Alternating Current (AC) and RMS Value

• Alternating current (AC) periodically reverses direction and changes magnitude continuously with time.
• Direct current (DC) flows in one direction.
• AC is used to power homes and industries because of its efficient transmission over long distances using transformers.
• An AC generator includes a coil rotating in a magnetic field, thus inducing a sinusoidal voltage.
• The instantaneous voltage (V) produced by an AC generator is described by V = V₀sin(ωt).
• V₀ represents the peak voltage or amplitude.
• ω is the angular frequency (ω = 2πf).
• f is the frequency of the AC.
• Common AC frequency in household circuits is 50 Hz or 60 Hz.

Root Mean Square (RMS) Value

• The RMS value of AC is equivalent to the DC value that produces the same heating effect in a resistor.
• RMS voltage (Vrms) represents the effective value of the alternating voltage.
• Vrms = V₀ / √2 ≈ 0.707 V₀.
• RMS current (Irms) represents the effective value of the alternating current.
• Irms = I₀ / √2 ≈ 0.707 I₀.
• V₀ and I₀ are the peak values for voltage and current.

Power in AC Circuits

• Instantaneous power (P) in an AC circuit is calculated as P = VI.
• Voltage and current are in phase in a purely resistive circuit.
• Average power (Pavg) dissipated in a resistor is Pavg = Vrms * Irms = (Vrms)² / R = (Irms)² * R.
• The average power equals half the peak power for sinusoidal AC: Pavg = P₀ / 2.
• Voltage and current may not be in phase in circuits featuring inductors and capacitors, leading to a power factor.

Phase Relationships

• Voltage and current are in phase in a purely resistive AC circuit.
• In a purely inductive AC circuit, current lags voltage by 90 degrees (π/2 radians).
• Current leads voltage by 90 degrees (π/2 radians) in a purely capacitive AC circuit.
• Phase relationships are important when calculating power in AC circuits with reactive components (inductors and capacitors).

AC Circuit Components

• Resistors (R) impede current flow and dissipate energy as heat.
• Inductors (L) store energy in a magnetic field when current flows through them.
• Inductive reactance (XL) is the opposition to current flow in an inductor: XL = ωL = 2πfL.
• Capacitors (C) store energy in an electric field when voltage is applied across them.
• Capacitive reactance (XC) is the opposition to current flow in a capacitor: XC = 1 / (ωC) = 1 / (2πfC).

Impedance in AC Circuits

• Impedance (Z) is the total opposition to current flow in an AC circuit, including resistance and reactance.
• For a series RLC circuit, Z = √(R² + (XL - XC)²).
• The phase angle (φ) between voltage and current is given by tan(φ) = (XL - XC) / R.

Resonance

• Resonance occurs in an RLC circuit when XL = XC.
• Impedance (Z) is at its minimum and equal to resistance (R) at resonance.
• The resonant frequency (f₀) is the frequency at which resonance occurs: f₀ = 1 / (2π√(LC)).
• Current is at its maximum, and the circuit is purely resistive at resonance.

Transformers

• A transformer is a device used to either increase or decrease AC voltage.
• Includes two coils (primary and secondary) that are wound around a common iron core.
• The voltage ratio is proportional to the turns ratio: Vp / Vs = Np / Ns.
• Vp and Vs represent the primary and secondary voltages.
• Np and Ns represent the number of turns in the primary and secondary coils.
• A step-up transformer has more turns in the secondary coil (Ns > Np) and increases voltage.
• A step-down transformer has fewer turns in the secondary coil (Ns < Np) and decreases voltage.
• Transformers are used in power transmission to reduce current and minimize energy loss due to resistance.

Power Transmission

• AC is utilized in power transmission as it can be transformed to high voltages for long-distance transmission.
• It can then be stepped down to lower voltages for use in homes and industries.
• High-voltage transmission reduces current, therefore reducing power loss due to resistance in transmission lines.
• Power loss (P_loss) in transmission lines is P_loss = I²R, where I is the current and R is the resistance of the lines.
• Transformers enable efficient and cost-effective power distribution over long distances.

Applications of AC

• Household appliances and lighting
• Electric motors
• Power grids and transmission
• Electronic devices and circuits
• Radio and telecommunications