Question

What is the power output in an ac series circuit with 12.0 Ω of resistance, 15.0 Ω of inductive reactance, and 10.0 Ω of capacitive reactance, when the circuit is connected to a 120-V rms power supply

Answer 1

Answer:

1022.485 Watt

Explanation:

resistance, R = 12 ohm

Inductive reactance, XL = 15 ohm

Capacitive reactance, Xc = 10 ohm

Vrms = 120 V

Power is given by

P = Vrms x Irms x CosФ

Where, CosФ is called power factor

CosФ = R / Z

Where Z is the impedance

Irms = Vrms / Z

So,

$P = \frac{\left (V_{rms}^{2}\times R \right )}{Z^{2}}$

$Z = \sqrt{R^2+\left ( X_{L}-X_{c} \right )^{2}}$

$Z = \sqrt{12^2+\left ( 15-10 \right )^{2}}$

Z = 13 ohm

So,

$P = \frac{\left (120^{2}\times 12 \right )}{13^{2}}$

P = 1022.485 W

Thus, the power is 1022.485 Watt.