A capacitor is charged to a certain potential and then allowed to discharge through a resistance R. The ratio of charge on the capacitor to current in the circuit

Options

A. changes with time
B. does not change with time and it is equal to time constant of circuit
C. does not change with time, but not equal to time constant of circuit
D. may or may not change depending upon the charge given to the capacitor

Answer

B

Explanation

Charge on capacitor at any time is
`q = QE^(-t//tau)` (i)
Differentating Eq. (i) with respect to time, we get the current
`I = (dq)/(dt) = (Q)/(tau)e^(-t//tau)` (ii)
Required ratio is `q//I = tau` [by diciding Eq. (i) by Eq.(ii)]