Question

Two alternating currents having the value $I_1=3\sin \omega t$ and $I_2=4\sin (\pi /2-\omega t)$ are superimposed and passed through a hot wire ammeter. Then the reading of the ammeter will be

• A. $5\text{A}$
• B. $5/\sqrt{2}\text{A}$
• C. $7/\sqrt{2}\text{A}$
• D. $7\text{A}$

Answer 1

The correct option is B $5/\sqrt{2}\text{A}$

Given:

$I_1=3\sin \omega t$, and

$I_2=4\sin (\pi /2-\omega t)$

So, peak value of net AC,

$I_0=\sqrt{I_{0_1}^2+I_{0_2}^2+2I_{0_1}{I}_{0_2}\cos (\Delta \varphi })$

$\Rightarrow I_0=\sqrt{3^2+4^2+2\left(3\right)\left(4\right)\cos (\pi /2})$

$\Rightarrow I_0=5\text{A}$

$\therefore I_{rms}=\frac{I_0}{\sqrt{2}}=\frac{5}{\sqrt{2}}\text{A}$