A coil of inductive reactance 31 Ωhas a resistance of 8 Ω. It is placed in series with a condens

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A coil of inductive reactance 31 Ωhas a resistance of 8 Ω....

A coil of inductive reactance $31 \Omega$ has a resistance of 8 $\Omega$. It is placed in series with a condenser of capacitative reactance $25 \Omega$. The combination is connected to an a.c. source of $110 \mathrm{~V}$. The power factor of the circuit is (a) $0.33$ (b) $0.56$ (c) $0.64$ (d) $0.80$

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Key Concepts

Impedance

Impedance is the total opposition to current flow in an AC circuit and is a combination of resistance (the opposition to both AC and DC) and reactance (the frequency-dependent component). It is expressed as a complex number, with the real part representing resistance and the imaginary part representing reactance. Calculating impedance is crucial for analyzing the performance and behavior of AC circuits.

Reactance

Reactance refers to the opposition that inductors and capacitors present to alternating current. In inductors, the opposition (inductive reactance) increases with frequency, while in capacitors, the opposition (capacitive reactance) decreases with frequency. This concept is fundamental in understanding how AC circuits behave, particularly in determining the phase relationship between current and voltage.

Power Factor

The power factor of an AC circuit is a measure of how effectively electrical power is converted into useful work. It is defined as the cosine of the phase angle between the applied voltage and the resulting current. A high power factor indicates that most of the power is being used effectively, whereas a low power factor suggests significant reactive power, which does not perform useful work.

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