A 120 V supply feeds a load with a power factor of 0.8 lagging and a current of 10 A. Determine the real power, reactive power, and apparent power.

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Multiple Choice

A 120 V supply feeds a load with a power factor of 0.8 lagging and a current of 10 A. Determine the real power, reactive power, and apparent power.

Explanation:
A 120 V supply with a current of 10 A gives an apparent power of S = V × I = 120 × 10 = 1200 VA. The power factor is 0.8 lagging, so real power is P = VI cos(phi) = 120 × 10 × 0.8 = 960 W. The reactive power comes from Q = VI sin(phi). Since cos(phi) = 0.8, sin(phi) = sqrt(1 − 0.8^2) = sqrt(0.36) = 0.6, so Q = 120 × 10 × 0.6 = 720 VAR. These values also satisfy S^2 = P^2 + Q^2: sqrt(960^2 + 720^2) = 1200 VA, confirming consistency. So the correct set is S = 1200 VA, P = 960 W, Q = 720 VAR.

A 120 V supply with a current of 10 A gives an apparent power of S = V × I = 120 × 10 = 1200 VA. The power factor is 0.8 lagging, so real power is P = VI cos(phi) = 120 × 10 × 0.8 = 960 W. The reactive power comes from Q = VI sin(phi). Since cos(phi) = 0.8, sin(phi) = sqrt(1 − 0.8^2) = sqrt(0.36) = 0.6, so Q = 120 × 10 × 0.6 = 720 VAR. These values also satisfy S^2 = P^2 + Q^2: sqrt(960^2 + 720^2) = 1200 VA, confirming consistency. So the correct set is S = 1200 VA, P = 960 W, Q = 720 VAR.

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