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Question

An alternating current is given by the equation i=i1sinωt+i2cosωt. The rms current will be:


A

12(i12+i22)1/2

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B

12(i12+i22)1/2

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C

12(i1+i2)2

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D

12(i1+i2)

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Solution

The correct option is B

12(i12+i22)1/2


Step 1. Given data

Current equation, i=i1sinωt+i2cosωt

Step 2. Finding the RMS value of the current, Irms

By using the formula,

I0=i12+i22+2i1i2cosθ=i12+i22+2i1i2cos90°=i12+i22+2i1i2(0)=i12+i22 [I0 is maximum value of current]

We know that,

Irms=I02

Thus, Irms=i12+i222

Hence, option B is correct.


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