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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/Tint_(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^(2)""_(avg).)=i_(0)/sqrt(3)`
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