Alternating CurrentMind Map

Alternating current and voltage change magnitude and direction periodically with time. In most circuits, they are represented by sine or cosine functions such as I = I0 sinωt and V = V0 sinωt. A complete repetition is one cycle, whose duration is the time period T. Frequency f is the number of cycles per second, and angular frequency is ω = 2πf. Since AC changes continuously, useful values include peak, RMS and mean values. RMS value is most important because it gives the equivalent DC heating effect. Mean value over a full cycle of symmetrical AC is zero, while mean over a half cycle is non-zero. Phase difference tells how much one AC quantity leads or lags another.

A resistor, inductor and capacitor respond differently to alternating current. In a pure resistor, current and voltage are in the same phase and energy is dissipated as heat. In a pure inductor, voltage leads current by 90° because the inductor opposes change in current; its opposition is inductive reactance XL = ωL. In a pure capacitor, current leads voltage by 90° because current is maximum when voltage changes fastest; its opposition is capacitive reactance XC = 1/ωC. These phase relations are best represented by phasor diagrams, where rotating vectors show relative phase. Ideal inductor and capacitor do not consume average power over a full cycle.

A series LCR circuit contains resistance, inductance and capacitance connected in series with an AC source. The resistor voltage is in phase with current, inductor voltage leads current by 90°, and capacitor voltage lags current by 90°. Their combined opposition is impedance, Z = √[R² + (XL - XC)²]. Resonance occurs when XL = XC, so inductive and capacitive reactances cancel. At resonance, impedance becomes minimum and equal to R, current becomes maximum, phase difference becomes zero and power factor becomes one. Resonance frequency is f0 = 1/(2π√LC). The quality factor describes sharpness of resonance. Resonance is used in radio tuning, filters and frequency selection circuits.

Power factor tells how effectively an AC circuit converts supplied electrical energy into useful work. In an AC circuit, voltage and current may have a phase difference ϕ. Average power consumed is Pavg = VrmsIrms cosϕ, where cosϕ is the power factor. If voltage and current are in phase, cosϕ = 1 and power use is maximum. If phase difference is 90°, as in an ideal inductor or capacitor, average power is zero and current is called wattless current. In practical circuits, low power factor increases current for the same useful power, causing greater transmission loss I²R. Power factor correction uses capacitors or suitable devices to reduce phase difference and improve efficiency.

A transformer is an AC device that changes voltage using mutual induction. It consists of primary and secondary coils wound on a laminated soft iron core. When AC flows in the primary coil, it produces changing magnetic flux in the core. This changing flux links the secondary coil and induces an emf according to Faraday’s law. In an ideal transformer, Vs/Vp = Ns/Np and input power equals output power, so VpIp = VsIs. A step-up transformer has more turns in the secondary and increases voltage while decreasing current. A step-down transformer has fewer secondary turns and decreases voltage while increasing current. Practical transformers have losses due to copper resistance, eddy currents, hysteresis and flux leakage.