The current in a discharging `LR` circuit is given by `I = i_0 e^(-t/tau)` where `tau` is the time constant of the circuit. Calculate the rms current for the period `t = 0` to `t = tau`.

Options

A. `(i_(0))/(e) sqrt(((e^(2) - 1))/(2))`
B. `(i_(0))/(e) sqrt(((e^(-2) + 1))/(2))`
C. `(i_(0))/(e) sqrt(((e + 2))/(3))`
D. `(i_(0))/(e) sqrt(((e^(2) - 1))/(2))`

Answer

A

Explanation

`i_("rms")^(2) = (int_(0)^(tau) i^(2) dt)/(int_(0)^(tau) dt)`