Concept:In a pure resistor, voltage and current are always in phase. Therefore, their signs are identical at every instant.
Formula / Reaction:$$P(t) = V_0 I_0 \sin^2(\omega t) \ge 0$$
Solution:- During the positive half-cycle: \(v > 0\) and \(i > 0 \implies P(t) = (+)(+) > 0\).
- During the negative half-cycle: \(v < 0\) and \(i < 0 \implies P(t) = (-)(-) > 0\).
- Because \(\sin^2(\omega t) \ge 0\), instantaneous power is always positive or zero, meaning energy is continuously dissipated as heat.
Why other options are incorrect:- Opt_A: Power is zero only at the discrete instant when the waveform crosses zero.
- Opt_C: Negative \(v\) multiplied by negative \(i\) yields positive power.
- Opt_D: Power dissipation in a resistor cannot be negative because resistors do not supply energy back to the source.
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