An ac voltage \( E=220\sqrt{2}\cos(50\pi t) \) volt drives a current in a circuit. How many times in one second does the current become zero?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 50
The current driven by a sinusoidal voltage has the same frequency as the source. Whatever its phase relative to the voltage, a sinusoidal current passes through zero twice in every cycle.
From \( E=220\sqrt{2}\cos(50\pi t) \), the angular frequency is \( \omega=50\pi\,\mathrm{rad\,s^{-1}} \). The frequency is:
\( \begin{aligned} \nu &= \frac{\omega}{2\pi} \\ &= \frac{50\pi}{2\pi}\,\mathrm{Hz} \\ &= 25\,\mathrm{Hz} \end{aligned} \)
In one second there are 25 cycles. The current is zero twice in each cycle, so the number of zeros in one second is:
\( \begin{aligned} N &= 2\nu\times1\,\mathrm{s} \\ &= 2\times25 \\ &= 50 \end{aligned} \)