The current in a certain circuit varies with time as shown in figure. Find the average current and the rms current in terms of `I_0`
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Answer

C

Explanation

Average current will be zero is positive and negative half cycles are symmetrical RMS current can also be obtained from 0 to `tau/2`.
`I=(I_0/(tau/2))t=((2I_0)/tau)t`
`i^2=((4I_0^2)/tau^2)t^2`
`(:I^2:)_((0-tau)//2)=(int_0^(tau///2)(4I_0^2)/tau^2t^2 dt)/(pi/2)`
or `(:I^2:)_((0-tau)//2)=I_0^2/3`
`implies I_("rms")=sqrt(I_(0)^(2)/(3))=(I_(0))/(sqrt(3))`.