An AC source of voltage V = 200 sin(100t) is connected to a series LCR circuit with L = 2 H, C = 50 microfarads, and R = 10 ohms. What is the average power dissipated in the circuit?

A. 2000 W — First, calculate the inductive reactance and capacitive reactance. Since the circuit is at resonance where XL equals XC, the impedance equals the resistance, and power is calculated using Vrms squared divided by R.

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$An AC source of voltage V = 200 sin (100 t) is connected to a series LCR circuit with L = 2 H, C = 50 μ F, and R = 10 Ω . What is the average power dissipated in the circuit?$

A. $2000 W$
B. $1000 W$
C. $500 W$
D. $250 W$

Show correct answer & step-by-step solution

Correct answer: A — $2000 W$

Solution

Calculate X_{L} = ω L = 200 Ω and X_{C} = 1/ (ω C) = 200 Ω . Since X_{L} = X_{C}, the circuit is at resonance, Z = R = 10 Ω . Average power P = V_{rms}^{2} / R = (200/ 2)^{2} /10 = 2000 W .

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An AC source of voltage V=200sin(100t) is connected to a series LCR circuit with L=2 H, C=50 μF, and R=10 Ω. What is the average power dissipated in the circuit?

Solution

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More AC Circuits practice questions

$An AC source of voltage V = 200 sin (100 t) is connected to a series LCR circuit with L = 2 H, C = 50 μ F, and R = 10 Ω . What is the average power dissipated in the circuit?$