Question

Two alternating voltage generators produce EMFs of the same amplitude $E_0$​ but with a phase difference of $\pi /3$. The magnitude of resultant EMF is

• A. $\sqrt{5}{E}_0$
• B. $E_0$
• C. $\sqrt{2}{E}_0$
• D. $\sqrt{3}{E}_0$

Answer 1

The correct option is D $\sqrt{3}{E}_0$

The magnitude of resultant EMF,

$E_0=\sqrt{E_{0_1}^2+E_{0_2}^2+2E_{0_1}{E}_{0_2}\cos (\Delta \varphi })$

$\Rightarrow E_0=\sqrt{E_0^2+E_0^2+2\left(E_0\right)\left(E_0\right)\cos (\pi /3})$

$\Rightarrow E_0=\sqrt{3}{E}_0$