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In an R-C a.c. circuit the maximum voltage and maximum current are 100 V and 1.1 A respectively. If X_C=60 Ω and R=80 Ω, then the power consumed in the circuit will be ______.

Asked in GUJCET 2013 · Average power and heating

Answer: (3) 44.0 W

Step-by-step solution

Given: V₀=100 V, I₀=1.1 A, R=80 Ω and X_C=60 Ω.

Impedance: Z=√R²+X_C²=√80²+60²=100 Ω.

Power factor: cos φ=R/Z=(80)/(100)=0.8.

Average power: P=VᵣₘₛIᵣₘₛ cos φ=(V₀I₀)/2 cos φ=(100×1.1)/2×0.8=44 W.

(The data are not fully consistent: (V₀)/Z gives 1.0 A, not 1.1 A. The question intends P=VᵣₘₛIᵣₘₛ cos φ with the values given.)

So the power consumed is 44.0 W.

Why the other options are wrong

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