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

Correct Answer: 2

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:

\[ 2 \, \text{A}. \]