In an AC circuit, the root mean square (rms) current is 2 A. If the wattless current (reactive component) is sqrt(3) A, what is the power factor of the circuit?

1 / sqrt(3)
1 / sqrt(2)
1 / 2
1 / 3

Correct answer: 1 / 2

Solution

The rms current I = 2 A is the vector sum of the active current (Ia) and the wattless (reactive) current (Ir = sqrt(3) A). So Ia = sqrt(I² - Ir²) = sqrt(4 - 3) = 1 A. Power factor = cos(phi) = Ia / I = 1/2.

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