Purely Resistive Ac Circuit

Question

When an alternating voltage is applied across a pure resistor, what is the phase relationship between the instantaneous current through the resistor and the instantaneous voltage across it?

RankGuru · Accepted Answer

As stated in NCERT Class 12, Chapter 7 (Alternating Current), for a purely resistive AC circuit Ohm's law applies at every instant, so $i = \frac{v}{R} = \frac{V_0 \sin\omega t}{R}$, which shows the current follows the same sinusoidal function as the voltage with no time delay. Therefore the current is exactly in phase with the applied voltage, and both reach their peaks and zeros simultaneously. The option claiming a ninety-degree lag describes a purely inductive circuit, not a resistive one. The option claiming a ninety-degree lead describes a purely capacitive circuit. The option stating a forty-five-degree lag would require equal resistance and reactance, which is absent here since there is no inductor or capacitor. A plausibility check reinforces this: a resistor stores no energy, so there is no mechanism to shift the current in time relative to the voltage, and consequently the power factor is exactly one, meaning all supplied power is dissipated as heat.

Purely Resistive Ac Circuit

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