Which of the following describes the relationship used in the power factor definition?

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Multiple Choice

Which of the following describes the relationship used in the power factor definition?

Explanation:
Power factor comes from how much of the circuit’s impedance is real (the resistive part) versus reactive. In AC circuits, impedance is Z = R + jX, with magnitude |Z| = sqrt(R^2 + X^2). The phase angle between voltage and current is phi, where cos(phi) = R / |Z|. So the power factor, which is cos(phi), is effectively the ratio of the resistance to the total impedance magnitude. If there’s no reactance (X = 0), PF = 1; with reactance, |Z| grows and PF drops. This is also why PF = P / S, since P = I^2 R and S = VI, giving PF = (I^2 R) / (VI) = R / |Z|.

Power factor comes from how much of the circuit’s impedance is real (the resistive part) versus reactive. In AC circuits, impedance is Z = R + jX, with magnitude |Z| = sqrt(R^2 + X^2). The phase angle between voltage and current is phi, where cos(phi) = R / |Z|. So the power factor, which is cos(phi), is effectively the ratio of the resistance to the total impedance magnitude. If there’s no reactance (X = 0), PF = 1; with reactance, |Z| grows and PF drops.

This is also why PF = P / S, since P = I^2 R and S = VI, giving PF = (I^2 R) / (VI) = R / |Z|.

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