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WAEC 2021 Physics · Question 42

The inductive reactance in a circuit of frequency 100Hz is 1ohms. Calculate the inductance of the inductor[π = 3.14]

Options

  1. A.2.00 x 10−3_{-3}H
  2. B.1.59 x 10−3_{-3}H
  3. C.1.09 x 10−3_{-3}H
  4. D.6.28x 10−3_{-3}H

Answer: B. 1.59 x 10−3_{-3}H

Explanation written with AI and checked against the answer key

Analyze the question: We are given the inductive reactance X_L = 1 Ω and frequency f = 100 Hz. We need to find the inductance L. Concept: Inductive reactance is the opposition an inductor offers to alternating current: X_L = 2πfL so L = X_L / (2πf) Solution: L = 1 / (2 × 3.14 × 100) L = 1 / 628 L = 0.001592 H L ≈ 1.59 × 10⁻³ H The options are written with "10₋₃", which is a formatting slip for 10⁻³. Answer: Option B (1.59 × 10⁻³ H) Tip: When you see "reactance" with a frequency, rearrange the formula first, then divide. For inductors, L = X_L / (2πf). For capacitors, C = 1 / (2πfX_C). Remember that 2π ≈ 6.28, so 1/6.28 ≈ 0.159. Spotting that "159" pattern lets you pick the answer quickly in the exam hall. Option D (6.28 × 10⁻³) is the trap for students who multiply by 2π instead of dividing.

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