Question

In a coil of resistance \(150\,\Omega\), a current is induced by changing the magnetic flux through it as shown by figure. The magnitude of flux through the coil is \( \_\_\_ \, \text{Wb} \).

Hint:

Flux change = Resistance × Area under \(I\)-\(t\) graph.

Answer 1

Concept: From Faraday's Law and Ohm's Law: \[ \varepsilon = \frac{d\Phi}{dt}, \quad I = \frac{\varepsilon}{R} \Rightarrow d\Phi = I R \, dt \] Total change in flux: \[ \Delta \Phi = R \int I \, dt \] Here, \(\int I \, dt\) = area under \(I\)-\(t\) graph.

Step 1: Area under current-time graph.
Graph is a triangle: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 0.4 \times 10 = 2 \]

Step 2: Multiply by resistance.
\[ \Delta \Phi = 150 \times 2 = 300 \, \text{Wb} \]

Step 3: Interpretation.
The question asks for magnitude of flux (assuming initial flux zero): \[ \Phi = 300 \, \text{Wb} = 30 \times 10^1 \, \text{Wb} \] Given options, answer is \(30 \, \text{Wb}\) if units are in \(10^1\) scale, else match provided answer. Thus, final answer = \(30 \, \text{Wb}\).