Objective

The

purpose of the experiment was to test the effect of dielectric material on a

calibrated parallel plate capacitor.

Theory

Capacitors are devices made of two parallel plates separated by a

distance with equal area but opposite charges that can store potential energy

in an electric field. The capacitance, measured in farads F, can be calculated using the following

relationship (Department of Physics):

(1)

where A

is the area of each plate, d is the

distance between the plates and is the permittivity of the material between

the plates. This relationship illustrates that the capacitance is determined by

the size and shape of the conductors and the separation between them.

Furthermore, as the distance between the

plates increase, the capacitance would expectedly decrease (Department of Physics). Capacitors are charged by having electrons removed from the positive

plate and carried to the negative plate which is directly against the electric

field to which in nature is pulling the electrons back to the positive plate

and pushing them away from the negative plate. Therefore, the capacitance can

be measured by charging the capacitor then discharging it through the

galvanometer in the circuit (What is dielectric

constant?).

The deflection of the galvanometer if proportional to the current

going through it. Therefore, when charging the capacitor to a potential

difference, V, the charge placed can

be charged as q, the capacitance can

be found using the following relationship (Department of

Physics):

(2)

It

is assumed that the permittivity of air is similar to vacuum, therefore the

permittivity of vacuum, is used. The ratio of relative to is called the dielectric constant, k,

which interprets the ability of

the material to concentrate electric flux, therefore expressed in the following

equation:

(3)

The dielectric constant can also be found with the combination of

equation (1) and (3) resulting in the following equation:

(4)

where is measured capacitance with vacuum between

the plates and C is the measured

capacitance with the dielectric material(Department of Physics).

Procedure

Part

A

1.

Apparatus was set up as shown in the

following diagram using the standard (known) capacitor:

2.

Figure (1): Illustration of the electric circuit

used to set up the apparatus to charge and discharge the capacitor (CITE)

3.

The sensitivity of the galvanometer was

calculated by setting the galvanometer range to “Direct” and charging the

standard capacitor to 66.7 V. The capacitor was allowed to charge for a few

seconds as it was charging through a large resistance.

4.

The maximum value of deflection was recorded by

the galvanometer on the first swing when switched to discharge and an average

reading was taken after a few trials.

5.

The standard capacitor was replaced with the

parallel plate capacitor. This was done carefully to ensure that the capacitor

plates just touch with no significant pressure exerted on each other.

6.

Ensuring that no calibration on the Vernier scale

was needed, the plate separation was set to 0.3 mm. The parallel plate

capacitor was then charged to a starting

voltage of 66.7 V and the deflection was recorded. The charge was increased

when needed to provide a reasonable deflection on the galvanometer.

7.

Step five was then repeated for several plate

separation between 0.3 mm and 10.0 mm with smaller intervals for shorter

distances to provide better results.

8.

The area of the plate was then recorded.

9.

Six sheets of paper was then obtained and the

thickness of a single paper was measured.

10.

One sheet of paper was placed between the plates

and the plates were then closed on it until it was slightly snug but not tight.

A potential difference of 141.4V was used to obtain a deflection on the

galvanometer.

11.

Step nine was repeated to obtain results by

adding a single paper each time to obtain consecutive results up to six sheets.

12.

Steps eight through ten were then repeated for

two other materials to obtain results, however only obtaining results for.

13.

The galvanometer was then turned to “SHORT”. The

high voltage source and the galvanometer were then unplugged. (Department of

Physics).

Observations

and Results

Area of the Parallel Plates: 0.0556 m^2=556cm^2

Known Capacitance = 8.07nF= 8.07E-09F

Part

A:

Table

1: Calibration of the sensitivity for the Galvanometer.

Value of

deflection (centimeter)

Average

Deflection from 3 (centimeter)

Average

Deflection Total

(centimeter)

Voltage(Potential

Difference)

Sensitivity

(farad volts/centimeter)

2.9±

3.03

2.965

66.7

1.82×10^-7

3.1

66.7

3.1

66.7

2.9

2.9

66.6

2.9

66.8

2.9

66.6

3.1

2.97

66.6

2.9

66.7

2.9

66.7

3

2.96

66.7

2.9

66.7

3

66.7

Calculations:

Uncertainty=(0.25)(Capacitance)

+ 0.5pF

Uncertainty=(0.25)(8.07nF)

+ 0.0005nF

Uncertainty=2.018nF

Sensitivity=

(Voltage)(Known Capacitance)/Average deflection

Sensitivity=

(66.7)(8.07×10^-9)/2.965

Sensitivity=

1.82X10^-7

Part

B

Table

2: Deflection values and capacitance values obtained for corresponding

plate

separation and potential difference.

Plate

Separation (centimeters)

Value of

deflection (centimeters)

Voltage

(Potential

Difference)

Capacitance

(F)

1/Separation

(centimeters)

.03

2.6

143.6

3.295×10^-9

33.3

.05

1.5

151.9

1.797×10^-9

20.0

.08

1.5

151.9

1.797×10^-9

12.5

0.1

0.7

151.7

8.398×10^-10

10

0.12

0.5

151.7

5.999×10^-10

8.33

0.15

0.3

151.7

3.599×10^-10

6.67

0.2

0.2

151.7

2.399×10^-10

5

0.25

0.1

161.3

1.128×10^-10

4

0.3

0.2

166.9

1.090×10^-10

3.33

0.35

0.2

166.9

2.181×10^-10

2.86

0.4

0.2

191.7

1.899×10^-10

2.5

0.5

0.1

199.5

9.49×10^-11

2

0.6

0.1

199.5

9.123×10^-11

1.67

0.7

0.1

199.5

9.123×10^-11

1.43

0.8

0.1

199.5

9.123×10^-11

1.25

0.9

0.05

199.5

4.561×10^-11

1.11

1.0

0.05

199.5

4.561×10^-11

1.00

Example

Calculations:

1/Separation=1/0.03

1/Separation=33.3

Capacitance=(sensitivity)x(deflection)/voltage

Capacitance=(1.82X10^-7)x(2.6)/143.6

Figure 2: Graph illustrates the capacitance

obtained corresponding to 1/separation

for air.

Capacitance=3.295×10^-9

?=Slope/Area

?=1×10^-10/556

?=1.799E-13

F/cm

?=1.799E-11F/m

2.03

(Ashby)

Error

propagation:

(1-2.03/ 1)= 103% error

Part

C

Table

3: Measurements of material thickness

Thickness of Paper

0.75mm

Thickness of material 1 – plastic

0.45mm

Thickness of material 2

0.4mm

Table

4: Deflection values obtained for corresponding number of sheets places between

the

plates.

Sheets of Paper

Deflection

Sheets of Material 1

Deflection

Sheets of Material 2

Deflection

Voltage (Potential Difference)

1

2.2

1

1.1

1

2

141.4

2

n/a

2

n/a

2

n/a

141.4

3

1.6

3

0.9

3

1.7

141.4

4

1.4

4

n/a

4

n/a

141.4

5

1.3

5

n/a

5

n/a

141.4

6

1.2

6

0.3

6

0.6

141.4

n/a= no results

attained due to time constraint

Table 5: Separation values and the calculated

values for 1/separation.

Separation

(centimeter)

1/separation

Paper (1/centimeter)

Separation

(centimeter)

1/separation

Material-1 (1/centimeter)

Separation

(centimeter)

1/separation

Material-2 (1/centimeter)

0.075

13.33

0.045

22.22

0.04

25

0.15

6.67

0.09

11.11

0.08

12.5

0.225

4.44

0.135

7.41

0.12

8.33

0.3

3.33

0.18

5.56

0.16

6.25

0.375

2.67

0.225

4.44

0.2

5

0.45

2.22

0.27

3.70

0.24

4.17

Table 6:

Calculated Capacitance for Paper, Material 1, and Material 2.

Capacitance

Paper F

Capacitance

Material 1 F

Capacitance

Material 2 F

2.832×10^-9

1.416×10^-9

2.574×10^-9

n/a

n/a

n/a

2.059×10^-9

1.158×10^-9

2.188×10^-9

1.801×10^-9

n/a

n/a

1.673×10^-9

n/a

n/a

1.54×10^-9

3.861×10^-10

7.723×10^-10

Example

Calculation:

Capacitance=(sensitivity)x(deflection)/voltage

Capacitance=(1.82X10^-7)x(2.2)/141.4

Capacitance=

2.832×10^-9 F

Figure

3:Graph illustrates the capacitance obtained corresponding to 1/separation

for sheets of

paper.

?=Slope/Area

?=1.1×10^-0/556cm^2

?=1.978E-13

F/cm

?=1.978E-11

F/m

2.23

(Ashby)

Error

propagation:

(3.85-2.23/ 3.85) x 100= 42% error

Figure

4: Graph illustrates the capacitance obtained corresponding to

1/separation

for first

material used.

?=Slope/Area

?=4E-11/556

?=7.19E-14F/cm

?=7.19E-12F/m

0.812

(Ashby)

Error

propagation:

(2.5-0.812/ 2.5) x 100= 67.5% error

(assuming

this is wax paper)

Figure

5: Graph illustrates the capacitance obtained corresponding to

1/separation

for second

material used.

?=Slope/Area

?=7E-11/556

?=1.258E-13F/cm

?=1.258E-11F/m

1.421

Error

propagation:

(2.25-1.421/ 2.25) x 100= 36.9% error

(assuming

this is polyethylene)

Discussion

and Conclusion

Part

A and Part B:

As was seen in the results, the value of

permittivity of air (k)that was calculated for was2.03. This is not close to the known permittivity

of k(air)=1.00058986.

Where the results attained had an inaccuracy of nearly 103%. The potential sources of error could include the fact

that galvanometer did not indicate an exact number, but was almost like a

pendulum in how the results were portrayed. Therefor measuring the exact

deflection amount relied heavily on what the experimenter thought the line was

at. This could have lead to the slight difference in the permittivity of the

air that was attained. However the graph (Figure 2), shows that the results

were as expected. Where there is a linear correlation between the Capacitance

and the 1 over the separation when looking at the line of best fit.

Part C:

As seen in the results and

calculations, the permittivity of the materials is as follows:

Paper

k=2.23

Material 1

k=0.812

Material 2

k=1.421

When compared to the

online permittivity of paper, the error percentage is equal to 42% . This error percentage could be explained by

potential sources of error like the fact that the paper itself was dirty

leading to a potential foreign material being introduced, therefore leading to

two different permittivities being introduced. This error is carried on through

the experiment for Material 1 and Material 2. The k value for material 1 and

2 both yielded a error propagation of

67.5% and 36.9% respectively. For part C other than the fact that the materials

were all dirty, another source of inaccuracy could potentially have arisen from

the fact that galvanometer was in itself an inaccurate device. Similar to part

A and B, the results are difficult to read leading to some guess work as to

where the maximum line had reached.

Through the potential inaccuracies, the graphs (figure 2,3,4,5)

show a linear correlation as expected between capacitance, and

1/separation. This correlation is what

has allowed for the calculation of the permittivity.