The figure shows an experimental plot discharging of a capacitor in an `RC` circuit. The time constant of this circuit lies between:

Options

A. 150 sec and 200 sec
B. 0 and 50 sec
C. 50 sec and 100 sec
D. 100 sec and 150 sec

Answer

D

Explanation

From Fig. max p.d. `V_(0) = 25` volt
Corresponding to `V = (V_(0))/(2) = (25)/(2) = 12.5 V`,
`t = 100 s`.
The discharging of a capacitor through resistance is governed by
`V = V_(0) e^(-t//tau)` when `V = (V_(0))/(2) , (V_(0))/(2) = V_(0) e^(-t//tai)`
`log_(e) 1 - log_(e) 2 = - (t)/(tau) log_(e) e = - (t)/(tau)`
`tau = (t)/(log_(e) 2) = (100)/(0.693) = 144.3 s`
Choice (d) is correct