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The circuit PQRS shown in the figure consists of two resistances $R_{1} & R_{2}$ connected to two ideal voltmeters $V_{1} & V_{2} .$ A time varying uniform magnetic field B(t) exists in a circular region of radius a and it is directed into the plane of the figure. $B (t) = B_{0} t$ where $B_{0}$ is a positive constant having proper dimensions and t is the time.

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The reading of $V_{1}$ is $\frac{π a^{2} B_{0} R_{1}}{R_{1} + R_{2}}$

Readings of two voltmeters $V_{1} and V_{2}$ are same.

The magnitude of emf induced in the circuit PQRS is $π a^{2} B_{0}$

The reading of $V_{2}$ is $\frac{π a^{2} B_{0} R_{1}}{R_{1} + R_{2}}$

answer is A, B.

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Detailed Solution

$ϕ = π a^{2} B_{0} t ε = - \frac{d ϕ}{d t}$

$\to ε = π a^{2} B_{0} (induced emf)$ $i = \frac{π a^{2} B_{0}}{R_{1} + R_{2}} (induced current)$ $I n l o o p A B G H,$

on applying loop law, we get $v_{1} = i R_{1} = \frac{π a^{2} B_{0} R_{1}}{R_{1} + R_{2}}$

$In similarly Δ V_{2} = i R_{2} = \frac{π a^{2} B_{0} R_{2}}{R_{1} + R_{2}}$

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