The magnetic flux through a coil placed in a magnetic field is given by:

$\phi= (5t^3 + 4t^2+2t-5) Wb$. The resistance of the coil is 10 Ω. The induced current through the coil at $t = 2\, s$ is

7.8 A

The correct answer is Option (1) → 7.8 A

Given:

$\phi = (5t^3 + 4t^2 + 2t - 5) \, \text{Wb}$

Resistance of coil = $R = 10 \, \Omega$

Induced emf is given by Faraday’s law:

$E = -\frac{d\phi}{dt}$

Differentiate $\phi$ with respect to $t$:

$\frac{d\phi}{dt} = 15t^2 + 8t + 2$

At $t = 2 \, \text{s}$:

$E = -(15(2)^2 + 8(2) + 2)$

$E = -(60 + 16 + 2) = -78 \, \text{V}$

Induced current:

$I = \frac{|E|}{R} = \frac{78}{10} = 7.8 \, \text{A}$

The induced current through the coil at $t = 2 \, \text{s}$ is $7.8 \, \text{A}$.