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Question

An alternating current is given by
i=i1cosωt+i2sinωt
The rms is given by

A
i1+i22
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B
|i1+i2|2
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C
i21+i222
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D
i21+i222
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Solution

The correct option is C i21+i222
i=i1cosωt+i2sinωt
divide and multiply RHS by i12+i22
i=i12+i22(i1cosωti12+i22+i2sinωti12+i22)
Assuming i1i12+i22=sinϕi2i12+i22=cosϕ
i=i12+i22(cosωt.sinϕ+sinωt.cosϕ)
i=i12+i22sin(ωt+ϕ)(1)
now this is in the form of i=i0sin(ωt+ϕ)
and here i RMS be i02
so similarly i RMS of equation (1) = i12+i222

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