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The current in a discharging LR circuit ...

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`.

Text Solution

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The mean square current is
`bar i^2` `= 1/(tau)` `int_0^(tau) i_0^2 (t/(tau)^2 dt= i_0^2/tau^3 int_0^tau dt= i_0^2/3`
Thus, the rms current is
`i_(rms) = sqrt(bar i^2) = i_0/(sqrt(3))`
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