Question

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

Answer 1

The emf $\varepsilon$ induced in the circuit is given by Faraday’s law:

$\varepsilon = -\frac{d\Phi}{dt}.$

Calculate $\frac{d\Phi}{dt}$:

$\frac{d\Phi}{dt} = 10t - 36.$

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

$\varepsilon = -(10 \cdot 2 - 36) = -(-16) = 16 \, \text{V}.$

The induced current $i$ in the circuit is:

$i = \frac{\varepsilon}{R} = \frac{16}{8} = 2 \, \text{A}.$

Thus, the induced current at $t = 2 \, \text{s}$ is:

$2 \, \text{A}.$