PHY 2092 03 Stetson University Physics Parallel Combination of Capacitors Experiment just rewrite the lab in different way and re arrange the data. the num

PHY 2092 03 Stetson University Physics Parallel Combination of Capacitors Experiment just rewrite the lab in different way and re arrange the data. the numbers should be the same PHY 2092 – 03
Experiment – 03
Capacitance
Date performed:
Date of report submission:
Report author:
Lab partner:
Instructor:
Introduction
The goal of this experiment was to study the working of a capacitor and the net capacitance for both
series and parallel combination of the capacitors. We also studied the relationship between
capacitance, charge and voltage.
Data
Part – I
Theoretical Capacitance (μF)
Measured Capacitance (μF)
Error (%)
Type of Circuit
Series
Parallel
Theoretcial
Capacitance (μF)
2.17
21.50
Capacitor – 1
6.80
7.60
11.76
Capacitor – 2
4.70
5.02
6.80
Capacitor – 3
10.00
12.72
27.20
Measured Capacitance
(μF)
2.44
25.34
Error (%)
Capacitance (μF)
7.60
5.02
12.72
2.44
Voltage (V)
0.93
2.60
6.10
9.63
Charge (μC)
7.07
13.05
77.59
97.71
Capacitance (μF)
7.60
5.02
12.72
25.34
Voltage (V)
10.00
10.00
10.00
30.00
Charge (μC)
76.00
50.20
127.20
253.40
12.44
17.86
Series Combination
Total
Parallel combination
Total
Part – II
Offset capacitance of wires (μF)
Measured Capacitance d = 8 cm (μF)
Measured Capacitance d = 3 cm (μF)
Plate Diameter (cm)
Calculated Capacitance at 3 cm (pF)
Calculated Capacitance at 8 cm (pF)
0.7
0.5
53.7
17.5
7.10
2.66
Part – III
Plate Separation
(cm)
11
10
9
8
7
6
5
4
3
Electrometer Voltage
(V)
5.0
4.8
6.0
8.0
9.0
9.0
15.0
18.0
21.0
Voltage vs separation
25.0
Voltage (V)
20.0
15.0
10.0
5.0
0.0
0
2
4
6
8
Plate Separation (in cm)
10
12
Data Analysis
Part – I
In this part we were supposed to study the series and parallel combination of a set of three capacitors.
In case of series combination, the overall potential difference i.e., the sum of potential across the
individual capacitor was 9.63 V which was closer to the supplied potential of 10 V from DC source.
The charge for all three capacitors separately using the definition of capacitance i.e.,
=

=
example
2 = 2 2 = 5.02 ∗ 2.60 μC = 13.05μC
The charge flowing through different capacitors was not same.
Equivalent series capacitance was calculated using the following formula:
1

=
1
1
1
+ +
1 2 3
1
1
1 −1
=(
+
+
) = 2.44μF
7.60 5.02 12.72
In case of parallel combination, the measured voltage along three capacitors was 10 V as predicted
from the theoretically.
For a parallel combination of capacitors, the capacitance is given by
= 1 + 2 + 3
= 7.60 + 5.02 + 12.72 = 25.34 μF
Part – II
In the second part of the experiment, we calculated the capacitance of a parallel plate capacitor from
its dimensions. It is calculated as
=
0

Where K is the dielectric constant, A is the area of a plate and d is the plate separation.
The value of ε0 = 8.854 * 10-12 Fm-1.
For 3 cm separation and 17.5cm diameter,
=
(1.00059 ∗ 8.854 ∗ 10−12 )( ∗ (0.0875)2 )
= 7.10
0.03
Part – III
In the last part of the experiment, we tried to verify the relationship between the separation of plates
and the potential difference. In the observed graph, the potential is decreasing with increase in plate
separation. Interestingly, this method can be used as an indirect approach to measure the charge
stored in a capacitor.
Discussion
Physics of the experiment
Physically, capacitance is defined as the ability of a body to store the electric charge. Since this quantity
is a property of a conductor, it depends on its shape ,size, dimension, environment etc. There is
another definition to calculate the capacitance, and it can be stated as “the ratio of charge and
potential difference across the plates.” Mathematically, we can rewrite the above equation as:
=

Here, V is relative assuming the potential of ground or lower side is zero.
Capacitance for the parallel plate capacitor is given as
=

Where d is the separation between the plates, and A is the area of a plate.
Sources of error
Starting with the uncertainity in the measurement using the capacitace meter and main power supply
from DC source are called the intrinsic random error. We were using the digital multimeter and the
value were fluctuating which affected our results badly, such an error is called the instrumental error.
Capacitor was discharging at a constant rate and hence the potential between the plates was varying
rapidly. This was another error and is called a systematic error. We were measuring the distance
between the plates and the diameter using a ruler which also affected the results. Such an error also
comes under the category of error. Other than that, the weather conditions and climate affects the
dielectric constant, so it also one of the possible reason.
Accuracy
In the first part, our data for parallel combination was expected, but for the series combination, it was
totally different. There was an unreasonable fluctuation in the voltage measurement across different
capacitors. Though total voltage was same, the charge flowing through the capacitors was different
which was opposite to the theoretical prediction. In the scond part, the calculated capacitance was
7.1nF with an error of almost 1000% in comparison to theoretical value of ~58µF. Fortunately, final
part of the experiment was well matching with the theoretically predicted data and we could see the
increase in charge stored between the plates with decrease in separation.
Conclusion
The goal of the experiment was to understand the working principle of a parallel plate capacitor and
the effective capacitance for the series and parallel combination. Our I and III parts were well matching
with the theoretical data, but second was not. Hence this experiment was more or less successful. In
this experiment, all group memebers contributed equally.

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