WAEC 2012 Physics · Question 35

An inductor is connected to a 24V, 50Hz mains supply. If the current through the inductor is 1.5A, calculate…

Question

An inductor is connected to a 24V, 50Hz mains supply. If the current through the inductor is 1.5A, calculate the inductance of the inductor ( $\pi = \frac{22}{7}$ )

A.8.0 x 102H
B.7.5 x 10oH
C.1.6 x 10oH
D.5.1 x 10-2H

Answer: D. 5.1 x 10-2H

Explanation written with AI and checked against the answer key

Analyze the question: An ideal inductor is on an AC supply. We are given V = 24 V, f = 50 Hz and I = 1.5 A, and we need the inductance L. Concept: An inductor opposes AC with inductive reactance: X_L = 2πfL and by an Ohm's-law-type relation: X_L = V / I Solution: Step 1: Find the reactance. X_L = V / I = 24 / 1.5 = 16 Ω Step 2: Equate this to 2πfL and solve for L. L = X_L / (2πf) With π = 22/7: 2πf = 2 × (22/7) × 50 = 2200/7 ≈ 314.29 L = 16 / 314.29 = (16 × 7) / 2200 = 112 / 2200 ≈ 0.0509 H L ≈ 5.1 × 10⁻² H Matching the options: The options are garbled in the question (the exponents appear as "102" and "10o"), but option D, 5.1 × 10⁻² H, matches our result. Tip: For inductor questions, find X_L = V/I first, then use L = X_L/(2πf). With π = 22/7 and f = 50 Hz, 2πf is about 314, so a reactance of a few tens of ohms always gives an inductance of a few hundredths of a henry. Checking the order of magnitude like this helps you spot the right option quickly.

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