A branch consisting of R = 10 Ω in series with Xʟ = 10 Ω is connected in parallel with a 20 Ω resistor. The combination is connected across 100 V RMS. If the total average power is 100N W, determine N.
Physics · AC Circuits · Parallel and Mixed AC Circuits
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Question

A branch consisting of R = 10 Ω in series with Xʟ = 10 Ω is connected in parallel with a 20 Ω resistor. The combination is connected across 100 V RMS. If the total average power is 100N W, determine N.

Physics · AC Circuits · Parallel and Mixed AC Circuits

G1 Physics · Accepted Answer

For the RL branch, P₁ = V²R/[R²+Xʟ²] = 10000×10/(100+100) = 500 W. For the 20 Ω branch, P₂ = V²/20 = 500 W. Total power = 1000 W = 100×10 W, so N=10.