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The magnetic flux through each turn of a coil having 200 turns is given as $\left(t^2-2 t\right) \times 10^{-3}$ Wb , where $t$ is in second. The emf induced in the coil at $t=3 \mathrm{~s}$ is
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0.8 V
Given magnetic flux
$\phi=\left(t^2-2 t\right) \times 10^{-3}$
On differentiating with recpect to time $t$
$\frac{d \phi}{d t}=(2 t-2) \times 10^{-3}$
At time $\quad t=3 \mathrm{~s}$
$\begin{aligned}\left|\frac{d \phi}{d t}\right|_{t=3 \mathrm{~s}} & =(2 \times 3-2) \times 10^{-3} \\ & =4 \times 10^{-3} \mathrm{~Wb} \mathrm{~s}^{-1} \\ \text { Now, }|e| & =N\left|\frac{d \phi}{d t}\right| \\ & =200 \times 4 \times 10^{-3} \\ & =800 \times 10^{-3}=0.8 \mathrm{~V}\end{aligned}$
$\phi=\left(t^2-2 t\right) \times 10^{-3}$
On differentiating with recpect to time $t$
$\frac{d \phi}{d t}=(2 t-2) \times 10^{-3}$
At time $\quad t=3 \mathrm{~s}$
$\begin{aligned}\left|\frac{d \phi}{d t}\right|_{t=3 \mathrm{~s}} & =(2 \times 3-2) \times 10^{-3} \\ & =4 \times 10^{-3} \mathrm{~Wb} \mathrm{~s}^{-1} \\ \text { Now, }|e| & =N\left|\frac{d \phi}{d t}\right| \\ & =200 \times 4 \times 10^{-3} \\ & =800 \times 10^{-3}=0.8 \mathrm{~V}\end{aligned}$
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