Verified Solution • 2025–26 Session moderate

QPages 306-313: Q87: HC Verma: Concepts of Physics - Volume 2 Electromagnetic Induction Pages 306-313: Q87 Solution: Two coils A and B have inductances 1.0 H and 2.0 H…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly assume the current ratio equals the inductance ratio or apply a single time constant to both circuits. You must calculate the distinct time constant $\tau = L/R$ for each coil and substitute the specific $t/\tau$ values into the exponential term $1 - e^{-t/\tau}$ for each circuit individually.

Two coils A and B have inductances 1.0 H and 2.0 H respectively. The resistance of each coil is 10 Ω10 \ \Omega. Each coil is connected to an ideal battery of emf 2.0 V at t = 0. Let iAi_A and iBi_B be the currents in the two circuit at time t. Find the ratio iA/iBi_A / i_B at a) t = 100 ms, b) t = 200 ms and c) t = 1 s.

Step-by-Step Verified Solution

**Answer:** (a) 1.6 (b) 1.4 (c) 1.0. **Step-by-Step Explanation:** __A = 1.0/10 = 0.1 s, __B = 2.0/10 = 0.2 s. i = 0.2(1 - e^(-t/_)). (a) t=100 ms: i_A/i_B = (1-e^(-1))/(1-e^(-0.5)) = 1.6. (b) t=200 ms: i_A/i_B = (1-e^(-2))/(1-e^(-1)) = 1.4. (c) t=1 s: both near steady state, ratio � 1.0 [citation:13].

All Questions in this Chapter

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