## Measurement Of High Resistance

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# Measurement of High Resistance by Leakage

When a capacitor of capacitance C and initial charge Q_{0}is allowed to discharge through a resistance R for a time t, the charge remaining on the capacitor is given by

Q = Q

_{0}e

^{-t/CR}

Q

_{0}/Q = e

^{t/CR}

log

_{e }Q

_{0}/Q = t/CR

. : R = t /C log

_{e}(Q

_{0}/Q) = t / 2.3026C log

_{10}(Q

_{0}/Q)

If R is high, CR will be high and the rate of discharge of capacitor will be very slow. Thus if we determine Q

_{0}/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 K

_{1}, K

_{2}, K

_{3}are tap keys.

Keeping K

_{2}and K

_{3}open, the capacitor is charged by depressing the key K

_{1}. K

_{1}is then opened and at once K

_{3}is closed. The capacitor discharges through the galvanometer which records a throw θ0 is proportional to Q

_{0}. The capacitor is again charged to the maximum value keeping K

_{2}and K

_{3}open and closing K

_{1}. K

_{1}is the open and K

_{2}is closed for a known time t. Some of the charge leaks through R. K

_{2}is opened and at once K

_{3}is closed. The charge Q remaining on the capacitor then discharges through the galvanometer. The resulting throw θ is noted. Then Q ∞ θ

Now, Q

_{0}/Q = θ

_{0}/θ

. : R = t/ 2.3026 C log

_{10}(θ

_{0}/θ)

A series of values of t and θ are obtained. A graph is plotted between t and log

_{10 }(θ

_{0}/θ) which is a straight line. Its slope gives the mean value of t / log

_{10}(θ

_{0}/θ). As C is known, the value of R can be calculated.

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