In an AC circuit, the complex number Z = V/I [Ω] obtained by dividing the voltage phasor by the current phasor. Its real part is the resistance R and its imaginary part the reactance X, written Z = R + jX. A coil has jωL and a capacitor 1/(jωC) = −j/(ωC), so their magnitudes change with frequency. The magnitude |Z| is the ratio of the voltage and current amplitudes, and the angle is the phase lead of the voltage over the current.
Impedance appears in 31 practice questions across 9 topics, including Analog and electronic circuits, Circuit Analysis: AC, Linear Circuits and Transients, Circuit and electromagnetism basics.
Y (star) and Δ (delta) connections of a three-phase load · View in diagrams
Impedance lets Ohm's law V = RI be written for AC as V = ZI with complex numbers. For Z = 3 + j4 Ω, the magnitude is √(3² + 4²) = 5 Ω and the angle is about 53.1°, so the current lags the voltage by 53.1°. The calculation rules are the same as for resistance: impedances add in series, and their reciprocals (admittances) add in parallel.
Component behavior that changes with frequency
A coil's reactance ωL increases in proportion to frequency, and a capacitor's reactance 1/(ωC) decreases in inverse proportion. So at DC a coil behaves like a short and a capacitor like an open circuit, and at high frequencies the reverse. Filters, resonant circuits and power-supply decoupling all exploit this frequency dependence.
Many kinds of "impedance"
Electronics uses the word in many settings: the input and output impedance of an amplifier, the characteristic impedance of a line, the impedance of a power-delivery path and more. All share the same idea: the ratio of voltage to current seen from a pair of terminals. For high-speed signals, reflections occur when the characteristic impedance of a line does not match the impedance of its termination.
The voltages across a resistor and an inductor are 90° out of phase, so they are combined as complex numbers (vectors), not added directly. Z = R + jXL = 30 + j40 Ω, with magnitude √(30² + 40²) = √2500 = 50 Ω. The current lags the voltage by φ = tan⁻¹(40/30) ≈ 53°, and the power factor is cos φ = 30/50 = 0.6.
In an ideal transformer the primary voltage is n = N1/N2 times the secondary voltage and the primary current is 1/n times the secondary current, so the impedance seen at the primary, V1/I1, is n² times the secondary's V2/I2: 10² × 8 Ω = 800 Ω. Because of this impedance transformation, transformers are also used for impedance matching, for example between an amplifier and a loudspeaker.
FAQ
How is impedance different from resistance?
Resistance is the case in which the ratio of voltage to current does not depend on frequency and there is no phase shift; it is the real part of the impedance. Impedance is a complex quantity that also includes the phase shift and frequency dependence caused by coils and capacitors.
Can power be calculated from the magnitude of the impedance alone?
No. To find the active power you must multiply the square of the current by the real part (the resistance), or use the power factor cos φ = R/|Z|. For example, 10 A through 8 + j6 Ω consumes 10² × 8 = 800 W; the 1,000 VA obtained with |Z| = 10 Ω is the apparent power.
Impedance in the explanations
In an ideal transformer the primary voltage is n = N1/N2 times the secondary voltage and the primary current is 1/n times the secondary current, so the impedance seen at the primary, V1/I1, is n² times the secondary's V2/I2: 10² × 8 Ω = 800 Ω.
Method 1 (conjugate matching): choosing ZL as the complex conjugate of Zth, 3 − j4 Ω, cancels the reactances, so the circuit impedance is just a 6 Ω resistance.