c) What is the ratio of the power dissipated in the resistor to the power that w

Question

c) What is the ratio of the power dissipated in the resistor to the power that would be dissipated if the inductor were not in the circuit? (Assume that Erms stays the same.)

Consider a series RL circuit with R = 73.0 ? and an unknown inductor L, driven by an AC emf with E = 32.0 V (rms) at frequency f = 7.70 kHz. If we measure the current in the circuit, we find I rms = 0.137 A. c) What is the ratio of the power dissipated in the resistor to the power that would be dissipated if the inductor were not in the circuit? (Assume that Erms stays the same.)

Explanation / Answer

impedence Z= Vrms/irms = 32/0.137 = 233.57 ohms

but Z^2 = R^2+ XL^2

so     XL = [233.57^2 -73^2]1/2 = 221.869 ohms

power across resistor = i^2R = 0.137*0.137 * 73 = 1.37 Watts

power across inductor = i^2XL = 0.137*0.137 * 221.869 = 4.164 Watts

ratio is, 1.37/4.164 = 0.329 or 32.9 %

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