Investigating the Capacitance of a Parallel-Plate.
Investigating the Capacitance of a Parallel-Plate
Capacitor Using a Reed Switch
Objective: To investigate the factors which affect the capacitance of a parallel-plate capacitor using a reed switch.
Apparatus: One reed switch, one signal generator, one pair of capacitor plates, polythene spacers, polythene sheet, one battery box, one voltmeter, one resistance substitution box, one light beam galvanometer, one 100g standard mass, connecting leads
THEORIES
Through the series of experiments, we would like to verify the following theories.
. Charge and Applied Potential Difference
As
With the increase of voltage supplied by battery, the current is increased.
Moreover, in a V-I graph, the slope m is the proportional constant fC. As we can obtain the generate our desired frequency f by a signal generator, we can obtain the capacitance .
Capacitance is the amount of charges which can be stored per unit voltage applied to the capacitor. The unit is defined as farad (F).
2.
Effect of Plate Separation and Area of Overlap
If the capacitor is charged up by voltage V, the charge density of the capacitor plates is given by where A is the area of the capacitor plate
The electric field inside the plates is given by
where is the permittivity in vacuum
Since
And,
and
As ,
and
With the increase of plate separation, the capacitance (C) is decreased. As Q = CV, with constant voltage supply, the number of charges stored (Q) is decreased.
With the decrease of area of overlap, the capacitance is also decreased. Hence, the number of charges stored is also decreased.
3.
Effect of Dielectric
It is known that by putting a dielectric between the plates could increase the capacitance.
A dielectric is a material that can be polarised by an electric field. When a dielectric material is placed in a uniform electric field, one surface will contain many positive ends of molecules and the other surface will contain many negative ends.
When a dielectric is placed between charged plates, the polarisation of the medium produces an electric field opposing the field of the charges on the plate.
As and ,
As the capacitance is inversely proportional to the electric field between the plates, and the presence of the dielectric reduces the effective electric field, the capacitance of the parallel plate is increased.
The permittivity is a characteristic of space, and the relative permittivity is a way to characterise the reduction in effective field because of the polarisation of the dielectric.
Assume the permittivity of the dielectric is.
The relative permittivity is defined as , where is the permittivity of free space.
Therefore, the capacitance of a capacitor with a dielectric is given by
As ,
As ,
Also, for constant electric field strength, area of overlap and frequency
So,
As ,
EXPERIMENTS
We have set up a circuit using the apparatus as shown below.
The battery box contains 4 batteries, which allows us to change the electromotive force (e.m.f.) in our investigations on the relationships ...
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Assume the permittivity of the dielectric is.
The relative permittivity is defined as , where is the permittivity of free space.
Therefore, the capacitance of a capacitor with a dielectric is given by
As ,
As ,
Also, for constant electric field strength, area of overlap and frequency
So,
As ,
EXPERIMENTS
We have set up a circuit using the apparatus as shown below.
The battery box contains 4 batteries, which allows us to change the electromotive force (e.m.f.) in our investigations on the relationships between e.m.f. and current.
The voltmeter measures the exact potential difference (p.d.) delivered by the batteries.
The resistance substitution box allows us to adjust the resistance.
The two parallel plates act as a parallel-plate capacitor to store charges.
The signal generator generates signal with a certain frequency which drives the reed switch.
The reed switch is a device which operates from an alternate current supply of known frequency driven by the signal generator. The switch repeatedly charges and discharges the plates at the same frequency.
The light-beam galvanometer is used to measure the current. Although it is an alternate current, the generated current pulses are so rapid that the light-beam galvanometer deflection remains steady. Hence, the current can be measured.
Experimental Setup
Circuit diagram
* All investigations are being done under frequency (f) = 400 Hz as set in the signal generator.
Investigation 1: Charge and Applied Potential Difference
We separate the capacitor plates with 4 polythene spacers, one at each corner. We then investigate the change of current with the change of voltage which is being done by connecting more cells.
Results:
V / V
.45 ± 0.05
2.95 ± 0.05
4.4 ± 0.1
5.8 ± 0.1
I /
0.23 ± 0.01
0.47 ± 0.01
0.73 ± 0.01
0.94 ± 0.01
The graph of I against V is drawn on a separate graph paper and is attached on the next page (page 7).
Measurements:
From the graph, it is easily observed that the relation between I and V is linear as the points nearly lie in a straight line.
The x-coordinate of the centroid of the three points =
Percentage error =
The y-coordinate of the centroid of the three points =
Percentage error =
The slope of the best fit =
Possible percentage error = 2.19% + 1.69% = 3.88%
Possible absolute error =
The slope of the best fit =
As the experiment is done under frequency (f) = 400Hz
By
Investigation 2: Effect of Plate Separation
We investigate the effect of plate separation by putting more spacers, one at four corners each time. We connect the parallel-plate capacitor to four batteries, i.e. 5.8V and this is unchanged during the whole investigation.
Results:
N
2
3
0.5
0.333
I /
0.94 ± 0.01
0.50 ± 0.01
0.35 ± 0.01
The graph of I against is drawn on a separate graph paper and is attached on the next page.
Measurements:
From the graph, it is easily observed that the relation between I and is linear as the points nearly lie in a straight line.
The x-coordinate of the centroid of the three points =
The y-coordinate of the centroid of the three points =
Percentage error =
The slope of the best fit =
Possible absolute error =
The slope of the best fit =
As
Possible absolute error =
The y-intercept is
Investigation 3: Effect of Area of Overlap
We investigate the effect of area of overlap by decreasing the overlapping area between the two plates. We connect the parallel-plate capacitor to four batteries, i.e. 5.8V and 1 spacer to separate them. These two are unchanged during the whole investigation.
Results:
x / cm
24.2 ± 0.1
6.0 ± 0.1
2.0 ± 0.1
I /
0.94 ± 0.01
0.64 ± 0.01
0.47 ± 0.01
The graph of I against x is drawn on a separate graph paper and is attached on the next page.
Measurements:
From the graph, it is easily observed that the relation between I and x is linear as the points nearly lie in a straight line.
The x-coordinate of the centroid of the three points =
The y-coordinate of the centroid of the three points =
Percentage error =
The slope of the best fit =
Possible absolute error =
The slope of the best fit =
Investigation 4: Effect of Dielectric
Its is known that, by putting a dielectric inside the parallel-plate capacitor, the capacitance will be larger. We can find the relative permittivity of a dielectric, which is compared with the permittivity in vacuum. We setup the parallel-plate capacitor with 3 layers of spacers and connect it to 4 batteries, i.e. 5.8 V as displayed by the voltmeter. The two plates are fully overlapped. We compare the differences on the current without a dielectric (I0) and with a dielectric (I).
Results:
I0: 0.94
I: 1.52
As
1.62
Possible percentage error =
= 1.72%
Possible absolute error =
= 0.0279
We could then verify that a dielectric substance is able to increase the permittivity.
CONCLUSIONS
Having done the series of experiments, we can conclude that there are some factors affecting the capacitance of a parallel-plate capacitor. These factors include plate separation, area of overlap and the existence of a dielectric. We find out that current is directly proportional to voltage supplied, current is inversely proportional to plate separation, current is directly proportional to the length of the plates. We also verify that the relative permittivity is equal to the ratio of current when having a dielectric in between the plates and that when having no dielectric.
DISCUSSIONS
Precautions
. The resistance of the variable resistor should neither be very high and very low. If the resistance is too high, the charges stored in the parallel-plate capacitor may not be fully discharged, so that the measured current is not accurate, which is definitely smaller. If the resistance is too low, it may have a chance to damage the light-beam galvanometer because of large current.
2. We should not assume the electromotive force (e.m.f.) provided by one battery is exactly 1.5V which is claimed to be. As there is current flow, the voltmeter, variable resistor, light-beam galvanometer and the reed switch may draw a little current, which results in lower potential difference (p.d.). Moreover, the battery may have been used for several times. It may not be able to convert chemical energy to electrical energy at the claimed rate. As we can see, the p.d. provided by different battery is slightly different.
3. The connecting wires should not touch the parallel plates. As we have observed, the reading of the light-beam galvanometer will be affected quite much if a connection wire touches one of the parallel plates. We found that the current would be larger, that is, the capacitance is larger. The possible reason is stray capacitance. This will be further discussed in Sources of errors section.
4. The reed switch should be connected with the low-impedance output of the signal generator. It is found that when connecting to high-impedance output, the light-beam galvanometer oscillates.
5. The supplied voltage should not be too large. Otherwise, the heating effect at the contact points of the reed switch may be too large which may result to damage of the reed switch.
6. The frequency generated by the signal generator should not be too large. If the switching frequency is too high, the reed switch may not be sensitive enough to respond and there may not be enough time for the capacitor to undergo complete discharge.
7. We should reset the voltmeter and the light-beam galvanometer to zero or make a zero reference point. Otherwise, the measured value is not correct.
Sources of errors
. There may be stray capacitance from the bench and the wall. As we can see from the I - graph that it does not pass through the origin, stray capacitance actually exists. Some field lines from or to the plates may actually come from or go to earth and other circuit component, such as connecting wire. We may say that one plate and earth or another conductor form an extra capacitor. In fact, any two materials can form a capacitor which can store charges. Hence, this is the major source of errors.
2. It is assumed that the edge effect of the plates can be ignored and all field lines between the plates are straight. In fact, the field lines curve at the edges. However, this error may not be significant as the separation between the plates is much smaller than the linear dimensions of the plates.
3. The reading of the voltmeter and the light-beam galvanometer may not be exactly the same as value its real value. But even though this error exists, it is too small that it is negligible.
4. The two parallel plates may not be of same area. This may affect the capacitance found. However, as we observed, the difference is too small that it is negligible.
5. The resistor may be too large so that the capacitor is not fully discharged. This will affect the calculated capacitance of the parallel-plate capacitor. This can be a significant error if it is not controlled well.
6. The frequency generated by the signal generator has not been actually measured. This can affect the obtained capacitance of the parallel-plate capacitor. However, this error may only affect our investigation between charge and applied p.d. as the other investigations are carried out by using the same frequency. It does not affect the other observations.
Possible Improvements
. Try to keep the parallel-plate capacitor away as far as possible to avoid stray capacitance.
2. Try to measure the frequency using a Cathode Ray Oscilloscope (CRO) so that the exact frequency can be measured. Hence, a more accurate result of the capacitance can be obtained.
3. Try to monitor the p.d. across the capacitor (or resistor) with a CRO. Adjust the resistance to a value that the capacitor can be fully discharged and that the light-beam galvanometer cannot be damaged.
Physics Practical Report
Page 1