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# Plotting the decay curve of charge in a capacitor

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Introduction

Student Name: WONG Wing Yan

Class and class no. : 6G2 (22)

Date of experiment: 29th April, 2009

Plotting the decay curve of charge in a capacitor

Objective

In this experiment, we are going to plot a decay curve of charge in a capacitor during a discharging process using an electrometer and a microammeter. From the decay curve, we can determine the half-life of the capacitor used.

Apparatus

 500μF capacitor Variable resistor (100kΩ) Electrometer with accessories Switch Milliammeter Microammeter Voltmeter5kΩ potentiometer 9V batteryStop watchConnecting leads

Theory

The electrometer basically acts as a voltmeter of very high internal resistance(~1013Ω) to measure voltage. It can be adapted to measure electric charge(~10-8C) and electric current(~10-10A).

When we try to discharge the capacitance C of a capacitor, the charge Q in the capacitor decaying through a resistor of resistance R is given by: where Q0 is the initial charge stored in the capacitor and t is the time taken after starting the discharging process. The time constant  is defined as: Middle                  1. The potentiometer was adjusted to apply 1V to the input sockets of the electrometer. The milliammeter should give a full-scale deflection, which means that the reading of the milliammeter having a full-scale deflection represents 1V. If not, the internal pre-set control of the electrometer should be adjusted or the other one can be used. The potentiometer was disconnected from the electrometer.
2. The 10-9F internal capacitor was connected up across the inputs of the electrometer.
3. The 1010Ω internal resistor was connected up across the inputs of the electrometer. A stop watch was started at the same time. The reading of the milliammeter, which represents the charge stored Q in the internal capacitor, was decreasing since the capacitor is discharging( Q=CV, full-scale deflection represents Q=10-9 C)
4. The time t was recorded when the reading of the milliammeter was decreasing in steps of 0.1x10-9 C, which indicated the charge Q remaining on the capacitor. The readings were tabulated.
5. A graph of the charge Q against time was plotted. It was called the decay curve of the charge in the capacitor.
1. Measurement of discharging current by a microammeter
1. The circuit as shown in Fig.2 was connected.                   Conclusion

The time constant affects the rate of discharge of a capacitor. A smaller  implies that the discharging process is complete in a short time. The capacitor is almost completely discharge when t = 5RC.

Conclusion

In this experiment, we try to study the process of discharging. We investigate the process of it and plot a decay curve of charge in a capacitor during a discharging process using an electrometer and a microammeter. We can determine the half-life of the capacitor used form the decay curve.

We compare the experimental value to theoretical value and find that the experimental one is a larger than the theoretical value, which is due to the error of this experiment.

It is also clear to see that t1 is very close to t2 for both 2 methods. we can know the relationship between Q and I, the charge Q remaining in the capacitor at any time is directly proportional to the current I.

We can improve the experiment by recording the time more accurately by taking more significant figure. We can also take more times of the measurement in order to obtain a more accurate result.

Reference

• New Way Physics for Advance Level – Book3(Fields, Electricity and Electromagnetism) ; Manhattan Press (H.K.) LTD, page 93-100
• http://en.wikipedia.org/wiki/Capacitor

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