Concept:A symmetrical sinusoidal alternating current completes one full cycle consisting of equal and opposite positive and negative half-cycles.
Formula / Reaction:$$I_{\text{avg}} = \frac{1}{T} \int_{0}^{T} I_0 \sin(\omega t)\, dt = 0$$
Solution:- During the first half-cycle \((0 \to T/2)\), the area under the current waveform is positive: \(+I_{\text{avg(half)}} = +\frac{2I_0}{\pi}\).
- During the second half-cycle \((T/2 \to T)\), the area under the current waveform is negative: \(-I_{\text{avg(half)}} = -\frac{2I_0}{\pi}\).
- Summing these values over a full period gives an exact net sum of zero.
Why other options are incorrect:- Opt_B: The current is continuously varying with time, not constant.
- Opt_C: The average over a full cycle cannot be positive because the negative half-cycle completely cancels the positive half-cycle.
- Opt_D: Maximum value corresponds to peak current \(I_0\), not the cycle average.
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