The electric mains in our homes is 220 V, 50 Hz. The instantaneous voltage can be written as
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 311\sin(100\pi t) \)
The mains rating of 220 V is an rms value. The instantaneous voltage \( v=v_m\sin\omega t \) needs the peak value \( v_m=\sqrt{2}\,V \) and the angular frequency \( \omega=2\pi\nu \).
The peak voltage is:
\( \begin{aligned} v_m &= \sqrt{2}\,V \\ &= 1.414\times220\,\mathrm{V} \\ &\approx 311\,\mathrm{V} \end{aligned} \)
The angular frequency is:
\( \begin{aligned} \omega &= 2\pi\nu \\ &= 2\pi\times50\,\mathrm{Hz} \\ &= 100\pi\,\mathrm{rad\,s^{-1}} \end{aligned} \)
Therefore, \( v=311\sin(100\pi t) \) volt.
NCERT (2026-27):
AC Voltage Applied to a Resistor
