The plane of a circular coil of resistance 7. | vedclass

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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 electro

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$30$

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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 $P = I^2 R = (2)^2 	imes 7.5 = 4 	imes 7.5 = 30 \ W$.

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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