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QPages 306-313: Q71: HC Verma: Concepts of Physics - Volume 2 Electromagnetic Induction Pages 306-313: Q71 Solution: A coil having inductance 2.0 H and resistance is connected to a …
⚠️ Common Exam Traps & Conceptual Pitfalls
Students often swap L and R when forming the time constant, using τ = R/L instead of the correct τ = L/R, which leads to an incorrect exponent in i(t)= (E/R)(1‑e^{-t/τ}). Always compute τ as L divided by R and then use the instantaneous current, not the steady‑state value, when evaluating magnetic energy $U=\tfrac12 L i^2$.
A coil having inductance 2.0 H and resistance is connected to a battery of emf 4.0 V. Find a) the current at the instant 0.20 s after the connection is made and b) the magnetic field energy at this instant.
Step-by-Step Verified Solution
**Answer:** (a) i = 0.17 A (b) U = 0.029 J.
**Step-by-Step Explanation:**
_ = L/R = 2.0/20 = 0.1 s. i = 0.2(1 - e^(-0.2/0.1)) = 0.2(1 - e^(-2)) = 0.173 A. U = _Li_ = 0.5 _ 2.0 _ (0.173)_ = 0.030 J [citation:4].
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