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

1022.485 Watt

Step-by-step 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 = (\left (V_(rms)^(2)* 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 = (\left (120^(2)* 12  \right ))/(13^(2))`

P = 1022.485 W

Thus, the power is 1022.485 Watt.