The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\phi= \left(5 t^{3}+4 t^{2}+2 t-5\right)$ Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at $t=2 \sec$ will be:

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Electromagnetic Induction

The magnetic flux through a coil perpendicular to its plane is varying according to the relation

ϕ = (5 t^{3} + 4 t^{2} + 2 t - 5)

Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at

t = 2 sec

will be:

(A)15.6 A✓ Correct
(B)16.6 A
(C)17.6 A
(D)18.6 A

Answer: (A)

Solution

Faraday's law gives the induced emf as the magnitude of the rate of change of flux,

∣ ε ∣ = \frac{d ϕ}{d t}

. Differentiating

ϕ = 5 t^{3} + 4 t^{2} + 2 t - 5

gives

\frac{d ϕ}{d t} = 15 t^{2} + 8 t + 2

, and at

t = 2 s

this equals

15 (4) + 8 (2) + 2 = 60 + 16 + 2 = 78 V

. The current then follows from Ohm's law for the coil,

I = \frac{∣ ε ∣}{R} = \frac{78}{5} = 15.6 A

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Single correct option

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