AC Circuits

Article 9 dealt with direct current, which flows one way. This article covers alternating current, the kind that comes out of a wall outlet: what it is, why the world runs on it, how resistors, capacitors and coils behave with it, how homes are wired for it, how to measure it and how to stay alive around it. RCL Circuits, article 11, builds on it.

About the analogies. Everyday comparisons appear only in shaded "Analogy" boxes beside the real physics, and each box says where the comparison stops working.

Mains AC can kill. The circuits in this article are for understanding, not for building on a live outlet. Section 10 explains why the current through your body matters and how to stay safe.

1. A short recap

2. What AC is, and why we use it

In alternating current (AC), the current periodically reverses direction, and the voltage reverses with it. In household AC the voltage follows a smooth curve called a sine wave.[1] On a schematic, an AC source is drawn as a circle with a wavy line inside.[2]

The main reason we use AC is the transformer. Sending power over long distances is far more efficient at high voltage and low current, because less current means smaller wires and less power lost as heat in their resistance. Transformers make it easy to step the voltage up for transmission and back down for use, and they need AC to work.[2] (Recap: the turns ratio.) AC generators and motors can also be simpler, more reliable and cheaper to build than DC ones.[2]

The war of the currents

In the 1880s, direct current, promoted by Thomas Edison, was the American standard. Its problem was that DC could not easily be converted to higher or lower voltages. Nikola Tesla championed AC, whose voltage a transformer could change easily. Edison, who earned royalties on his DC patents, campaigned against AC, claiming it was more dangerous and publicly electrocuting animals to make the point.[3] AC won. In 1893 George Westinghouse, who had licensed Tesla's AC induction motor, underbid General Electric to light the Chicago World's Fair with AC. Westinghouse also won the contract to generate power at Niagara Falls, and on 16 November 1896 AC from the falls lit Buffalo, New York, and General Electric soon switched to AC too.[3] DC is making a comeback: high-voltage DC lines now carry power long distances, and electronics, LEDs, solar cells and electric vehicles all run on DC.[3]

The frequency of the mains, how many complete cycles it makes each second, differs by region. North America uses 60 cycles per second, or 60 hertz (Hz); Europe uses 50 Hz.[2] A U.S. outlet supplies 120 V at 60 Hz; a European one supplies 220 to 240 V at 50 Hz.[4]​[5]

3. The sine wave

Figure 1 labels the parts of one cycle.

Anatomy of the U.S. mains sine wave, drawn to scale A graph of voltage against time from 0 to 25 milliseconds, showing one and a half cycles of a sine wave. The wave rises from zero to a peak of plus 170 volts at about 4.2 milliseconds, falls through zero at 8.3 milliseconds, reaches minus 170 volts at 12.5 milliseconds and returns to zero at 16.7 milliseconds, which is marked as one period. A double arrow from zero to the first crest is labeled peak, 170 volts. A double arrow from the lowest point to the highest is labeled peak-to-peak, 340 volts. Dashed horizontal lines at plus and minus 120 volts are labeled RMS level, 120 volts, the same heating as 120 volts DC. 0 5 10 15 20 25 Time (milliseconds) +170 +120 0 −120 −170 Voltage (V) RMS level: 120 V (same heating as 120 V DC) Peak 170 V Peak-to- peak 340 V One cycle: period T = 1/60 s ≈ 16.7 ms
Figure 1. One and a half cycles of U.S. mains voltage, drawn to scale: 170 V peak, 340 V peak-to-peak, 120 V RMS and a period of 16.7 ms. Values from OpenStax and calculated.

RMS: the number on the label

Since AC spends half its time negative, its plain average is zero, which is useless. Instead, AC is rated by its RMS (root-mean-square) value: square the wave, take the average, then take the square root.[1] The practical meaning is simple. An RMS value is the DC value that would heat a resistor equally. Ten volts RMS into 2 Ω produces the same 50 W of heat as a 10 V battery.[2] With RMS values, Ohm's law and the power formulas work for AC exactly as for DC.[1]

For a sine wave, Vrms = Vpeak / √2 ≈ 0.707 × Vpeak. Household "120 V" is an RMS figure, so the voltage actually swings from +170 V (1.414 × 120) to −170 V and back 60 times every second.[1] Peak-to-peak it is about 340 V (calculated). Unless a value is marked otherwise, AC voltages and currents are quoted as RMS.[1]

Phase, in degrees and radians

A sine wave repeats the same way a wheel turns, so one cycle is described as one full turn: 360 degrees. The wave starts at zero at 0°, peaks at 90°, crosses zero again at 180°, bottoms out at 270° and is back at the start at 360°.[2] Two waves of the same frequency that do not peak at the same moment are out of step by a phase shift, also measured in degrees (Figure 2).[2] At 60 Hz, a 90° shift is a quarter cycle, about 4.2 ms (calculated).

Physics formulas use a second angle unit, the radian. One full turn is 2π radians (about 6.28), so 360° = 2π rad, 180° = π, 90° = π/2, and one radian is about 57.3°.[6] That is why AC formulas are full of 2π: multiplying the frequency by 2π turns cycles per second into radians per second, the angular frequency ω (omega).[6] For U.S. mains, ω = 120π ≈ 377 rad/s.[4]

Phase: wave B lags wave A by 90 degrees Two sine waves of the same size and frequency over one cycle. Wave A, solid, starts at zero and peaks at 90 degrees. Wave B, dashed, starts at its lowest point and peaks at 180 degrees, a quarter cycle later; an arrow between the two peaks marks the 90 degree lag. Two scales run along the bottom: degrees 0, 90, 180, 270 and 360, and the same points in radians, 0, pi over 2, pi, 3 pi over 2 and 2 pi. B peaks 90° (a quarter cycle) after A Degrees Radians 0° 0 90° π/2 180° π 270° 3π/2 360° 2π Wave A Wave B (lags A by 90° = π/2 rad)
Figure 2. Two sine waves of the same frequency, with B lagging A by 90° (π/2 radians), a quarter of a cycle. The scale along the bottom shows the same cycle in degrees and in radians. Sources: Kuphaldt; OpenStax.

4. How AC is generated

A generator spins a coil in a magnetic field, or a magnet inside coils. As the coil turns, the magnetic flux through it keeps changing, and by Faraday's law a changing flux induces a voltage.[7] (Recap: Faraday's law.) A coil turning at a steady speed in a uniform field produces a voltage that varies as a sine wave.[7] It depends on the angle of the coil in the field: largest when the coil's sides cut straight across the field, zero when they move along it, and reversed every half turn (Figure 3).[7] One turn of this simple generator makes one cycle, so it would have to spin at 60 turns per second, 3,600 revolutions per minute, to make 60 Hz (calculated). A motor is the same machine run the other way, with current in and rotation out.[7]

A one-coil AC generator and its sine-wave output Left: a red north magnet pole and a blue south magnet pole face each other, with magnetic field lines running across the gap from north to south. Between them a coil, seen end-on as a line with a wire cross-section at each end, turns on a central axle; a curved arrow shows the rotation. Right: a graph of the output voltage against coil angle from 0 to 360 degrees is one cycle of a sine wave. It is zero at 0 degrees, largest at 90 degrees where the coil sides cut straight across the field, zero again at 180 degrees where they move along the field, largest in the reverse direction at 270 degrees, and back to zero at 360 degrees. N pole S pole Magnetic field runs N to S; the coil (seen end-on) turns on its axle 0° 90° 180° 270° 360° Output voltage Largest: sides cut across the field Zero: sides move along the field Largest again, reversed Coil angle (one full turn = one cycle)
Figure 3. A one-coil generator. The coil turns between two magnet poles; its output is a sine wave, zero when the coil sides move along the field and largest when they cut straight across it. Source: OpenStax.

5. Resistors, capacitors and coils in AC

Resistors: in phase

In a resistor, current is simply V/R at every instant, so voltage and current rise and fall together. They are in phase, and a resistor behaves the same at any frequency.[8]​[9]

Capacitors: current leads by 90°

A capacitor's current depends on how fast its voltage is changing, not on the voltage itself.[10] On a sine wave the voltage changes fastest as it crosses zero and not at all at the peaks, so the current is largest at the zero crossings and zero at the peaks. The current reaches its peak a quarter cycle before the voltage does: in a capacitor, current leads voltage by 90°, or π/2 radians.[10]​[9]

The capacitor's opposition to AC, its capacitive reactance, is measured in ohms:[8]

XC = 1 / (2πfC)

Larger capacitors and higher frequencies give less reactance.[8] A 10 µF capacitor at 60 Hz has XC = 1 / (2π × 60 × 0.000010) ≈ 265 Ω; at 120 Hz, half that (calculated). (Recap: blocking DC, passing AC.)

Coils: current lags by 90°

A coil does the reverse. Its voltage depends on how fast its current is changing, because it pushes back against every change in current.[11] So the voltage peaks while the current is crossing zero, and in a coil current lags voltage by 90°.[8] Its inductive reactance is[8]

XL = 2πfL

Unlike a capacitor's, it rises with frequency. A 100 mH coil at 60 Hz has XL = 2π × 60 × 0.1 ≈ 37.7 Ω (calculated). (Recap: passing DC, opposing AC.)

Voltage and current phase in a resistor, a capacitor and a coil Three side-by-side graphs, each showing one cycle of voltage as a solid sine wave and current as a smaller dashed sine wave. Resistor: the current wave peaks at the same moment as the voltage, labeled in step. Capacitor: the current wave peaks a quarter cycle before the voltage, labeled current leads by 90 degrees. Coil: the current wave peaks a quarter cycle after the voltage, labeled current lags by 90 degrees. Resistor 0 180° 360° In step (in phase) Capacitor 0 180° 360° Current leads by 90° Coil (inductor) 0 180° 360° Current lags by 90° Voltage Current (drawn smaller to fit)
Figure 4. Voltage (solid) and current (dashed) in a resistor, a capacitor and a coil on the same AC source. In the resistor they are in step. In the capacitor the current peaks a quarter cycle earlier; in the coil, a quarter cycle later. Sources: OpenStax; Kuphaldt.

A memory aid: "ELI the ICE man." Write E for voltage. In an inductor (L), E comes before I: voltage leads current. In a capacitor (C), I comes before E: current leads voltage.[12] The phrase only helps you remember the order. The reason is the one above: a capacitor's current follows the rate of change of its voltage, and a coil's voltage follows the rate of change of its current.

Impedance, gently

Real circuits mix resistance and reactance. Their combined opposition to AC is the impedance, Z, also in ohms, and I = V/Z works just like Ohm's law.[13] But resistance and reactance do not simply add, because they are out of step. For a resistor and a coil in series, Z = √(R2 + XL2).[13] With 30 Ω of resistance and 40 Ω of reactance, Z = √(900 + 1,600) = 50 Ω, not 70; on 120 V that draws 2.4 A (calculated). Coils and capacitors partly cancel each other, which leads to resonance, the subject of article 11.[13]

6. Power in AC: watts, VARs and VA

In a resistor, all the power becomes heat or light. A perfect capacitor or coil uses none: it stores energy and hands it back each cycle. Yet it still draws current and drops voltage, which is why AC needs three kinds of power:[14]

The three form a right triangle (Figure 5). The power factor is real power divided by apparent power, which is also the cosine of the phase angle between voltage and current: 1 for a pure resistance and less for anything reactive.[14] In the 30 Ω plus 40 Ω example (calculated): real power is 2.42 × 30 ≈ 173 W, reactive power 2.42 × 40 ≈ 230 VAR, apparent power 120 V × 2.4 A = 288 VA, and the power factor 173 / 288 = 0.6.

The power triangle for a 30 ohm, 40 ohm reactance load on 120 volts A right triangle. The horizontal base is real power, P equals 173 watts. The vertical side is reactive power, Q equals 230 volt-amperes reactive. The sloping hypotenuse is apparent power, S equals 288 volt-amperes. The angle phi between the base and the hypotenuse is marked. A box beside it works the example: resistance 30 ohms and inductive reactance 40 ohms on 120 volts give impedance 50 ohms and current 2.4 amperes, so P is about 173 watts, Q about 230 volt-amperes reactive, S is 288 volt-amperes, and the power factor P over S, the cosine of phi, is 0.6, with phi about 53 degrees. φ Real power P = 173 W Reactive power Q = 230 VAR Apparent power S = 288 VA Worked example (calculated) R = 30 Ω, X = 40 Ω (coil), on 120 V Z = √(30² + 40²) = 50 Ω I = 120 / 50 = 2.4 A P = I²R ≈ 173 W Q = I²X ≈ 230 VAR S = V × I = 288 VA PF = P/S = cos φ = 0.6 (φ ≈ 53°)
Figure 5. The power triangle for 30 Ω of resistance in series with 40 Ω of inductive reactance on 120 V: 173 W real, 230 VAR reactive, 288 VA apparent, power factor 0.6. Values calculated; the relationship is from Kuphaldt.

Analogy: a horse towing a rail car from beside the track (the U.S. Department of Energy's own comparison).[15] Only the part of its pull along the rails moves the car (real power). The sideways part is wasted effort (reactive power). The horse's total effort is the apparent power, and the closer it walks to the track, the nearer the power factor gets to 1.

Where it breaks down: the horse's sideways effort is simply lost, while reactive energy is not consumed. It flows back and forth between the source and the load, and the harm comes from the extra current it takes to carry it.

Household examples. Motors are inductive, so motor loads have power factors below 1.[15] A University of Kentucky survey of published figures lists a resistive water heater at 1.0, refrigerators at 0.8 to 0.99, and washing machines at only 0.55 to 0.59.[16] A 520 W washer at a power factor of 0.57 draws 520 ÷ (0.57 × 120) ≈ 7.6 A, against 4.3 A for a 520 W heater (calculated).

Why utilities care. The utility must generate and deliver the whole current, not just the useful part. Low power factor means more current for the same work, which needs more generating and transmission capacity and causes voltage drops. The DOE fact sheet, written for industrial plants, notes that many utilities charge an extra fee when a customer's power factor falls below 0.95.[15] The usual cure is a capacitor near the motor, whose leading current cancels the coil's lagging current.[14]

7. Household power in the US

Split-phase 120/240 V

American homes get split-phase power, usually called 120/240 V. The utility transformer's secondary winding is center-tapped, so it acts as two 120 V sources in series.[5] (Recap: the center-tapped winding.) The two outer wires, the hot legs, are 240 V apart, and each is 120 V from the center wire, the neutral. Lights and ordinary outlets connect between one hot leg and neutral; the heaviest loads use both hot legs for 240 V. The neutral carries only the difference between the two sides' currents.[5] Splitting the voltage this way keeps currents low and wiring economical while keeping the voltage at each outlet lower and safer.[5]

U.S. split-phase service: two hot legs, a neutral and a ground A pole transformer has a high-voltage primary coil on the left and a secondary coil on the right with a tap at its center. Three wires run from the secondary to the service panel: L1, a hot wire, from the top end; N, the neutral, from the center tap; and L2, the other hot wire, from the bottom end. Arrows show 120 volts from L1 to neutral, 120 volts from neutral to L2, and 240 volts from L1 to L2, which big loads such as dryers and ranges use. Inside the panel the neutral is bonded to a ground rod in the earth. A 120 volt branch circuit runs a hot and a neutral wire through a load inside an appliance, and a separate ground wire connects the appliance metal case back to the panel ground; it normally carries no current. Utility high voltage Pole transformer (center-tapped secondary) L1 (hot) N (neutral) L2 (hot) 120 V 120 V 240 V Big loads (dryer, range) connect L1 to L2: 240 V Service panel Neutral bonded to earth (ground rod) at the panel hot neutral ground wire normally no current Appliance load inside a metal case 120 V branch circuit
Figure 6. U.S. split-phase service. The center-tapped utility transformer gives two hot legs 240 V apart, each 120 V from neutral. Neutral is bonded to earth; the ground wire connects metal cases to earth and carries current only during a fault. Sources: Kuphaldt; OpenStax.

Hot, neutral and ground

Modern wiring uses three wires to each outlet.[17]

Why the ground wire matters. If worn insulation lets the hot wire touch a metal case, the ground wire gives the fault current an easy path, a large current flows, and the breaker trips. Without it, the appliance may keep working normally while its case sits at 120 V, waiting for someone to touch it and a faucet at the same time.[17] That is why the third prong must never be cut off. Appliances sold with two-prong plugs are double-insulated, with nonconducting cases.[17] Wire colors vary by country and by installer, so always test rather than trust a color.[17]

GFCIs and AFCIs

A ground-fault circuit interrupter (GFCI) compares the current going out on the hot wire with the current coming back on the neutral. If they differ by about 5 mA, some current must be taking another path, possibly through a person, and the GFCI cuts the power in as little as 1/40 of a second.[18] It senses the difference with a coil that both wires pass through.[17] A GFCI will not protect someone who touches both the hot and the neutral wires, because then the two currents still match.[18]

An arc-fault circuit interrupter (AFCI) protects against fire, not shock. It watches the current for the signature of dangerous arcing, which an ordinary breaker would not detect.[19] Such arcs often occur in damaged or deteriorated wires and cords.[20] It is designed to ignore the harmless arcs from a switch opening or a plug being pulled.[20]

The U.S. National Electrical Code (NEC, NFPA 70) sets where each is required, and NFPA says it is enforced in all 50 states.[21] In the 2023 edition, section 210.8 requires GFCI protection for dwelling receptacles in bathrooms, kitchens, garages, outdoors, basements, laundry areas and within 6 feet of a sink, among other places; section 210.12 requires AFCI protection for 120 V, 15 and 20 A circuits in most living spaces, including bedrooms, kitchens, living rooms, hallways and closets.[22] NFPA has since published a reorganized 2026 edition,[21] and local adoption varies, so check which edition applies where you live.

Three-phase power, briefly

Large power systems use three-phase power: three hot wires whose sine waves are spaced 120° apart (Figure 7). Generators make it with three sets of windings spaced 120° around the machine.[5] For the same power, it needs much less conductor current, so thinner, cheaper wire, than single-phase. Three-phase motors also start and run in a fixed direction without help; swapping any two hot wires reverses them. Single-phase motors need an extra winding, often with a capacitor, to get started.[5] Homes usually get split-phase, while large distribution systems and industry run on three-phase.[5]

Three-phase power: three sine waves 120 degrees apart Three equal sine waves over one cycle from 0 to 360 degrees. Phase A, solid, peaks at 90 degrees. Phase B, dashed, is shifted 120 degrees later and peaks at 210 degrees. Phase C, dotted, is shifted 240 degrees later and peaks at 330 degrees. At any moment the waves are at different points in their cycles. 0° 120° 240° 360° A peaks at 90° B peaks at 210° C peaks at 330° Phase A Phase B (120° later) Phase C (240° later)
Figure 7. Three-phase power: three sine waves of equal size, each 120° (one third of a cycle) behind the one before. Source: Kuphaldt.

8. Measuring AC

True-RMS and average-responding meters

Many cheaper meters do not measure RMS at all. An average-responding meter measures the average of the rectified wave and multiplies it by 1.11, which gives the right answer only for a pure sine wave. A true-RMS meter calculates the real heating value for any wave shape.[23]​[24] On distorted waveforms, such as the current drawn by computers, the difference matters: Fluke's table shows an average-responding meter reading 10 percent high on a square wave and up to 40 percent low on the current into a single-phase rectifier.[23] If a tool does not say "true-rms," it is most probably average-responding.[23] (Recap: measuring DC with a multimeter.)

Measurement categories (CAT ratings)

A meter's voltage rating is not enough. Mains wiring can carry brief high-energy transients, such as spikes from lightning, and if one causes an arc inside a meter connected to a high-energy circuit, the current can sustain the arc and produce an arc blast, an explosion that injures more people each year than electric shock does.[25] The IEC 61010 standard therefore sorts locations into measurement categories:[26]​[25]

A higher category means more power available and higher-energy transients. Within a category, a higher voltage rating is better, but across categories a CAT III 600 V meter is tested against transients with six times the current of a CAT II 1000 V meter's, so it is the safer meter despite the lower number.[25] Never exceed the rating of the lowest-rated part, whether meter, leads or accessory.[26]

Meter measurement categories from the utility to the outlet Three zones from left to right. CAT IV, origin of installation: a utility pole and transformer, the service drop wire and the utility meter on the outside wall. CAT III, distribution inside the building: the main panel with its breakers, feeders, fixed wiring and hard-wired equipment. CAT II, plug-in loads: an outlet and an appliance plugged into it. An arrow along the bottom points toward the utility end, labeled closer to the utility supply means more energy available in a fault or transient. CAT IV Origin of installation CAT III Distribution inside CAT II Plug-in loads Pole and service drop Utility meter (outside wall) Main panel Fixed wiring, feeders, hard-wired equipment Outlet Plug-in appliance Closer to the utility supply: more energy available in a fault or transient
Figure 8. Measurement categories, from the utility connection inward: CAT IV at the service entrance and meter, CAT III at the panel and fixed wiring, CAT II at outlets and plug-in loads. The closer to the source, the more energy a fault can deliver. Sources: Fluke.

Oscilloscopes, and a deadly mistake

An oscilloscope displays a changing voltage against time,[2] so you see the waveform's shape, peaks, frequency and phase rather than one number. An ordinary bench scope has a hidden danger. Its probe ground clips are connected to earth through the scope's power cord.[27] Tektronix's rule is to connect probe ground leads to earth ground only.[27] Clip one to a mains hot wire and you connect that wire straight to earth through the probe lead: a short circuit. Some people "float" the scope by defeating its ground pin to get around this. Tektronix warns that this, or connecting a ground lead to anything other than ground, can leave dangerous voltages on the scope's connectors, controls and other surfaces; never do it. For measurements that are not referenced to earth, use a differential or isolated probe.[27]

Why a scope probe ground clip must never go on mains hot Left, labeled wrong: a bench oscilloscope is grounded to earth through its three-prong power cord. Its probe tip touches the neutral wire and its ground clip touches the 120 volt hot wire, where a spark is drawn. A dashed arrow traces fault current from the hot wire through the ground clip, through the scope chassis and down the cord to earth: a short circuit. A note says probe grounds belong on earth ground only. Right, labeled safer: a differential probe connects one input to hot and one to neutral and sends its output to the scope. The scope is still grounded, but the probe inputs are not tied to earth, so neither one connects the mains to earth. Wrong: ground clip on the hot wire Hot, 120 V Neutral Bench oscilloscope probe tip ground clip 3-prong cord Fault current: hot → clip → scope chassis → earth Probe grounds belong on earth ground only Safer: differential probe Hot, 120 V Neutral Differential probe (inputs not tied to earth) Bench oscilloscope still grounded The probe measures between its two inputs, so neither one connects mains to earth
Figure 9. A bench oscilloscope's probe ground is tied to earth through its power cord. Clipping it to the mains hot wire shorts the hot wire to earth through the probe lead. A differential or isolated probe avoids the problem. Source: Tektronix.

9. Changing AC to DC and back

AC to DC. Nearly all electronics run on DC, so power supplies use diodes to rectify AC into one-way pulses and a capacitor to smooth them. (Recap: rectifiers; smoothing; a complete linear supply.)

DC to AC. An inverter switches a DC input back and forth very rapidly, using transistors as switches, and filters the result into something close to a sine wave.[28] (Recap: a MOSFET as a switch.) Solar panels generate DC, so a home solar system needs an inverter to feed AC into the grid.[28] Grid-connected inverters follow a signal from the grid to time their switching.[28] Solar and battery installations involve high DC and AC voltages and must be installed to code. (Recap: a note on solar and battery systems.)

10. Safety

Mains voltage is lethal. Never work on a live circuit. Switch off and lock out the breaker, then prove the circuit is dead with a meter you have just checked on a known live source. If in doubt, call a licensed electrician.

It is the current that kills. The effect of a shock depends mainly on the current through the body, along with its path, its duration and its frequency.[29] Voltage matters because it drives that current through the body's resistance (I = V/R). With dry skin, about 200 kΩ, touching 120 V passes about 0.6 mA, which is harmless. Soaking wet, at about 10 kΩ, the same 120 V drives 12 mA, above the "can't let go" threshold.[29] The figures below are for 60 Hz through the trunk for one second.[29] (Recap: low voltage can still be dangerous.)

Effects of 60 Hz current through the body
CurrentTypical effect
1 mAThreshold of feeling[29]
5 mAMaximum harmless current[29]; a GFCI trips at about this level[18]
10–20 mASustained muscle contraction: cannot let go; breathing may stop during the shock[29]. OSHA gives the let-go range as 6–25 mA for women and 9–30 mA for men[30]
50–150 mAExtreme pain, respiratory arrest; death is possible[30]
100–300+ mAVentricular fibrillation possible, often fatal[29]

Ventricular fibrillation is a massively irregular, often fatal beating of the heart.[29] The let-go threshold matters because the muscles that close the fingers are stronger than those that open them, so a hand gripping a live wire clamps tighter and cannot release it.[29] Ironically, the body is most sensitive at the 50 and 60 Hz frequencies used for mains power.[29] Low-frequency AC causes this sustained contraction, while DC more often causes a single jolt that throws the victim clear.[31] Mains current can also burn: OpenStax lists the onset of burns at about 300 mA.[29]

Habits that save lives.

When to call an electrician. NFPA advises calling a qualified electrician or your landlord for breakers that trip or fuses that blow frequently, a tingle when you touch an appliance, warm or discolored outlets, a burning or rubbery smell, flickering or dimming lights, or sparks from an outlet. A qualified electrician should also add outlets and install AFCIs.[33]

The whole story in brief

Coming up in this section: 11 RCL Circuits.

Sources

All links were checked in October 2026. External links open in a new tab.

  1. OpenStax, College Physics 2e, section 20.5 "Alternating Current versus Direct Current": https://openstax.org/books/college-physics-2e/pages/20-5-alternating-current-versus-direct-current
  2. Tony R. Kuphaldt, Lessons In Electric Circuits, Volume II (AC), chapter 1, "Basic AC Theory": https://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_1.html
  3. U.S. Department of Energy, "The War of the Currents: AC vs. DC Power" (2014): https://www.energy.gov/articles/war-currents-ac-vs-dc-power
  4. OpenStax, University Physics Volume 2, section 15.1 "AC Sources": https://openstax.org/books/university-physics-volume-2/pages/15-1-ac-sources
  5. Tony R. Kuphaldt, Lessons In Electric Circuits, Volume II (AC), chapter 10, "Polyphase AC Circuits": https://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_10.html
  6. OpenStax, College Physics 2e, section 6.1 "Rotation Angle and Angular Velocity": https://openstax.org/books/college-physics-2e/pages/6-1-rotation-angle-and-angular-velocity
  7. OpenStax, College Physics 2e, section 23.5 "Electric Generators": https://openstax.org/books/college-physics-2e/pages/23-5-electric-generators
  8. OpenStax, College Physics 2e, section 23.11 "Reactance, Inductive and Capacitive": https://openstax.org/books/college-physics-2e/pages/23-11-reactance-inductive-and-capacitive
  9. OpenStax, University Physics Volume 2, section 15.2 "Simple AC Circuits": https://openstax.org/books/university-physics-volume-2/pages/15-2-simple-ac-circuits
  10. Tony R. Kuphaldt, Lessons In Electric Circuits, Volume II (AC), chapter 4, "Reactance and Impedance: Capacitive": https://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_4.html
  11. Tony R. Kuphaldt, Lessons In Electric Circuits, Volume II (AC), chapter 3, "Reactance and Impedance: Inductive": https://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_3.html
  12. OpenStax, University Physics Volume 2, section 15.3 "RLC Series Circuits with AC": https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac
  13. OpenStax, College Physics 2e, section 23.12 "RLC Series AC Circuits": https://openstax.org/books/college-physics-2e/pages/23-12-rlc-series-ac-circuits
  14. Tony R. Kuphaldt, Lessons In Electric Circuits, Volume II (AC), chapter 11, "Power Factor": https://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_11.html
  15. U.S. Department of Energy, Motor Challenge fact sheet "Reducing Power Factor Cost" (PDF): https://www.energy.gov/sites/prod/files/2014/04/f15/mc60405.pdf
  16. H. C. Anderson, A. Al Hadi, E. S. Jones and D. M. Ionel, "Power Factor and Reactive Power in US Residences: Survey and EnergyPlus Modeling," ICRERA 2021, SPARK Laboratory, University of Kentucky (PDF): https://sparklab.engr.uky.edu/sites/spark/files/2024-07/2021_1001_ICRERA2021_ReactivePowerandPF_SEJ.pdf
  17. OpenStax, College Physics 2e, section 23.8 "Electrical Safety: Systems and Devices": https://openstax.org/books/college-physics-2e/pages/23-8-electrical-safety-systems-and-devices
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  20. Electrical Safety Foundation International, "Arc Faults and Electrical Safety" (PDF): https://www.esfi.org/wp-content/uploads/2021/06/Arc-Faults-and-Electrical-Safety-394D.pdf
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  22. Mike Holt Enterprises, "GFCI and AFCI, based on the 2023 NEC" (December 2023): https://www.mikeholt.com/newsletters.php?action=display&letterID=2750
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  24. Tony R. Kuphaldt, Lessons In Electric Circuits, Volume II (AC), chapter 12, "AC Metering Circuits": https://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_12.html
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