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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Options

A. average current is `I_(0)/sqrt(3)`
B. average current is zero
C. rms current is `I_(0)/sqrt(3)`
D. rms current is `2I_(0)/sqrt(3)`

Answer

A, C

Explanation

average current =`("Total charge")/("time")`
Total charge will be equal to area of I-t graph, which is zero for `T//2` to `3T//2`, hence average current will be zero for this time interval for `T//2` to `3T/2`:
`I=(2I_(0)t)/(T)-2I_(0)`
`I_(rms) = sqrt((int_(T//2)^(3T//2) I^(2)dt)/(3T//2-T//2))=I_(0)//sqrt(3)`.