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V and I in an A.C. circuit are given by the following equations: V=100 sin(100t) V, I=100 sin (100t+π/3) mA. The power in the circuit is equal to ______ W.

Asked in GSEB Board July 2016 · Average power and heating

• (1) 10
• (2) 10⁴
• (3) 2.5
• (4) 5.0

Step-by-step solution

Why the other options are wrong

• (1) 10 W is V₀I₀=100×0.1, the product of the peak values with neither the factor 1/2 nor cos φ. Average power is 1/2V₀I₀ cos φ.
• (2) No single slip gives 10⁴ W. It is 100×100: the peak values multiplied with the current left as 100 (milliamperes read as amperes), and without the 1/2 or cos φ. Sanity check: 1/2(100)(0.1)cos 60°=2.5 W.
• (4) 5.0 W is VᵣₘₛIᵣₘₛ=(100)/(√2)×(0.1)/(√2) with the power factor left out. The current leads by 60°, so only cos 60°=1/2 of this is real power.

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