Question

The r.m.s. value of a current given by i = (i₁ cos θt + i₂ sin ωt) is ______.

पर्याय

• `1/sqrt2 (i_1 + i_2)`

• `1/sqrt2 (i_1 - i_2)`

• `1/sqrt2 sqrt((i_1^2 + i_2^2))`

• `1/sqrt2 (i_1^2 + i_2^2)`

Answer 1

The r.m.s. value of a current given by i = (i₁ cos θt + i₂ sin ωt) is `bbunderline(1/sqrt2 sqrt((i_1^2 + i_2^2))`

Explanation:

`i_(rms) = sqrt((i_0^2)/2`, where i₀ is the peak value of current

Now i = (i₁ cos θt + i₂ sin ωt), then

`i_(rms) = sqrt((i_1^2 + i_2^2 + i_1 i_2 cos 90^circ)/2)`

`i_(rms) = sqrt((i_1^2)/2 + i_2^2/2`

`i_(rms) = sqrt((i_1^2 + i_2^2)/2`

`i_(rms) = 1/sqrt2 + sqrt(i_2^2 + i_2^2)`