Question 2 of 16beginner🔧 ApplyNumerical2 marks

A pure inductor of 25.0 mH is connected to a source of 220 V. Find the inductive reactance and rms current in the circuit if the frequency of the source is 50 Hz.

Correct Answer

Inductive Reactance: The inductive reactance is calculated using the formula:

XL=2πνLX_L = 2\pi \nu L

Substituting the given values, ν=50 Hz\nu = 50 \text{ Hz} and L=25.0×10−3 HL = 25.0 \times 10^{-3} \text{ H}:

XL=2×3.14×50×25×10−3Ω=7.85ΩX_L = 2 \times 3.14 \times 50 \times 25 \times 10^{-3} \Omega = 7.85 \Omega

RMS Current: The rms current in the circuit is calculated using Ohm's law:

I=VXLI = \frac{V}{X_L}

Substituting V=220 VV = 220 \text{ V} and XL=7.85ΩX_L = 7.85 \Omega:

I=220 V7.85Ω=28 AI = \frac{220 \text{ V}}{7.85 \Omega} = 28 \text{ A}
Exercise: Example 7.2 | Q: Example 7.2 | (Page 7)
For More Understanding

Explanation

The solution is derived directly from the provided textbook context for Example 7.2. First, the inductive reactance (XLX_L) is found using the formula 2πνL2\pi \nu L. The value of inductance is converted from mH to H for the calculation. Second, the rms current (II) is determined by dividing the voltage (VV) by the calculated reactance (XLX_L).

Solution Steps

  1. Step 1: Calculate inductive reactance using XL=2πνL=2×3.14×50×25×10−3Ω=7.85ΩX_L = 2\pi \nu L = 2 \times 3.14 \times 50 \times 25 \times 10^{-3} \Omega = 7.85 \Omega.

  2. Step 2: Calculate rms current using I=V/XL=220 V/7.85Ω=28 AI = V / X_L = 220 \text{ V} / 7.85 \Omega = 28 \text{ A}.

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