Question

Two alternating voltage generators produce emfs of the same amplitude $E_0$ but with a phase difference of $\frac{\pi}{3}$ . The resultant e.m.f.is

• A. $E_0\,\sin\left(\omega t+\frac{\pi}{3}\right)$
• B. $E_0\,\sin\left(\omega t+\frac{\pi}{6}\right)$
• C. $\sqrt3 E_0\,\sin\left(\omega t+\frac{\pi}{6}\right)$
• D. $\sqrt3 E_0\,\sin\left(\omega t+\frac{\pi}{2}\right)$

Answer 1

Answer: (C)

$E_1=E_0\,\sin\,\omega\,t;E_2=E_0\,\sin(\omega t +\pi/3)$
$E=E_2+E_1$
$=E_0\,\sin(\omega +\pi /3)+E_0\,\sin \,\omega t$
$=2E_0\,\sin(\omega t +\pi/6)\cos (\pi/6)$
$=\sqrt{3}E_0\,\sin(\omega t+\pi/6)$