Question

In a coil of resistance \(100\,\Omega\), a current is induced by changing the magnetic flux through it. The current versus time variation is as shown. The magnitude of change in flux through the coil is

• A. \(250\,\text{Wb}\)
• B. \(275\,\text{Wb}\)
• C. \(20\,\text{Wb}\)
• D. \(225\,\text{Wb}\)

Hint:

For current induced in a coil: \[ e=iR \] \[ \Delta\Phi=\int e\,dt = R\int i\,dt \] So, \[ \text{Change in Flux} = R \times \text{(Area under }i\text{-}t\text{ graph)} \] This shortcut is very useful in electromagnetic induction MCQs.

Answer 1

The Correct Option is A

Step 1:Calculate the area under the \(i-t\) graph. The graph is a triangle with \[ \text{height}=10\,\text{A} \] and \[ \text{base}=0.5\,\text{s} \] Therefore, \[ \text{Area} = \frac{1}{2}\times 10\times 0.5 \] \[ =2.5\ \text{A s} \]

Step 2: Calculate the change in magnetic flux. Given, \[ R=100\,\Omega \] Thus, \[ \Delta\Phi = R\times \text{Area} \] \[ = 100\times 2.5 \] \[ =250\,\text{Wb} \]

Step 3: State the answer. \[ { \Delta\Phi=250\,\text{Wb} } \] Hence, the correct option is \[ {(A)} \]