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`.

Explanation

Since `i=i_(0)^(-t//tau)`
`i_2=1/tauint_(0)^taui_(0)^2 e^(-2t//tau)dt`
`=(i_(0)^2)/(tau)int _(0)^tau e^(-2t//tau)dt`
`= i_(0)^2/tau xx [tau/2e^(-2t/tau)]_(0)^e`
`= -i_(0)^2/tau xx tau/2 xx [e^(-2) -1]`
`sqrt (i^2)2e^2 = sqrt((-i_(0)^2)/2(1/e^2-1))`
`=sqrt((i_(0)^2)/(2e^2)(e^2-1))`
`=i_0/e sqrt((e^2-1)/2)`