Question:
The magnetic flux linked with a coil varies as $\phi = 2.5t^2 + 5t + 7$ (t in s). If the induced electric power at t = 3 s is 2 W, then the power at t = 5 s is:
The magnetic flux linked with a coil varies as $\phi = 2.5t^2 + 5t + 7$ (t in s). If the induced electric power at t = 3 s is 2 W, then the power at t = 5 s is:
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Power in induced circuits depends on square of induced emf.
Updated On: Jun 17, 2026
- 5.5 W
- 3.5 W
- 2.5 W
- 4.5 W
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The Correct Option is D
Solution and Explanation
Step 1: Induced emf is given by Faraday’s law: \[ \mathcal{E} = \frac{d\phi}{dt} \]
Step 2: Differentiate flux: \[ \phi = 2.5t^2 + 5t + 7 \Rightarrow \mathcal{E} = 5t + 5 \]
Step 3: At t = 3 s: \[ \mathcal{E}_3 = 5(3) + 5 = 20V \]
Step 4: Power relation: \[ P = \frac{\mathcal{E}^2}{R} \]
Step 5: Given P = 2 W at t = 3 s: \[ 2 = \frac{20^2}{R} \Rightarrow R = 200\ \Omega \]
Step 6: At t = 5 s: \[ \mathcal{E}_5 = 5(5) + 5 = 30V \]
Step 7: \[ P_5 = \frac{30^2}{200} = \frac{900}{200} = 4.5W \]
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