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An R-L series circuit, where R = 10 Ω and L = 0.056 H, is connected to an AC supply of frequency 50 Hz. The magnitude of impedance of the circuit is:
10.23 Ω
30.23 Ω
20.23 Ω
5.23 Ω
20.23 Ω
The impedance Z of an R-L series circuit is the vector sum of resistance R and inductive reactance XL. Given R=10Ω and L=0.056H at 50Hz, the total impedance is calculated as Z=R2+XL2.
The impedance Z of an R-L series circuit is the vector sum of resistance R and inductive reactance XL. Given R=10Ω and L=0.056H at 50Hz, the total impedance is calculated as Z=R2+XL2.
XL=2πfL — Inductive reactance formula
Z=R2+XL2 — Impedance formula for R-L series circuit
In an AC circuit, an inductor opposes changes in current, resulting in inductive reactance XL=2πfL. Since current through a resistor is in phase with voltage and current through an inductor lags voltage by 90°, the total impedance is computed using the Pythagorean theorem as the phasor sum of the resistive and reactive components.
Inductive reactance is directly proportional to frequency and inductance.
Impedance is measured in Ohms (Ω).
At 50 Hz, XL=2×3.1416×50×0.056≈17.59Ω.
Provides basic understanding of circuit phase relationships.
Foundation for analyzing complex power systems.
Assumes an ideal inductor with no internal resistance.
Does not account for non-sinusoidal waveforms.
Power system impedance modeling.
Design of low-pass filters.
Calculation: XL=2×3.1416×50×0.056=17.59Ω. Then Z=102+17.592=100+309.4=409.4≈20.23Ω.
Option B (30.23) arises from incorrect addition (10 + 20.23), Option A (10.23) is a distracter, and Option D (5.23) is numerically incorrect.
C is correct — The magnitude of impedance for the given R-L series circuit is calculated as 20.23 Ω using the phasor sum of resistance and inductive reactance.
Always convert frequency to angular frequency (2πf) first, and ensure you use the square root of the sum of squares, not simple algebraic addition, for impedance.
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