(C) The magnetic flux through the coil is given by $\phi = 2t^2 + 3t - 2$. According to Faraday's law of electromagnetic induction,the induced electro

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(C) The magnetic flux through the coil is given by $\phi = 2t^2 + 3t - 2$. According to Faraday's law of electromagnetic induction,the induced electromotive force $(e)$ is given by $e = -\frac{d\phi}{dt}$. $e = -\frac{d}{dt}(2t^2 + 3t - 2) = -(4t + 3)$. The magnitude of the induced $EMF$ is $|e| = 4t + 3$. At time $t = 3 \ s$,the induced $EMF$ is $|e| = 4(3) + 3 = 12 + 3 = 15 \ V$. The induced current in the coil is $I = \frac{|e|}{R} = \frac{15 \ V}{7.5 \ \Omega} = 2 \ A$. The induced power $(P)$ in the coil is given by $P = I^2 R = (2)^2 \times 7.5 = 4 \times 7.5 = 30 \ W$.

Class 12 Physics Electromagnetic Induction Mix Examples-Electromagnetic Induction

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The plane of a circular coil of resistance $7.5 \ \Omega$ is placed perpendicular to a uniform magnetic field. The flux $\phi$ (in weber) through the coil varies with time $t$ (in second) as $\phi = 2t^2 + 3t - 2$. The induced power in the coil at time $t = 3 \ s$ is (in $W$)

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$7.5$
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$15$
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$30$
D
$20$

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The magnetic field in the region shown in the figure increases at a constant rate of $20 \, mT/sec$. Each side of the square loop $ABCD$ has a length of $1 \, cm$ and a resistance of $4 \, \Omega$. Find the current in the wire $AB$ if the switch $S$ is closed.

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The bob of a simple pendulum is replaced by a magnet. The oscillations are set along the length of the magnet. $A$ copper coil is added so that one pole of the magnet passes in and out of the coil. The coil is short-circuited. Then which one of the following happens?

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An inductance of $2\,H$ carries a current of $2\,A$. To prevent sparking when the circuit is broken,a capacitor of $4\,\mu F$ is connected across the inductance. The voltage rating of the capacitor is of the order of

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The network shown in the figure is part of a complete circuit. If at a certain instant the current $i$ is $5 \, A$ and is decreasing at the rate of $10^3 \, A/s$, then $V_B - V_A$ is: (in $ \, V$)

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The plane of a circular coil of resistance $7.5 \ \Omega$ is placed perpendicular to a uniform magnetic field. The flux $\phi$ (in weber) through the coil varies with time $t$ (in second) as $\phi = 2t^2 + 3t - 2$. The induced power in the coil at time $t = 3 \ s$ is (in $W$)

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The magnetic field in the region shown in the figure increases at a constant rate of $20 \, mT/sec$. Each side of the square loop $ABCD$ has a length of $1 \, cm$ and a resistance of $4 \, \Omega$. Find the current in the wire $AB$ if the switch $S$ is closed.

The bob of a simple pendulum is replaced by a magnet. The oscillations are set along the length of the magnet. $A$ copper coil is added so that one pole of the magnet passes in and out of the coil. The coil is short-circuited. Then which one of the following happens?

$A$ small bar magnet of dipole moment $M$ is moving with speed $v$ along the $x$-direction towards a small closed circular conducting loop of radius $a$ with its centre $O$ at $x=0$ (see figure). Assume $x >> a$ and the coil has a resistance $R$. Which of the following statement$(s)$ is/are true?

An inductance of $2\,H$ carries a current of $2\,A$. To prevent sparking when the circuit is broken,a capacitor of $4\,\mu F$ is connected across the inductance. The voltage rating of the capacitor is of the order of

The network shown in the figure is part of a complete circuit. If at a certain instant the current $i$ is $5 \, A$ and is decreasing at the rate of $10^3 \, A/s$, then $V_B - V_A$ is: (in $ \, V$)

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