A series alternating current (AC) circuit consists of a resistor of resistance R = 40\ \Om… — JAMB UTME

A series alternating current (AC) circuit consists of a resistor of resistance $R = 40\ \Omega$ , an inductor with inductive reactance $X_L = 70\ \Omega$ , and a capacitor with capacitive reactance $X_C = 40\ \Omega$ , connected to an AC voltage supply of $100\ \text{V}$ . What is the power factor of the circuit?

Answer: 0.8

Answer

The power factor of the circuit is 0.8.

The total impedance

Z

of the series circuit is found using

Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{40^2 + (70 - 40)^2} = 50\ \Omega

. The power factor is the ratio of resistance to impedance:

\cos\phi = \frac{R}{Z} = \frac{40}{50} = 0.8

Step-by-Step Solution

Calculate the net reactance of the circuit.

X = X_L - X_C = 70\ \Omega - 40\ \Omega = 30\ \Omega

In a series RLC circuit, the net reactance is the arithmetic difference between the inductive reactance and the capacitive reactance.

Calculate the total impedance of the circuit.

Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{40^2 + 30^2} = \sqrt{2500} = 50\ \Omega

Impedance represents the combined opposition to current flow from resistance and net reactance in quadrature.

Determine the power factor of the circuit.

\cos\phi = \frac{R}{Z} = \frac{40}{50} = 0.8

The power factor is equal to the cosine of the phase angle, which is defined as the ratio of resistance to total impedance.

Key Concept

Power Factor in AC Circuits

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic