The magnetic flux phi (in weber) linked with | vedclass

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(C) According to Faraday's law of electromagnetic induction,the induced electromotive force $(EMF)$ $\varepsilon$ is given by $\varepsilon = -\frac{d\

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$2$

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(C) According to Faraday's law of electromagnetic induction,the induced electromotive force $(EMF)$ $\varepsilon$ is given by $\varepsilon = -\frac{d\phi}{dt}$.Given $\phi = 5t^2 - 36t + 1$.Differentiating with respect to $t$,we get $\frac{d\phi}{dt} = 10t - 36$.Thus,$\varepsilon = -(10t - 36) = 36 - 10t$.At $t = 2 \ s$,the induced $EMF$ is $\varepsilon = 36 - 10(2) = 36 - 20 = 16 \ V$.The induced current $i$ is given by $i = \frac{|\varepsilon|}{R}$,where $R = 8 \ \Omega$.Therefore,$i = \frac{16 \ V}{8 \ \Omega} = 2 \ A$.

The magnetic flux $\phi$ (in weber) linked with a closed circuit of resistance $8 \ \Omega$ varies with time (in seconds) as $\phi = 5t^2 - 36t + 1$. The induced current in the circuit at $t = 2 \ s$ is . . . . . . $A$.

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