Impedance (Z) is the total opposition a circuit presents to alternating current (AC), combining both standard resistance (R) and frequency-dependent reactance (X) into a single complex value measured in ohms. It dictates the actual current draw, phase shift, and real power delivered in any AC installation, meaning ignoring it leads to undersized breakers, overheated THHN wire, and inefficient motors. People commonly confuse impedance with pure DC resistance, assuming a standard multimeter's ohms reading on a motor winding tells them how it will behave under a 120V or 240V AC load—it doesn't. When makers and DIYers search for questions on electrical engineering fundamentals, the confusion almost always traces back to misunderstanding how AC circuits differ from the simple DC Ohm's Law models they learned first.
The Core Theory: Resistance vs. Reactance vs. Impedance
In a DC circuit, resistance is the only thing limiting current. In an AC circuit, the voltage and current are constantly reversing direction, which introduces reactance—the opposition to current flow caused by energy storage in magnetic fields (inductors) or electric fields (capacitors).
- Resistance (R): Real opposition that dissipates energy as heat. Measured in Ohms (Ω). Unchanged by AC frequency.
- Inductive Reactance (XL): Opposition from coils/transformers. Increases as frequency increases. Formula: XL = 2πfL
- Capacitive Reactance (XC): Opposition from capacitors. Decreases as frequency increases. Formula: XC = 1 / (2πfC)
Because reactance causes the current and voltage waveforms to shift out of time alignment (phase shift), you cannot simply add Resistance and Reactance together like standard numbers. They are orthogonal vectors. You must calculate the total Impedance (Z) using the Pythagorean theorem:
Z = √(R² + (XL - XC)²)
According to the foundational texts on AC impedance and admittance, failing to account for this vector addition is the primary reason junior engineers and hobbyists miscalculate AC current draw, resulting in tripped breakers or melted terminal lugs.
Worked Numeric Example: Calculating AC Motor Current
Let's look at a real-world scenario: you are wiring a 1/2 HP single-phase AC compressor motor on a 120V, 60Hz branch circuit. You put your multimeter in resistance mode and measure the motor winding at 4.0 Ω. If you blindly apply DC Ohm's Law (I = V/R), you'd calculate 120V / 4.0Ω = 30 Amps, and you might mistakenly install a 35A breaker and 8 AWG wire.
Here is what actually happens when 60Hz AC power is applied. The motor winding is a massive inductor. Let's assume the inductance (L) is 0.05 Henrys.
- Calculate Inductive Reactance (XL):
XL = 2 × π × 60Hz × 0.05H = 18.85 Ω - Calculate Total Impedance (Z):
Z = √(4.0² + 18.85²) = √(16 + 355.32) = √371.32 = 19.27 Ω - Calculate Real AC Current (I):
I = 120V / 19.27Ω = 6.22 Amps
The actual running current is 6.22A, not 30A. For this circuit, NEC Article 430 guidelines would have you size the branch circuit conductors at 125% of the motor full-load ampacity (roughly 8A), meaning 14 AWG THHN copper wire and a standard 15A breaker (or a motor-rated breaker) is the correct, safe choice. The DC resistance reading was practically useless for sizing the AC circuit.
Where You Meet This in Practice
You will run into impedance and phase shift issues in three main areas of DIY and prosumer electrical work:
- HVAC and Refrigeration: Single-phase compressor motors rely on run capacitors to introduce capacitive reactance (XC). This cancels out the motor's inductive reactance (XL), bringing the impedance phase angle closer to zero. If the capacitor degrades, XL dominates, the phase shift worsens, the power factor drops, and the motor draws excessive current until its internal thermal overload trips.
- Solar and Inverter Systems: High-frequency inverters (like the Victron MultiPlus or Growatt 48V systems) must manage the impedance of the AC loads they feed. Feeding a highly inductive load (like a well pump) directly to a high-frequency inverter without a soft-start or proper power factor correction can cause the inverter's IGBTs to overheat and fail due to reactive power bouncing back into the DC bus.
- Audio Crossovers: In speaker building, a tweeter and woofer present complex, frequency-varying impedance curves. A passive crossover network uses capacitors and inductors to exploit XC and XL, routing high frequencies to the tweeter and low frequencies to the woofer based entirely on how reactance changes with audio frequencies (20Hz - 20kHz).
Decision Path: Sizing Run Capacitors and Fixing Power Factor
When troubleshooting AC motors or correcting power factor in a home workshop, use this decision tree to isolate the fault and select the exact replacement component. The U.S. Department of Energy's motor systems guidelines emphasize that correcting power factor at the motor terminals is the most efficient method for reducing line losses.
| Symptom / Measurement | Diagnostic Step | Root Cause | Concrete Fix / Part Pick |
|---|---|---|---|
| Motor hums, runs hot, draws 20%+ over nameplate FLA. | Disconnect power, discharge capacitor, test capacitance with a multimeter's CAP function. | Run capacitor has lost >10% of its rated µF value due to dielectric degradation. | Buy: Dayton 2MEV5 45µF 370VAC Run Capacitor (Match exact µF and voltage; never exceed voltage rating). |
| Workshop 240V subpanel shows poor power factor (PF < 0.85) on a power analyzer; utility bills include reactive penalties. | Measure total inductive kVAR draw of heavy machinery (table saws, air compressors) while running. | Multiple inductive motors running simultaneously are pulling massive reactive current from the grid. | Buy: Eaton 5 kVAR 240V Power Factor Correction Capacitor Bank (Install at the subpanel bus to correct bulk inductive lag). |
| Audio crossover network sounds muddy; tweeter is overpowering the woofer at the crossover point. | Measure driver impedance at the target crossover frequency (e.g., 2500Hz) using an LCR meter, not just the nominal DC resistance. | Crossover components were calculated using the 8Ω 'nominal' DC rating instead of the true 11Ω AC impedance at 2500Hz. | Action: Recalculate capacitor values using the true AC impedance. Replace with a Dayton Audio 10µF 250V Metallized Polypropylene Capacitor. |
Frequently Asked Questions on Electrical Engineering Basics
Q: Why does my 15A breaker trip when my 12A motor starts up, even though the impedance math says it only draws 12A?
A: The impedance calculation above applies to running conditions. When an AC motor starts, the rotor is stationary, meaning there is no 'back-EMF' generated to limit current. The only opposition is the tiny DC resistance of the winding (Locked Rotor Current). This startup surge can be 6 to 8 times the running current (e.g., 72A to 96A) for a few hundred milliseconds. You must use a time-delay breaker (like a Square D QOB series) or a motor protection breaker that allows this brief magnetic inrush without tripping the thermal mechanism.
Q: Can I use a higher voltage capacitor than specified if I can't find the exact match?
A: Yes. The voltage rating on a run capacitor (e.g., 370VAC or 440VAC) is the maximum dielectric breakdown threshold, not the operating voltage. Replacing a 370VAC capacitor with a 440VAC capacitor of the exact same microfarad (µF) rating is perfectly safe and often results in a longer lifespan. Never go the other direction (e.g., replacing a 440V with a 370V), and never change the µF value, as that alters the phase angle and will overheat the motor's start winding.
Q: Does wire gauge affect impedance in long AC runs?
A: Wire gauge primarily affects resistance (R), which causes voltage drop. However, in very long, tightly bundled AC runs, the inductive reactance (XL) of the cable itself becomes a factor, especially in 3-phase industrial feeders. For standard residential 120V/240V branch circuits under 100 feet, the wire's reactance is negligible, and you only need to calculate for DC-style resistance voltage drop (keeping it under 3% per NEC recommendations).
When dealing with AC power, always default to measuring true RMS current with a clamp meter (like the Fluke 325) under load rather than relying on theoretical calculations alone. If you are replacing motor components, match the microfarad rating exactly, upgrade the voltage rating if necessary, and always verify the circuit is de-energized and locked out before touching the terminals.
