1) The document describes an experiment measuring the transient behavior of RC circuits. Students used alligator clips to construct circuits with resistors and capacitors and measured the voltage over time as capacitors charged and discharged. 2) Graphs of voltage versus time were produced and showed either linear or exponential patterns, characterizing charging and discharging behavior. Capacitance was calculated from the graphs' time constants and slopes. 3) Percent errors between measured and expected capacitance values were low, between 5-10%, validating the theory that charging and discharging capacitors follows the equation q = CVe-t/RC.

1. Ethan Vanderbyl
Dr. Chen
Physics237
Date: 3/20/21
Title:TransientBehaviorinRCcircuits
Date: 2/28/14
Lab Partners: ChristinaHouck,AnthonyMen9dez
Purpose:Identifythe nature andcharacteristicsof a chargingand dischargingCapacitor.
Procedure:
Initiallywe setupthe circuitwithalligatorclips,one resistor,andone capacitor.Eachwere
placedinparallel.Aftersettingupeachindividual circuitwe chargedthe capacitorwithourpower
source for 30 seconds.Thenwe abruptlymeasuredthe Voltage vs.Time of the Capacitorinthe Data
Studio.We usedthissame processforfour differentcircuits,andthenwe graphedthe data.Each trial
deducedintotwographsone linearandthe otherexponential.Thesegraphsdescribe the characteristics
of eachcapacitor setup ina differentcircuit.Finallywe plottedachargingcapacitorinpart C, and we
graphedthe data withthe workshop.
ChargingCapacitor DischargingCapacitor
R
VO C
R
C

2. Data:
y = 8.4047e-0.015x
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120 140 160
Votage(V)
Time (s)
Graph 2: Circuit 1 Run #2 Volatge vs. Time
y = 8.5046e-0.013x
0
2
4
6
8
10
0 50 100 150 200
Voltatge(V)
Time (s)
Graph 1: Circuit 1 Run # 1 Voltage vs.
Time

3. Results:
Graph Manufactured
Capacitance (μFarads)
Graph Capacitance
(μ Farads)
% difference
1 22000 24,150 9.77%
2 22000 21,000 4.5%
Calculations:
1. I = 𝑉𝑒−𝑡/𝑅𝐶
y = 8.4705e-0.029x
0
1
2
3
4
5
6
7
8
9
0 10 20 30 40 50 60 70 80 90
Voltage(V)
TIme (s)
Graph 3: Circuit 2, Run #1 Voltage vs. time
y = 8.3245e-0.007x
0
1
2
3
4
5
6
7
8
9
0 50 100 150 200 250 300 350
AxisTitle
Axis Title
Graph 4: CIrcuit 3, Run #1 Voltage vs.
Time

4. 2. Time constant = 𝑚−1
3. C= time constant/R
4. %error=(Caccepted – Ccalculated )/Caccepted x 100
Sample Calculations:
1. I = 1𝑉𝑒
(−
170
(3300∗22000)
)
= 1A
2. 78.402
3. 𝐶 =
78.402
3.26𝑘𝑜ℎ𝑚𝑠
= .02415
4. %𝑒𝑟𝑟𝑜𝑟 =
22000−24150
22000
∗ 100 = 9.77%
Questions(Analysis):
1.
2. 𝑖 =
𝑑𝑞
𝑑𝑡
𝑉𝑐 = 𝑉𝑒−𝑡/𝑅𝐶 𝑞 = 𝐶𝑉𝑒−𝑡/𝑅𝐶 = 𝐼𝑒−𝑡/𝑅𝐶
Graph 5: Voltage vs.Time

5. y = -0.0127x + 2.1406
-0.5
0
0.5
1
1.5
2
2.5
0 50 100 150 200
Voltage
Time (s)
Graph 1: Circuit 1 Run # 1 Voltage vs.
Time
y = -0.0146x + 2.1288
-0.5
0
0.5
1
1.5
2
2.5
0 20 40 60 80 100 120 140 160
Voltaage(V)
Time (s)
Graph 2: Ciruit 1 Run #2 Voltage vs.
Time
3.

6. 4.
Value Voltage (V) Time (s)
VO 8.655 0
τ 3.185 76.28
VO to .5V 1.593 131.24
.5VO to .25VO 0.796 186.2
.25VO to .125VO 0.398 241.16
y = -0.0068x + 2.1192
0
0.5
1
1.5
2
2.5
0 50 100 150 200 250 300 350
Voltage(V)
Time (s)
Graph 4: Circuit 3, Run #1 Voltage vs.
Time (Parallel)
y = -0.0285x + 2.1366
-0.5
0
0.5
1
1.5
2
2.5
0 20 40 60 80 100
Voltage(V)
Time (s)
Graph 3: Circuit 2 Run #1 Voltage vs.
TIme (Series)

7. 5.
Graph Slope (m) Time Constant(s)
1 -.0127 78.7402
2 -.0146 68.4932
3 -.0285 35.0877
4 -.0068 147.059
6.
Graph Time Constant(s) Capacitance (C)
1 78.7402 .02415
2 68.4932 .0210
3 35.0877 .0108
4 147.059 .0451
7.
Graph Manufactured
Capacitance (μFarads)
Graph Capacitance
(μ Farads)
% difference
1 22000 24,150 9.77%
2 22000 21,000 4.5%
8.
Graph CalculatedValues(μFarads) ExpectedValues(μFarads)
3 10800 11000
4 45100 11000
Conclusion:
The principle thatwasprovedinthislabis the fact that a charging dischargingcapacitoris
describedby 𝑞 = 𝑉𝐶𝑒−𝑡/𝑅𝐶.The graphsin thislabdescribe the capacitorswithrespecttovoltage vs.
time.Fromthe graphs we were able todefine how differentcircuitsetupseffectthe efficiencyof the
capacitor,whicheffectthe capacitorscharacteristicswithrespect tovelocityandtime.The slope relates
to the time constant,whichwe usedtofindthe Capacitance.We accomplishedthe purpose of thislab
because ourpercenterrorsof the Capacitance are verylow.Our percenterrorsbetweenourcalculated
value andthe exceptedvalue were9.8% and 4.5%.
Thisexperimentcouldhave beenimprovedif ourerrorswere eliminated.Some of these errors
includedthe time we chargedanddischargedthe capacitor.If were able tomake these readingsmore
precise ourpercenterrorswouldhave beenless.We alsoencounterederrorsbecauseof the constant
resistance inanimperfectcircuit.These errorscouldhave beenavoidedbyusingamechanical device to

8. take the time measurementsandthe circuitcouldhave beenmade betterbyusingbettermetalsas
conductors.Overall the errorsthatoccurred were minimal andtherefore we achievedgoodpercent
errors.