QUESTION

# Write a 2 pages paper on capacitors using charge sensors. Capacitors Using Charge SensorsAbstract The major objective of this lab was to determine the capacitance of different conductor-dielectric geo

Write a 2 pages paper on capacitors using charge sensors. Capacitors Using Charge Sensors

Abstract

The major objective of this lab was to determine the capacitance of different conductor-dielectric geometries by use of “charge-sharing technique. In addition, the lab also involves calculating the amount of voltage cumulated as the result of charge sharing process. From this process, an unknown capacitance is also figured out.

Objective

The purpose of the lab is to determine the capacitance of variety of conductor-dielectric by making use of charge sharing methodology. This would provide benchmark for exploring the principle of conservation of charge in a system. The application of various capacitors with different capacitance also makes it important to determine unknown capacitance besides voltage calculation by using the equation (Q=CV)

Procedure

Six different capacitors were obtained from the lab and their capacitance measured. A parallel circuit was created composing of 1.0μF capacitor and 0.1μF capacitor (making 1.1μF. A second capacitor of 1.0μF was charged into 5V. The charged capacitor was then touched to the 1.1μF capacitor (uncharged) in the circuit. The 1.1μF was again discharged. The aforementioned steps were then repeated with a 0.1μF capacitor used in place of 1.0μF as the charge transfer capacitor. Then, instead of discharging the 1.1μF capacitor the 0.1μF capacitor was recharged to 5.0V followed by reconnecting it. The 1.1μF capacitor was then charged to 5.0V followed by sharing its charge with uncharged capacitor that has unknown capacitance. The final reading was made from the voltmeter and then used to arrive at the unknown capacitance by use of the equation Q=CV. The unknown capacitance was then directly measured from the digital voltmeter.

A parallel-plate capacitor was constructed through inserting a waxed paper in between aluminium plates. The construct was then pressed together by placing on top a 1.0kg weight. A charge sensor was then mounted with a 0.01μF capacitor. The combined capacitance of 0.01μF capacitor, together with the charge sensor, was then measured by using the digital voltmeter’s capacitance capability. This formed the standard capacitor for the lab. The standard capacitor was charged to 5.0 V using the power supply. Charge-sharing method was then used to determine unknown capacitances, that is capacitances of a length of coaxial cable and a parallel-plate capacitor.

Experimental data

The digital voltmeter was used to measure the voltage for 1.0μF, 0.1μF and 0.01μF. The unknown capacitor value was measured 0.48μF. The sensor capacitance was measured to be 19.65μF and the aluminum 9.6μF. The following is a table showing the results:

capacitor

capacitance

Initial voltage

touching

250

1.0μF

5.000V

0.415 V

100/105 k

0.1μF

5.000V

2.412 V

103 g

0.01μF

5.000V

0.045 V

Black

0.48μF

5.000V

1.538 V

Calculating unknown capacitance

(.02 + )

(.02 + )

= – 0.02 X 10-6

From the law of conservation of charge

1 μF share to 1.1 μF:

0.1 μF share to 1.1 μF:

First time:

Second time:

Third time:

Theoretical value

Actual value

Discrepancy

First time

0.415V

0.48%

Second time

0.833V

0.801V

3.84%

Third time

1.118V

1.152V

2.5%

Unknown capacitance capacitor:

Aluminum plates:

Coaxial cable:

= 1.92 x 10-9F

Discussion

The lab made use of “charge-sharing” technique in combination with equation used in determining capacitance of a variety of capacitors. DVM (digital voltmeter) was used to measure voltage and to determine the actual capacitance. From charge sharing, 1μF to 1.1 μF, the difference between the actual and the measured was 1.34% while that for 0.1μF to 1.1μF was 0.38%, 3.85% and 0.5%. Further, we were able to calculate the unknown capacitance value as 0.3μF while the measured value was 0.48, which gave a percentage difference of 60.3%. This was the biggest gap difference and could be contributed to experimental errors. The error could have arose from not discharging well the sensor once it was used. Some errors could have also arose from rounding off to significant figures. When looking at the results, we confirm that Q start is always equal to Q end. In which case Qstart =Cstart*Vstart = Cend*Vend. From the equation, we isolate the unknown, which is Cend and solved it. Consequently, this confirms the applicability of principles of conservation of charge.

Conclusion

In conclusion, the experiment was successful in meeting the stated objectives with most errors being less than 5% between the actual and the measured values. The only exception is for the unknown capacitance capacitor which gave a bigger percentage difference as the result of experimental errors. By applying “charge sharing” methodology, we were able to determine the he capacitance of different conductor-dielectric geometries.