Magnetic flux (in weber) in a closed circuit of resistance $20\,\Omega$ varies with time $t(s)$ as $\phi = 8t^2 - 9t + 5$. The magnitude of the induced current at $t = 0.25$ s will be ______ mA

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Electromagnetic Induction

Magnetic flux (in weber) in a closed circuit of resistance

20 Ω

varies with time

t (s)

ϕ = 8 t^{2} - 9 t + 5

. The magnitude of the induced current at

t = 0.25

s will be ______ mA

Answer: 250

Solution

By Faraday's law, the induced emf is:

ε = - \frac{d ϕ}{d t}

Given

ϕ = 8 t^{2} - 9 t + 5

\frac{d ϕ}{d t} = 16 t - 9

ε = - (16 t - 9)

t = 0.25

ε = - (16 \times 0.25 - 9) = - (4 - 9) = 5 V

The magnitude of induced current:

I = \frac{∣ ε ∣}{R} = \frac{5}{20} = 0.25 A = 250 mA

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Integer answer

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