The power for a purely resistive circuit is zero, when?

Question

Examoogle · Accepted Answer

Either current or voltage is zero

Explanation: In a purely resistive circuit, the instantaneous power is defined by the product of voltage and current. Since power is given by the relation $P = VI$, if either the instantaneous voltage $v(t)$ or the instantaneous current $i(t)$ becomes zero, the product becomes zero.

Working Principle: In an AC resistive circuit, both voltage and current follow a sinusoidal waveform: $v(t) = V_m \sin(\omega t)$ and $i(t) = I_m \sin(\omega t)$. At points where $\omega t = 0, \pi, 2\pi, ...$ etc., the sine function is zero, forcing either $v(t)$ or $i(t)$ to zero. Consequently, the power $p(t) = v(t)i(t) = V_m I_m \sin^2(\omega t)$ also hits zero at these specific time intervals.

Key Formulas: $P = VI$ — Basic power relationship in DC or instantaneous AC; $p(t) = V_m I_m \sin^2(\omega t)$ — Instantaneous power in a purely resistive AC circuit

Key Points: Instantaneous power is zero whenever the load terminal voltage or the branch current passes through zero.; For purely resistive circuits, voltage and current are in phase.; The average power is non-zero, but instantaneous power cycles between zero and maximum value.

Advantages: Allows for easy calculation of power using Ohm's Law.; No phase shift means unity power factor.

Disadvantages: Does not account for reactive components like inductors or capacitors.; Instantaneous power fluctuates and is not constant in AC.

Applications: Electric heaters; Incandescent bulbs

Additional Info: The condition where current is zero (Option A) or voltage is zero (Option B) are specific subsets of the general condition.. Option D is the most comprehensive answer as it covers all scenarios where the product of the two variables results in zero.

Answer: D is correct — The power in a resistive circuit is zero if and only if either the instantaneous voltage or the instantaneous current is zero, as power is the product of these two quantities.

Exam Tip: Remember that in AC circuits, 'Power is zero' usually refers to instantaneous power. Average power in a resistive circuit is $I^2R$, which is only zero if current is zero.

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