A current `i_(0)` is flowin through on L-R circyuit of time constant `t_(0)`. The source of current is seitched off at time t=0. Let r be the value of (-di/dt) at tiemt t=0. Assuming this rate to be constant, the current will reduce to zero in a time interval of

Options

A. `t_(0)`
B. `et_(0)`
C. `(t_(0))/(e)`
D. `(1 - (1)/(e)) t_(0)`

Answer

A

Explanation

`i = i_(0) e^(-t//t0)`
`(-(di)/(dt)) = (i_(0))/(t_(0)) e^(-t//t_(0))`
`(-(di)/(dt)) = (i_(0))/(t_(0)) = r` (at `t = 0`)
`:.` The desired time is `(i_(0))/(r )` or `t_(0)`.