Power And Power Factor

Average power in an AC circuit is delivered only by the in-phase component of current, so it equals the product of RMS voltage, RMS current and the power factor (\cos\phi), giving (P_{avg} = V_{rms} I_{rms}\cos\phi). The reactive part of the current carries energy back and forth without net dissipation. Substituting (V_{rms} = 100) V, (I_{rms} = 4) A and (\cos 60^\circ = 0.5) yields (P_{avg} = 100 \times 4 \times 0.5 = 200) W. The option 400 W is the apparent power (V_{rms}I_{rms}), which ignores the phase factor. The option 100 W mistakenly applies (\cos\phi) twice. The option 346 W uses (\sin 60^\circ), which would give the wattless reactive power instead. This is the NCERT distinction between true, apparent and reactive power, where true power is measured in watts, apparent power in volt-amperes, and reactive power in volt-amperes reactive. Improving the power factor toward unity, for instance by adding a correcting capacitor to an inductive load, reduces the current needed to deliver the same useful power and so cuts transmission losses. A plausibility check confirms the true power must be smaller than the apparent power whenever a phase difference exists, and is exactly half here because the power factor is 0.5, consistent with a moderately reactive load drawing substantial wattless current.