Alternating Current (AC): Waveforms, Frequency, Voltage

• Alternating current (AC) periodically reverses direction and changes its magnitude continuously with time.
• AC powers homes, businesses, and industry.

AC Waveform

• The standard AC power waveform in electric power circuits is a sine wave.
• Triangular and square waves are also possible waveforms.
• An alternator, a device converting mechanical energy into electrical energy, produces AC.

Frequency

• Frequency is the number of complete cycles in one second, measured in Hertz (Hz).
• AC power systems have varying frequencies by country; 60 Hz is common in North America, and 50 Hz is common in Europe.

Voltage

• The voltage of an AC source varies sinusoidally with time.
• Root Mean Square (RMS) voltage is the effective voltage of an AC supply.
• RMS voltage is the equivalent DC voltage that would produce the same power dissipation in a resistive load.

Current

• In a purely resistive AC circuit, current is in phase with the voltage.
• Current and voltage are out of phase in circuits with reactive components (capacitors or inductors).

AC Circuits with Resistance (R)

• Voltage and current are in phase in purely resistive circuits.
• Ohm's Law (V = IR) applies instantaneously.
• Power dissipated is P = I²R = V²/R.
• Power is always positive, with resistors only dissipating energy.

AC Circuits with Inductance (L)

• Inductors oppose changes in current.
• Current lags behind the voltage by 90 degrees in a purely inductive circuit.
• Inductive reactance is XL = ωL, where ω is the angular frequency (2πf) and L is the inductance.
• Voltage leads the current.
• Inductors store energy in a magnetic field but do not dissipate it.

AC Circuits with Capacitance (C)

• Capacitors oppose changes in voltage.
• Current leads the voltage by 90 degrees in a purely capacitive circuit.
• Capacitive reactance is XC = 1/(ωC), where ω is the angular frequency (2πf) and C is the capacitance.
• Capacitors store energy in an electric field but do not dissipate it.
• Voltage lags the current.

Impedance

• Impedance (Z) is the total opposition to current flow in an AC circuit, including resistance and reactance.
• It is measured in ohms (Ω).
• For a series RLC circuit, Z = √(R² + (XL - XC)²).
• Impedance in AC circuits corresponds to resistance in DC circuits.

Phase Angle

• Describes the phase difference between voltage and current in an AC circuit.

Power in AC Circuits

• Instantaneous power in an AC circuit varies with time.

Average (Real) Power

• Average power (P) is the power actually dissipated in the circuit, typically by the resistor.
• P = Vrms * Irms * cos(φ), where φ is the phase angle between voltage and current.
• It is measured in watts (W).

Reactive Power

• Reactive power (Q) is the power exchanged between the source and reactive components (inductors and capacitors).
• Q = Vrms * Irms * sin(φ).
• It is measured in volt-amperes reactive (VAR).
• Reactive power does no useful work.

Apparent Power

• Apparent power (S) is the product of Vrms and Irms.
• S = Vrms * Irms
• It is measured in volt-amperes (VA).
• It represents the total power supplied by the source, including both real and reactive power.
• S² = P² + Q².

Power Factor

• The power factor (PF) is the ratio of real power to apparent power.
• PF = P/S = cos(φ).
• It indicates how effectively the supplied power is being used.
• A power factor of 1 (unity) indicates that all power is being used effectively (resistive load).
• A low power factor indicates a large portion of the power is reactive and not doing useful work.
• Power factor correction involves adding capacitors or inductors to the circuit to bring the power factor closer to 1 and improve efficiency.

Series RLC Circuits

• A series RLC circuit contains a resistor, inductor, and capacitor connected in series.
• The impedance is Z = √(R² + (XL - XC)²).
• The phase angle is φ = tan⁻¹((XL - XC)/R).
• The circuit can be inductive (XL > XC), capacitive (XC > XL), or resistive (XL = XC), depending on the component values and frequency.

Resonance in Series RLC Circuits

• Resonance occurs when XL = XC.
• At resonance, the impedance is at its minimum (Z = R), and the current is at its maximum.
• The resonant frequency is f₀ = 1/(2π√(LC)).
• At resonance, voltage and current are in phase (φ = 0°) and the power factor is 1.

Parallel RLC Circuits

• A parallel RLC circuit contains a resistor, inductor, and capacitor connected in parallel.
• The analysis is more complex than for series circuits; often admittance (the inverse of impedance) is used.
• At resonance in a parallel RLC circuit, the impedance is at its maximum, and the current from the source is at its minimum.

Transformers

• Transformers step up or step down AC voltages.
• They consist of two or more coils of wire wound around a common core.
• The ratio of the number of turns in the primary coil (Np) to the number of turns in the secondary coil (Ns) determines the voltage transformation ratio (Vp/Vs = Np/Ns).
• Step-up transformers increase voltage (Ns > Np), while step-down transformers decrease voltage (Ns < Np).
• Power in the primary coil is ideally equal to the power in the secondary coil (VpIp = VsIs), assuming no losses.

AC Power Transmission

• AC is used for long-distance power transmission because it can be efficiently stepped up to high voltages using transformers, reducing current and minimizing I²R losses in the transmission lines.
• High-voltage AC is then stepped down to lower voltages for distribution to homes and businesses.