What is the power output in an ac series circuit with $12.0 \Omega$ of resistance, $15.0 \Omega$ of inductive reactance, and $10.0 \Omega$ of capacitive reactance, when the circuit is connected to a $120 - \mathrm { V }$ rms power supply?
A) $3.21 \mathrm {~kW}$
B) $1.02 \mathrm {~kW}$
C) $6.00 \mathrm {~kW}$
D) $4.49 \mathrm {~kW}$

Question

Quizplus · Accepted Answer

The power output in an AC series circuit can be calculated using the formula $P = \frac{V^2}{Z^2} R$, where $V$ is the rms voltage, $R$ is the resistance, and $Z$ is the impedance of the circuit. The impedance $Z$ can be found using the formula $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $X_L$ is the inductive reactance and $X_C$ is the capacitive reactance. Substituting the given values:1. Calculate the impedance: $Z = \sqrt{12.0^2 + (15.0 - 10.0)^2} = \sqrt{144 + 25} = \sqrt{169} = 13.0 \Omega$.2. Calculate the power: $P = \frac{120^2}{13.0^2} \times 12.0 = \frac{14400}{169} \times 12.0 \approx 1020 \, \text{W} = 1.02 \, \text{kW}$.

What Is the Power Output in an Ac Series Circuit 12.0Ω12.0 \Omega12.0Ω

What Is the Power Output in an Ac Series Circuit $12.0 \Omega$