A voltage v = 200 sinωt + 100 sin3ωt V is applied across a 10 Ω resistor. Determine the average power dissipated in the resistor.
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A voltage v = 200 sinωt + 100 sin3ωt V is applied across a 10 Ω resistor. Determine the average power dissipated in the resistor.

G1 Physics · Accepted Answer

The two sinusoidal terms have different frequencies, so their mean-square values add. Vᵣₘₛ² = 200²/2 + 100²/2 = 25000 V². Hence P = Vᵣₘₛ²/R = 25000/10 = 2500 W.