Question 12 of 16beginner🔧 ApplyNumerical1 mark

A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.

Correct Answer

The rms value of current in the circuit is 15.9 A (approximately).

Exercise: EXERCISES | Q: 7.3 | (Page 24)
For More Understanding

Explanation

This numerical problem is similar to Example 7.2 in the textbook. For a pure inductor connected to an AC supply, we first calculate the inductive reactance using the formula XL = 2πvL, where v is frequency and L is inductance. Then, the rms current is found using Ohm's law for AC circuits: I = V/XL. The inductor offers opposition to AC current through inductive reactance, which depends on both frequency and inductance value.

Solution Steps

  1. Step 1: Calculate the inductive reactance using XL = 2πvL XL = 2×3.142 \times 3.14 × 50×4450 \times 44 × 10⁻³ Ω XL = 13.82 Ω

  2. Step 2: Calculate the rms current using I = V/XL I = 220 V / 13.82 Ω I = 15.9 A

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