Question

When the current in a coil decreases from 10 A to \( I \) in a time of 2 seconds, the induced emf in the coil is \( \varepsilon_1 \). When the current in the coil decreases from \( I \) to zero in 4 seconds, the induced emf in the coil is \( \varepsilon_2 \). If the ratio of the induced emfs \( \varepsilon_1 : \varepsilon_2 = 2 : 3 \), then the value of \( I \) is

• A. 3.75 A
• B. 7.5 A
• C. 5 A
• D. 2.5 A

Hint:

Use emf proportionality: \( \varepsilon \propto \frac{dI}{dt} \). Setting up ratios carefully helps avoid algebraic mistakes.

Answer 1

The Correct Option is C

We use Faraday’s law of electromagnetic induction: \[ \varepsilon = -L \frac{dI}{dt} \] Given: \[ \frac{\varepsilon_1}{\varepsilon_2} = \frac{(10 - I)/2}{I/4} = \frac{4(10 - I)}{2I} = \frac{2(10 - I)}{I} \] Set the ratio to 2:3: \[ \frac{2(10 - I)}{I} = \frac{2}{3} \Rightarrow \frac{10 - I}{I} = \frac{1}{3} \Rightarrow 3(10 - I) = I \Rightarrow 30 - 3I = I \Rightarrow 4I = 30 \Rightarrow I = 7.5 \] Wait — answer marked as **5 A**. Let's recheck: Assume the ratio is: \[ \frac{(10 - I)/2}{I/4} = \frac{4(10 - I)}{2I} = \frac{2(10 - I)}{I} \Rightarrow \frac{2(10 - I)}{I} = \frac{2}{3} \Rightarrow \frac{10 - I}{I} = \frac{1}{3} \Rightarrow 10 - I = \frac{I}{3} \Rightarrow 30 - 3I = I \Rightarrow 4I = 30 \Rightarrow I = 7.5 \text{ A} \] **So the correct answer should be (2) 7.5 A,** but the image says (3) 5 A. **This indicates an error in the marked key. Please confirm the correct answer.**