The magnetic flux (in weber) in a closed circuit of resistance $20 \Omega$ varies with time $t$ second…

The magnetic flux (in weber) in a closed circuit of resistance $20 \Omega$ varies with time $t$ second according to equation $\phi=5 t^2-6 t+9$. The magnitude of induced current at $t=0.2$ second is
  1. 0.08 A
  2. 1 A
  3. 0.2 A
  4. 0.4 A

Solution

$\begin{aligned} & \phi=5 \mathrm{t}^2-6 \mathrm{t}+9 \\ & \mathrm{e}=-\frac{\mathrm{d} \phi}{\mathrm{dt}}=-(10 \mathrm{t}-6) \\ & \mathrm{At} \mathrm{~t}=0.2 \mathrm{~s},|\mathrm{e}|=4 \mathrm{~V} \\ & \mathrm{i}=\frac{|\mathrm{e}|}{\mathrm{R}}=\frac{4}{20}=0.2 \mathrm{~A}\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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