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The magnetic flux through a loop of resistance $10 \Omega$ varying according to the relation $\phi=6 \mathrm{t}^2+7 \mathrm{t}+1$, where $\phi$ is in milliweber, time is in second at time $t=1 \mathrm{~s}$ the induced e.m.f. is
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$19\ mV$
Given $\mathrm{R}=10 \Omega, \phi=6 \mathrm{t}^2+7 \mathrm{t}+1 \mathrm{mWb}, \mathrm{t}=1 \mathrm{~s}$
From $\mathrm{e}=\frac{\mathrm{d} \phi}{\mathrm{dt}}$,
$e=\frac{d}{d t}\left(6 t^2+7 t+1\right)=12 t+7$
Put $\mathrm{t}=1$ in the above equation,
$\therefore \quad \mathrm{e}=19 \mathrm{mV}$
From $\mathrm{e}=\frac{\mathrm{d} \phi}{\mathrm{dt}}$,
$e=\frac{d}{d t}\left(6 t^2+7 t+1\right)=12 t+7$
Put $\mathrm{t}=1$ in the above equation,
$\therefore \quad \mathrm{e}=19 \mathrm{mV}$
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