Q. 220 V, 50 Hz AC is applied to a resistor. The instantaneous value of voltage is
A) $220\sqrt{2}\sin{100\pi t}$
B) $220\sin{100\pi t}$
C) $220\sqrt{2}\sin{50\pi t}$
D) $220\sin{50\pi t}$
Explanation
(a) Here, $V_{rms} = 220V,\ v = 50\ Hz$
Peak value of voltage $V_{0} = \sqrt{2}\ V_{rms} = 220\sqrt{2}\ V$
$\therefore$The instantaneous value of voltage is
$V = V_{0}\sin{2\pi vt = 220}\sqrt{2}\sin{2\pi \times 50t}$
$\ \ \ \ = 220\sqrt{2}\sin{100\pi t}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.