A loop circuit is placed in uniform magnetic field B and flux through the loop is given by - -4t- Find the power supplied to the 6 V battery-

From Faraday's law of induction, ℰ=| d ϕdt|=| ddt(4t)| = 4 V nbsp; Because the flux is increasing into the paper, so the current will be in anticlockwise di ...

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Standard XII

Physics

Dependence of Resistance on Temperature

A loop circui...

Question

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

5 W

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3 W

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2 W

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6 W

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Solution

The correct option is D $6 W$
From Faraday's law of induction,

$E = ∣ ∣ ∣ - \frac{d ϕ}{d t} ∣ ∣ ∣ = ∣ ∣ ∣ - \frac{d}{d t} (4 t) ∣ ∣ ∣ = 4 V$

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

Hence, the total emf is $E_{t o t a l} = 8 + 4 - 6 = 6 V$ in the anticlockwise direction.

As, $I = \frac{E_{t o t a l}}{R}$

where, $R = 4 + 2 = 6 Ω$

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

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

Power, $P = V I = 6 (1) = 6 W$

Hence, option $(A)$ is the correct answer.

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A loop (circuit) is placed in uniform magnetic field →B and flux through the loop is given by ϕ=4t. Find the power supplied to the 6 V battery.

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