An alternating voltage \(v=v_m\sin\omega t\) has an instantaneous value of 110 V when \(\omega t=\pi/6\). The rms value of this voltage is about
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 156 V
The given instantaneous value gives the peak value \( v_m \) of the voltage. The rms value is then \( V=v_m/\sqrt{2} \).
\( \begin{aligned} v_m\sin\frac{\pi}{6} &= 110\ \mathrm{V} \\ v_m &= \frac{110}{0.5} \\ &= 220\ \mathrm{V} \end{aligned} \)
\( \begin{aligned} V &= \frac{v_m}{\sqrt{2}} \\ &= \frac{220}{1.414} \\ &\approx 156\ \mathrm{V} \end{aligned} \)
NCERT (2026-27):
AC Voltage Applied to a Resistor – “… Let this potential difference, also called ac voltage, be given by”
\( v=v_m\sin\omega t \qquad (7.1) \)
“where vm is the amplitude of the oscillating potential difference and ω is its angular frequency.”
AC Voltage Applied to a Resistor – “Similarly, we define the rms voltage or effective voltage by”
\( \displaystyle V=\frac{v_m}{\sqrt{2}} \)\( =0.707\,v_m \qquad (7.8) \)