An alternating current \( i=2\sin(100\pi t) \) A flows through a wire. The net charge that crosses a cross-section of the wire between \( t=0 \) and \( t=0.02\,\mathrm{s} \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → zero
The net charge carried across a section in a time interval is the average current over that interval multiplied by the time. A sinusoidal current is positive for one half of each cycle and negative for the other half. So over one complete cycle its average is zero. The charge that flows one way in the first half cycle flows back in the second half.
The time period of the given current is:
\( \begin{aligned} T &= \frac{2\pi}{\omega} \\ &= \frac{2\pi}{100\pi\,\mathrm{s^{-1}}} \\ &= 0.02\,\mathrm{s} \end{aligned} \)
So the interval from \( t=0 \) to \( t=0.02\,\mathrm{s} \) is one complete cycle. The net charge is:
\( \begin{aligned} q &= \bar{i}\times T \\ &= 0\times0.02\,\mathrm{s} \\ &= 0 \end{aligned} \)
NCERT (2026-27):
AC Voltage Applied to a Resistor – “We see that, like the applied voltage, the current varies sinusoidally and has corresponding positive and negative values during each cycle. Thus, the sum of the instantaneous current values over one complete cycle is zero, and the average current is zero.”