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 = e^t/CR
        log_e Q₀/Q = t/CR
. :            R = t /C log_e (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/θ
    . :    R = t/ 2.3026 C log₁₀ (θ₀/θ)

A series of values of t and θ are obtained. A graph is plotted between t and log₁₀ (θ₀/θ) which is a straight line. Its slope gives the mean value of t / log₁₀ (θ₀/θ). As C is known, the value of R can be calculated.