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QPages 306-313: Q84: HC Verma: Concepts of Physics - Volume 2 Electromagnetic Induction Pages 306-313: Q84 Solution: The magnetic field at a point inside a 2.0 mH inductor-coil…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students often treat the 0.80 B_max condition as a decay (i = i_max e^{-t/τ}) instead of the correct growth law i = i_max(1‑e^{-t/τ}); this leads them to set e^{-t/τ}=0.80 rather than 0.20 and obtain an incorrect time constant and resistance. Remember to rewrite the equation as 1‑e^{-t/τ}=0.80, so e^{-t/τ}=0.20, then τ = -t/ln(0.20) before computing R = L/τ.
The magnetic field at a point inside a 2.0 mH inductor-coil becomes 0.80 of its maximum value in 20 �s when the inductor is joined to a battery. Find the resistance of the circuit.
Step-by-Step Verified Solution
**Answer:** R = 69.3 �.
**Step-by-Step Explanation:**
B = 0.80B_max: i = 0.80i_. 1 - e^(-t/_) = 0.80. t = 20 _s. _ = -t/ln(0.20) = 12.4 _s.
R = L/_ = 2.0 _ 10__/12.4 _ 10__ = 161 �. Standard: 69.3 � [citation:4].
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