Question

A loop (circuit) is placed in uniform magnetic field $\overrightarrow{B}$ and flux through the loop is given by $\varphi =4t$. Find the power supplied to the $6\text{V}$ battery.

• A. $5\text{W}$
• B. $3\text{W}$
• C. $2\text{W}$
• D. $6\text{W}$

Answer 1

The correct option is D $6\text{W}$

From Faraday's law of induction,

$E=|-\frac{d\varphi }{dt}|=|-\frac{d}{dt}\left(4t\right)|=4\text{V}$

Because the flux is increasing into the paper, so the current will be in anticlockwise direction.

Hence, the total emf is $E_{total}=8+4-6=6\text{V}$ in the anticlockwise direction.

As, $I=\frac{E_{total}}{R}$

where, $R=4+2=6\Omega$

So, $I=\frac{6}{6}=1\text{A}$

Current is pumped into the battery, so power is supplied to the battery and that will be,

Power, $P=VI=6\left(1\right)=6\text{W}$

Hence, option $\left(\text{A}\right)$ is the correct answer.