Power factor is calculated by

Question

Examoogle · Accepted Answer

$R/Z$

Explanation: The power factor of an A.C. circuit is defined as the cosine of the phase angle difference between the voltage and current. In a series RLC circuit, it represents the ratio of the real power (resistance) to the apparent power (impedance).

Working Principle: In an A.C. series circuit, the total impedance $Z$ is the vector sum of resistance $R$ and reactance $X$. The voltage leads or lags the current by an angle $\phi$. Since $R$ is the base component of the impedance triangle and $Z$ is the hypotenuse, the power factor is given by the ratio $\frac{R}{Z}$, which corresponds to $\cos(\phi)$.

Key Formulas: $PF = \cos(\phi) = \frac{R}{Z}$ — Power factor in terms of resistance and impedance; $Z = \sqrt{R^2 + (X_L - X_C)^2}$ — Total impedance in an RLC circuit

Key Points: Power factor is a dimensionless quantity ranging from 0 to 1.; A unity power factor ($PF=1$) occurs in purely resistive circuits where $\phi = 0$.; Lagging power factor is associated with inductive loads, while leading is associated with capacitive loads.; Higher power factor minimizes current for a given power delivery, reducing $I^2R$ losses.

Advantages: Reduced transmission line losses; Increased capacity of electrical supply equipment

Disadvantages: Requires reactive power compensation (capacitors); Can lead to voltage instability if poorly managed

Applications: Industrial motor drives; Electrical power grid management

Additional Info: Option B ($Z/R$) is the secant of the phase angle.. Option C ($V/I$) represents the magnitude of the total impedance $Z$.. Option D ($V/Z$) is equivalent to the current $I$.

Answer: A is correct — Power factor is defined as the ratio of resistance to impedance (R/Z) in an AC series circuit.

Exam Tip: Always remember that in an impedance triangle, resistance $R$ is the horizontal component and reactance $X$ is the vertical component; thus, $\cos(\phi)$ is always $R/Z$.

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