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Exp 6 - detailed work.
Calculus Based Phys:Elec/Mag (Orange Coast College)
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PHYSICS 280 EXPRIMENT # 6: CAPACITORS-CALIBRATION & A PROBLEM
Professor Faridi
Part A
Objective:
1. In this experiment we will determine how voltages are distributed in capacitor circuits
and explore series and parallel combinations of capacitors. The capacitance is a
measure of a device’s ability to store charge. Capacitors are passive electronic devices
which have fixed values of capacitance and negligible resistance.
2. Calibration of three capacitors by comparison of discharge times of a standard
capacitor CS an unknown capacitor CX.
3. Study of charging and discharging of a capacitor by measuring the potential
difference (voltage) across the capacitor as a function of time.
The experiment
Using various series and parallel combinations of the marked capacitors, verify given
equations for equivalent capacitance of series and parallel connected capacitors by charge. This
can be done by following these steps: discharge all capacitors and connect standard capacitor to
the terminals of the voltmeter.
By comparing discharge times ts and tx of a standard Cs and an unknown Cx through the
same voltmeter resistance R, the Cx can be determined. The relationship is
CX/CS = (tx/ts)(ln(Vs/Vso)/ln(Vx/Vxo))
We use this relation to determine the three unknown capacitances C1, C2, and C3, and also
C1, C2 in series, in parallel. The data recorded as the following table:
Data with standard capacitor
Data with unknown Cx
Computed
Cs (µF)
Vso(V)
Vs(V)
ts(s)
Vxo(V)
Vx(V)
tx(s)
Cx(µF)
0.5
150
50
7.6
150
50
14.24
C1 = 1
0.6
150
50
9.61
150
50
32.53
C2 = 2
0.7
150
50
10.73
150
50
58.51
C3 = 5
0.8
150
50
12.2
150
50
23.49
C1C2 series = 0.67
1
150
50
15.43
150
50
25.53
C1C2 parallel = 3
Part B
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Objective: Measure the experimental time constant and use it to determine the
experimental value of the capacitance of the capacitor.
The experiment
Given C1, C2, and C3 values as determined in part A. Capacitor C3 is initially connected to
a variable D.C. voltage source, and charged to an assigned voltage Vo.
The capacitor C3 is then disconnected from the source and connected to a series
combination of C1 and C2 capacitors, as shown in figure 2. Repeat with C1 and C2 in parallel.
From the theoretical solution of the problem, compute the final voltage V3 across C3 for
both series and the parallel case. Then connect the capacitors as shown, and use an oscilloscope
or a VTVM as a voltmeter across C3 to measure the final voltage across C3. Then compare the
tow values as part of the report. Repeat with C1 and C2 in parallel.
C1C2 series
t(s)
0
4
8
12
16
20
24
28
32
36
V3(V)
150
86.1
73.3
64.9
59.3
54.6
50
45.9
42.3
38.8
The exponential graph of V3 vs. t
f(x) = NaN exp( NaN x )
V3 vs. t
12
V3( V)
10
8
6
4
2
0
0
2
4
6
8
t (seconds)
The expofit relation of V3 vs t is : y = 120.8e-0.123x
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C1C2 parallel
t(s)
0
4
8
12
16
20
24
28
32
36
V3(V)
150
36
29.4
25.1
22.1
19.6
17.7
16
14.5
13.3
The exponential graph of V3 vs. t
V3 vs t
160
140
V3 (Voltage)
120
100
80
60
f(x) = 60.39 exp( − 0.05 x )
40
20
0
t (seconds)
The expofit relation of V3 vs t is: y = 60.392e-0.049x
Conclusion:
There are two ways to connect two passives (no polarity) components in an electronic
circuit: in series or in parallel. In a series connection, the components are connected at a single
point, end to end as shown at right. For a series connection, the charge on each capacitor will be
the same. In the parallel case, the components are connected at both ends. When the capacitors
are first connected, electrons leave the positive plates and go to the negative plates until
equilibrium is reached - when the voltage on the capacitors is equal to the voltage of the battery.
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