voltage, ½Vmax ( ) / Time forV = ½ Vmax,
t1/2 ( ) / Capacitance, C (µF) / Internal Resistance of Voltmeter,
Rint ( )
1 / 10
2 / 22
3 / 47
Average internal resistance of voltmeter, Rave( ): / ±
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 threeRintvalues, determine a sample uncertainty for the internal resistance of the voltmeter.
Trial 1:
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 / 2.25Time, 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
Graph: Plot the naturallogarithm 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,
τexp( ) / Theoretical time constant,
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?
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.
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: CapacitorsUpdated 04/17/14