When voltage and current are in phase, angle between them is

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Explanation: When voltage and current are in phase, they reach their peak and zero values at the same time, resulting in a phase difference of 0 radians or 0 degrees. This condition typically occurs in purely resistive circuits where the impedance is purely real.

Working Principle: In an A.C. circuit, the phase angle $\phi$ represents the time displacement between the voltage waveform $v(t) = V_m \sin(\omega t)$ and the current waveform $i(t) = I_m \sin(\omega t - \phi)$. When $\phi = 0$, the impedance $Z$ of the circuit consists only of resistance $R$, as there are no inductive or capacitive components to cause a phase shift. Consequently, the power factor, defined as $\cos(\phi)$, reaches its maximum value of unity (1).

Key Formulas: $P = VI \cos(\phi)$ — Power in an AC circuit where $\phi = 0$ results in $P = VI$; $Z = R + j(X_L - X_C)$ — General impedance formula; for $\phi = 0$, $(X_L - X_C) = 0$

Key Points: Phase difference ($\phi$) is the angular difference between voltage and current phasors.; A phase angle of $0^\circ$ indicates a unity power factor.; This occurs in pure resistive loads like incandescent bulbs or heaters.

Advantages: Maximum active power transfer for a given voltage and current; No reactive power consumption ($Q = 0$)

Disadvantages: Limited to purely resistive components; Rarely achieved in industrial power systems containing motors or transformers

Applications: Electrical heating elements; Incandescent lighting circuits; Reference standard for phase measurement

Additional Info: The phase difference is measured in degrees ($^\circ$) or radians.. Options B, C, and D represent lagging or leading phase angles which occur in reactive circuits.

Answer: A is correct — The phase difference between voltage and current in a purely resistive circuit is $0^\circ$.

Exam Tip: Always remember that inductive circuits cause current to lag ($90^\circ$) while capacitive circuits cause current to lead ($90^\circ$); resistive circuits are the only ones keeping them in phase.

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