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Measurement of High Resistance by Leakage

When a capacitor of capacitance C and initial charge Q0 is allowed to discharge through a resistance R for a time t, the charge remaining on the capacitor is given by
            Q = Q0e-t/CR
            Q0/Q = et/CR
        loge Q0/Q = t/CR
. :            R = t /C loge (Q0/Q) = t / 2.3026C log10 (Q0 /Q)

If R is high, CR will be high and the rate of discharge of capacitor will be very slow. Thus if we determine Q0/Q from experiment, then R can be calculated.
C is a capacitor of known capacitance, R is the high resistance to be measured, B.G. is a ballistic galvanometer, E is a cell, and K1, K2, K3 are tap keys.
Keeping K2 and K3 open, the capacitor is charged by depressing the key K1. K1 is then opened and at once K3 is closed. The capacitor discharges through the galvanometer which records a throw θ0 is proportional to Q0. The capacitor is again charged to the maximum value keeping K2 and K3 open and closing K1. K1 is the open and K2 is closed for a known time t. Some of the charge leaks through R. K2 is opened and at once K3 is closed. The charge Q remaining on the capacitor then discharges through the galvanometer. The resulting throw θ is noted. Then Q ∞ θ

    Now,     Q0/Q = θ0
    . :    R = t/ 2.3026 C log100/θ)

A series of values of t and θ are obtained. A graph is plotted between t and log10 0/θ) which is a straight line. Its slope gives the mean value of t / log100/θ). As C is known, the value of R can be calculated.

Measurement of High Resistance

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