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The electric current in a circuit is giv...

The electric current in a circuit is given by `I = i_0 (t/(tau))` for some time. Calculate the rms current for the period `t = 0` to `t= (tau)`.

Text Solution

Verified by Experts

The mean square current is
`(i^(2))_("avg")=(1)/(T)int_(0)^(T)i_(0)^(2)(t//T)^(2)"dt"=(i_(0)^(2))/(T^(3))int_(0)^(T)t^(2)"dt"=(i_(0)^(2))/(3)`
Thus the rms current is
`i_("rms")=sqrt(i_("avg")^(2))=(i_(0))/(sqrt(3))`
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