Power in Alternating-Current Circuits — Question 2

Question 2

A wattmeter separates the resistive part from impedance magnitude

A series RL load draws 2.00 A rms from 100 V rms at $\omega=500$ radians per second. A wattmeter reads 120 W, and current lags voltage.

1. Infer R, inductive reactance, and L.

2. Find power factor and reactive power.

Question 2 - Solution

A wattmeter separates the resistive part from impedance magnitude

(a) Method and calculation

$$Z=V/I=50.0\,\Omega,\quad R=P/I^2=30.0\,\Omega.$$$$\boxed{X_L=\sqrt{Z^2-R^2}=40.0\,\Omega,\quad L=X_L/\omega=.0800\,H}.$$

(b) Interpretation and further calculation

$$\cos\phi=P/(VI)=120/200=.600.$$$$\boxed{Q_r=I^2X_L=160\,var}.$$

Physical check

Voltage and current alone give only impedance magnitude; real power supplies the missing resistive information.