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Q.

Magnetic flux through a coil perpendicular to its plane is varying according to the relation $ϕ = 8 t^{2} - 9 t + 5$ weber. The magnitude of the induced current at $t = 0.25 s$ will be______mA.(resistance of the coil is 20 $Ω$ )

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answer is 250.

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Detailed Solution

We have magnetic flux given as, $ϕ = 8 t^{2} - 9 t + 5$
Induced emf $= - \frac{d ϕ}{d t} = - (16 t - 9)$
At t= $t = 0.25 s$
Emf= $[(16 \times 0.25) - 9] = 5 V$
So, current $= \frac{E m f}{Re s i s \tan c e} = \frac{5 V}{20 Ω}$
$\Rightarrow \frac{1}{4} A = \frac{1000}{4} m A = 250 m A$

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