What is Impedance?
Impedance is the total opposition an AC circuit offers to current flow, combining resistance and reactance into a single complex quantity. It's the AC counterpart to resistance in DC circuits.
Impedance Z = R + jX combines resistance R and reactance X; its magnitude is |Z| = √(R² + X²), measured in ohms (Ω).
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Step-by-step worked examples
A circuit has R = 30 Ω and capacitive reactance X = 40 Ω. Find |Z|.
|Z| = √(R² + X²) = √(30² + 40²) = √(900 + 1600) = √2500 = 50 Ω
An inductor L = 0.2 H is driven at f = 60 Hz. Find its reactance XL.
XL = 2πfL = 2π × 60 × 0.2 = 75.4 Ω
A capacitor C = 50 µF is driven at f = 60 Hz. Find its reactance XC.
XC = 1/(2πfC) = 1/(2π × 60 × 0.00005) = 1/0.01885 ≈ 53.05 Ω
Flashcards
Quick quiz
Q1.Impedance combines resistance with:
Q2.The magnitude of impedance is given by:
Q3.The formula for inductive reactance XL is:
Q4.As frequency increases, capacitive reactance XC:
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Common mistakes
Adding resistance and reactance directly: Z = R + X. — Correct: Use the Pythagorean sum: |Z| = √(R² + X²), since R and X are 90° apart in phase.
Treating impedance as constant regardless of frequency. — Correct: Reactance changes with frequency, so impedance changes too.
Confusing impedance with plain resistance. — Correct: Resistance is only the real part of impedance; reactance is the imaginary part.
Swapping the XL and XC formulas. — Correct: XL = 2πfL increases with frequency; XC = 1/(2πfC) decreases with frequency.
FAQ
What is impedance?
Impedance is the total opposition to current flow in an AC circuit, combining resistance and reactance.
What is the formula for impedance?
Z = R + jX, with magnitude |Z| = √(R² + X²), measured in ohms.
What are examples of impedance calculations?
Impedance calculations appear in RLC circuits, audio filters, speaker matching and power systems.
How do you calculate impedance in an AC circuit?
Combine the resistance with the net reactance (XL − XC), then apply |Z| = √(R² + X²).