The magnetic flux $\phi$ (in weber) linked with a closed circuit of resistance $8 \Omega$ varies with time (in seconds) as $\phi=5 t^{2}-36 t+1$. The induced current in the circuit at $\mathrm{t}=2 \mathrm{~s}$ is ______ A.

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Electromagnetic Induction

The magnetic flux

ϕ

(in weber) linked with a closed circuit of resistance

8Ω

varies with time (in seconds) as

ϕ = 5 t^{2} - 36 t + 1

. The induced current in the circuit at

t = 2 s

is ______ A.

Answer: 2

Solution

Induced emf is

ε = - \frac{d ϕ}{d t}

. With

ϕ = 5 t^{2} - 36 t + 1

\frac{d ϕ}{d t} = 10 t - 36

t = 2

\frac{d ϕ}{d t} = 20 - 36 = - 16

, so

∣ ε ∣ = 16

V.

Induced current

i = \frac{ε}{R} = \frac{16}{8} = 2 A

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Integer answer

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