A coil carrying a steady current is short-circuited. The current in it decreases `alpha` times in time `t_(0)`. The time constant of the circuit is

Options

A. `tau = t_(0)` In `alpha`
B. `tau = (t_(0))/(In alpha)`
C. `tau = (t_(0))/(alpha)`
D. `tau = (t_(0))/(alpha - 1)`

Answer

B

Explanation

`I = (I_(0))/(alpha)` at `t = t_(0)`
Since `I = I_(0)e^(-t_(0)//tau) rArr (1)/(alpha) = e^(-t_(0)//tau)`
`alpha = e^(-t_(0)//tau) rArr t_(0) = tau log_(e) alpha`
`tau = (t_(0))/(log_(e) alpha)`