A current `i_(0)` is flowing through an `L-R` circuit of time constant `i_(0)`. The source of the current is switched off at time `t = 0`. Let `r` be the value of `(-di//dt)` at time `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)`.