Correct Answer

Direct FormulaElectricalBasic Electrical

Option A

31.4

Quick Summary: Given: Frequency f = 50Hz, Inductance L = 100mH (or 0.1H)

📋 Given

Frequency f = 50Hz, Inductance L = 100mH (or 0.1H)

🔢 Formula Used

XL=2πfLX_L = 2 \pi f LXL​=2πfL

🔢 Step-by-Step Solution

Convert Inductance units

The given inductance is $L = 100\text{ mH}$ . To use it in the standard reactance formula, convert it to Henrys (H).

L=100×10°−3 H=0.1 HL = 100 \times 10°{-3}\text{ H} = 0.1\text{ H}L=100×10°−3 H=0.1 H

Identify Inductive Reactance formula

The inductive reactance $X_L$ is given by the product of angular frequency $\omega$ and inductance $L$ , where $\omega = 2\pi f$ .

XL=2πfLX_L = 2 \pi f LXL​=2πfL

Substitute values and calculate

Substitute $f = 50\text{ Hz}$ and $L = 0.1\text{ H}$ into the formula.

XL=2×3.14159×50×0.1=31.416≈31.4X_L = 2 \times 3.14159 \times 50 \times 0.1 = 31.416 \approx 31.4XL​=2×3.14159×50×0.1=31.416≈31.4  Ω\OmegaΩ

✅

A is correct because substituting the frequency and inductance into the reactance formula $X_L = 2 \pi f L$ yields approximately $31.4$ $\Omega$ .

Core Concepts Used

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Inductive Reactance A.C. Circuit Analysis Angular Frequency

💡 EXAM TIP

Remember that capacitive reactance $X_C = \frac{1}{2 \pi f C}$ behaves inversely to frequency, whereas inductive reactance $X_L$ is directly proportional to frequency.

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