An alternating current is given by i = i1 cos(omega t) + i2 sin(omega t). What is its r.m.s. value?

(1/sqrt(2)) * (i1² + i2²)^(1/2)
(1/sqrt(2)) * (i1 + i2)
(1/sqrt(2)) * (i1 + i2)²
(1/2) * (i1² + i2²)^(1/2)

Correct answer: (1/sqrt(2)) * (i1² + i2²)^(1/2)

Solution

cos and sin terms are 90 degrees out of phase, so they add like perpendicular vectors: the resultant amplitude is sqrt(i1² + i2²). The r.m.s. value of any pure sinusoid is its amplitude divided by sqrt(2).

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