Electronics
What is impedance?
Impedance, Z, is a circuit's total opposition to alternating current, in ohms. It combines resistance, R, with reactance, X, from capacitors and coils. They don't simply add: for a resistor and a capacitor in series, |Z| = √(R² + X²), like the long side of a right-angled triangle.
Voltages that don't add up
Put a resistor and a capacitor in series across a 10 V peak sine, and measure each part's peak: the resistor might show 6 V and the capacitor 8 V. That's 14 V from a 10 V source.
Nothing's broken. The capacitor's voltage lags the resistor's by a quarter cycle, 90°, so their peaks never happen at the same moment. At every single instant, the two voltages do add up to the source. Their peaks add like the sides of a right-angled triangle:
Check: 6² + 8² = 100 = 10².
Live experiment
Walk the impedance triangle
A 10 V peak sine drives a resistor and a capacitor in series. Change R and X and watch the long side of the triangle: 3 kΩ and 4 kΩ make 5 kΩ, not 7. Below, the two voltages peak a quarter cycle apart but add to the source at every instant.
“Impedance and phase” is lesson 3 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 23 before it first.
|Z| = √(R² + X²)
R and X combine the same way:
Then Ohm's law works with Z: I = V ÷ |Z|, and each part's voltage is I × R or I × X.
Example: 10 V peak with R = 3 kΩ and XC = 4 kΩ.
So VR = 2 mA × 3 kΩ = 6 V and VC = 2 mA × 4 kΩ = 8 V, the puzzle's numbers.
Phase and power
The current through a series RC circuit leads the source voltage by tan⁻¹(XC ÷ R), here about 53°, and the capacitor's voltage lags the source by the other 37°. A coil works the same way with XL in the triangle, except its voltage leads the current.
Only the resistor gets warm: P = Irms² × R. The capacitor stores energy for a quarter of a cycle and hands it back the next. In general, average power is Vrms × Irms × cos φ, where φ is the phase angle; cos φ is the power factor.
Engineers often write impedance as a complex number, Z = R − jXC for a capacitor or R + jXL for a coil, where j marks the 90° turn.
Where you'll meet it
The ohms printed on speakers and headphones are impedances: a coil's wire resistance combined with its inductance's reactance. Radio cables are rated in ohms too, usually 50 Ω or 75 Ω, and matching impedances is how a transmitter delivers the most power to its antenna.
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
“Impedance and phase” is lesson 3 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 23 before it first.
Or start from the very first lesson, no account neededWork it out
Practice questions
Three quick questions from the lessons. Pick an answer to check it.
Show the answer
Answer: 90° out of phase. The resistor's voltage is in phase with the current, and a capacitor's voltage lags its current by a quarter cycle. So they're 90° out of phase, at the same frequency.
- Why not “in phase”? The resistor's voltage follows the current, but the capacitor's voltage trails it by a quarter cycle, so they can't be in step.
- Why not “180° out of phase”? 180° would be exactly upside down. A capacitor's voltage is only a quarter cycle, 90°, behind the resistor's.
Show the answer
Answer: an ideal capacitor. An ideal capacitor stores energy for a quarter of a cycle and hands it all back the next, so it limits the current without getting warm. A resistor or a lamp turns its power into heat and light.
- Why not “a resistor”? A resistor turns power into heat on every cycle, so it takes power on average.
- Why not “a lamp”? A lamp is a resistor that glows, so it takes real power and turns it into heat and light.
Show the answer
Answer: the steady voltage that heats a resistor the same. A sine's average over a cycle is zero, since it spends half its time negative. RMS is the steady DC voltage that would heat a resistor just as much, about 0.707 of the peak.
- Why not “its highest value”? The highest value is the peak. RMS is smaller, about 0.707 of the peak for a sine.
- Why not “its average over a cycle”? A sine spends half its time negative, so its average over a cycle is zero. RMS is chosen to match heating instead.
“Impedance and phase” is lesson 3 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 23 before it first.
Questions people ask
What is impedance?
A circuit's total opposition to alternating current, in ohms. It combines resistance, which turns energy into heat, with reactance, which stores it and hands it back each cycle. For a resistor and a capacitor or coil in series, |Z| = √(R² + X²).
Why can't you just add resistance and reactance?
Because their voltages peak a quarter cycle, 90°, apart. Two things at right angles add like the sides of a right-angled triangle, so 3 kΩ of resistance and 4 kΩ of reactance make 5 kΩ, not 7 kΩ.
What does an 8 Ω speaker rating mean?
It's a nominal impedance: the resistance of the speaker's coil combined, triangle-style, with the reactance of its inductance. It changes with frequency, so 8 Ω is a nominal figure for the audio band, not a fixed resistance.
What is the phase angle?
How far the current is out of step with the voltage. In a series RC circuit the current leads the source by tan⁻¹(X_C ÷ R). With R = 3 kΩ and X_C = 4 kΩ that's about 53°; the capacitor's own voltage lags the source by the other 37°.
Related topics
- Capacitive and inductive reactance explainedWhy a capacitor passes treble and a coil passes bass: X_C, X_L and Ohm's law for AC.
- AC voltage and RMS explainedPeak, period, frequency and RMS: the numbers that describe an AC sine wave.
- Low-pass filter explainedA resistor and a capacitor that pass the bass and fade the treble, and where the cutoff sits.
- Impedance matching explainedA load takes the most power when its resistance equals the source's: why radio is 50 Ω, and how to match.