Alternating current (AC) is electric current whose direction reverses periodically, usually with a magnitude that also changes over time. It differs from direct current (DC), which flows in one direction. Alternating voltages and currents are commonly represented by sinusoidal waveforms, although AC need not be sinusoidal. AC is the principal form of electricity used in power distribution because its voltage can be changed efficiently by transformers, enabling high-voltage transmission and lower-voltage delivery to consumers. (energy.gov)
Waveforms and frequency
A sinusoidal alternating current can be expressed as
[ i(t)=I_{\mathrm{pk}}\sin(2\pi ft+\phi), ]
where (i(t)) is instantaneous current, (I_{\mathrm{pk}}) is its peak magnitude, (f) is frequency, and (\phi) is the initial phase angle. Frequency counts complete cycles per second; the period is (T=1/f). Phase specifies a waveform’s position within its cycle and allows comparison between currents or voltages of the same frequency. (archives.standards.doxcelerate.com)
The United States power system operates at a nominal frequency of 60 hertz: 60 complete cycles per second, not 60 individual direction reversals. A sinusoidal current changes direction twice per cycle. Its signed average over a complete cycle is zero, but this does not mean that it transfers no energy. When current and voltage reverse together in a resistive load, their product remains nonnegative. (energy.gov)
Effective values and electrical power
AC magnitudes are frequently specified using the root mean square (RMS), rather than the peak value. For a periodic current,
[ I_{\mathrm{rms}} =\sqrt{\frac{1}{T}\int_0^T i^2(t),dt}. ]
This definition uses an integral to average the squared current over one period. The RMS current produces the same average heating in a fixed resistor as a direct current of that magnitude. For a sinusoid,
[ I_{\mathrm{rms}}=\frac{I_{\mathrm{pk}}}{\sqrt{2}}, \qquad V_{\mathrm{rms}}=\frac{V_{\mathrm{pk}}}{\sqrt{2}}. ]
The square-root-of-two relationship is specific to sinusoidal waveforms, not a universal conversion for AC. (openstax.org)
Instantaneous electrical power is (p(t)=v(t)i(t)). For sinusoidal voltage and current separated by phase angle (\theta), average power is
[ P=V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\theta. ]
The factor (\cos\theta) is the power factor in this sinusoidal case. Ideal capacitors and inductors alternately absorb and return energy, giving zero average power dissipation, whereas resistance converts electrical energy into heat. (openstax.org)
Resistance, reactance, and impedance
The behavior of an AC circuit depends on frequency as well as its components. In an ideal resistor, voltage and current are in phase, and Ohm’s law applies instantaneously. In an ideal capacitor, current leads voltage by one-quarter cycle; in an ideal inductor, current lags voltage by one-quarter cycle. (openstax.org)
The opposition associated with capacitance or inductance is called reactance. Its magnitudes are
[ X_C=\frac{1}{2\pi fC}, \qquad X_L=2\pi fL, ]
where (C) is capacitance and (L) is inductance. Capacitive reactance decreases with increasing frequency, while inductive reactance increases. Thus, a component’s response cannot generally be described by a single frequency-independent resistance. (openstax.org)
Resistance and reactance combine into electrical impedance. For a series resistor–inductor–capacitor circuit, its magnitude is
[ |Z|=\sqrt{R^2+(X_L-X_C)^2}. ]
Both the current amplitude and its phase relative to the source depend on this impedance. When (X_L=X_C), the reactive contributions cancel: the series circuit reaches electrical resonance, and its impedance is purely resistive in the ideal model. (openstax.org)
Generation and voltage transformation
An electric generator produces alternating voltage through electromagnetic induction. Relative rotation between coils and a magnetic field changes the magnetic flux through the coils. In an idealized generator rotating uniformly in a uniform field, the induced voltage varies sinusoidally. Mechanical energy supplied to the generator is thereby converted into electrical energy. (openstax.org)
An electrical transformer transfers energy between windings through changing magnetic flux. For an ideal transformer,
[ \frac{V_s}{V_p}=\frac{N_s}{N_p}, ]
where (N_p) and (N_s) are the primary and secondary winding turns. Raising voltage reduces the current needed to transmit a given power under otherwise comparable conditions. This reduces resistive line losses, proportional to (I_{\mathrm{rms}}^2R). Transformers consequently allow an electrical grid to use different voltage levels for transmission and local distribution. A steady DC input does not sustain this ordinary transformer action. (openstax.org)
Three-phase systems
Large power systems commonly use three-phase electric power. A balanced three-phase supply has three sinusoidal voltages of equal magnitude and frequency, displaced from one another by 120 degrees, or one-third of a cycle. Three-phase equipment serves industrial loads, including electric motors, and can also supply single-phase loads. (ferc.gov)
Windings and loads may be connected in star, also called wye, or delta arrangements. In a balanced star connection, line-to-line voltage is (\sqrt{3}) times the phase voltage. In a delta connection, line voltage equals phase voltage. The distinction matters when specifying equipment voltages and calculating currents and total power. (archives.standards.doxcelerate.com)
Historical development and electronic conversion
AC distribution expanded during the late nineteenth-century competition known as the war of the currents. George Westinghouse’s company developed AC systems using technologies that included Nikola Tesla’s polyphase inventions. The 1893 Chicago World’s Fair and the Niagara Falls project, which delivered power to Buffalo in 1896, were prominent demonstrations of AC power’s commercial application. (energy.gov)
AC can also be produced electronically rather than by a rotating generator. A power inverter converts DC into AC by controlled switching, with filtering used to shape the output waveform. Such conversion connects DC-producing solar cells and batteries to AC networks. Inverters use transistors made from semiconductor materials; their controls can coordinate output with the grid and regulate reactive-power exchange. (energy.gov)