The power factor of a D.C. circuit is always ______

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Examoogle · Accepted Answer

Unity

Explanation: In a direct current (DC) circuit, the current and voltage are constant with respect to time, meaning there is no phase displacement between them. Since the power factor ($\cos \phi$) is defined as the cosine of the phase angle $\phi$ between voltage and current, and for DC $\phi = 0^\circ$, the power factor is $\cos(0^\circ) = 1$.

Working Principle: In DC circuits, the impedance consists only of pure resistance ($R$), as frequency ($f$) is zero, rendering inductive ($X_L = 2\pi f L$) and capacitive ($X_C = \frac{1}{2\pi f C}$) reactances null. Consequently, the phase difference $\phi$ between the voltage and current vectors is zero degrees. Since the power factor is the ratio of real power ($P = VI$) to apparent power ($S = VI$), it remains consistently unity ($1.0$).

Key Formulas: $\cos \phi = \frac{R}{Z}$ — General power factor formula; $\phi = 0^\circ$ — Phase difference in pure DC resistive circuits; $\cos(0^\circ) = 1$ — Power factor value for DC

Key Points: DC circuits have zero frequency, eliminating reactive components.; The phase angle $\phi$ is always zero in a DC circuit.; Unity power factor indicates that the load is purely resistive.; No reactive power ($VAR$) is produced or consumed in a purely DC circuit.

Advantages: No phase shift related power losses.; Simplified power calculations ($P = VI$).

Disadvantages: DC cannot be easily transformed to higher voltages for long-distance transmission.; Switching and interrupting high-voltage DC is more difficult than AC.

Applications: Batteries and Electrochemical cells; Electronic power supplies and DC motors

Additional Info: A power factor of unity is the ideal value in electrical systems, as it indicates maximum efficiency in power delivery.. Option A is incorrect because less than unity implies reactive power existence. Option C is impossible as the maximum value of cosine is 1. Option D would imply a purely reactive circuit, which cannot exist in steady-state DC.

Answer: B is correct — The power factor of a DC circuit is always unity because there is no phase difference between voltage and current.

Exam Tip: Always remember that $PF = \cos \phi$. In any exam question, if the frequency is 0Hz, the phase angle is 0, and the PF is always 1.

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