An alternating voltage v = vm sin ωt applied to a resistor R drives a current i = im sin ωt in the resistor, im = vm/R. The current is in phase with the applied voltage.
The current through the capacitor is π/2 ahead of the applied voltage. As in the case of inductor, the average power supplied to a capacitor over one complete cycle is zero.
In a purely inductive or capacitive circuit, cos φ = 0 and no power is dissipated even though a current is flowing in the circuit. In such cases, current is referred to as a wattless current.
The phase relationship between current and voltage in an ac circuit can be shown conveniently by representing voltage and current by rotating vectors called phasors. A phasor is a vector which rotates about the origin with angular speed ω. The magnitude of a phasor represents the amplitude or peak value of the quantity (voltage or current) represented by the phasor. The analysis of an ac circuit is facilitated by the use of a phasor diagram.
An interesting characteristic of a series RLC circuit is the phenomenon of resonance. The circuit exhibits resonance, i.e., the amplitude of the current is maximum at the resonant frequency. The quality factor Q is an indicator of the sharpness of the resonance, the higher value of Q indicating sharper peak in the current.
A circuit containing an inductor L and a capacitor C (initially charged) with no ac source and no resistors exhibits free oscillations. The charge q of the capacitor satisfies the equation of simple harmonic motion. The energy in the system oscillates between the capacitor and the inductor but their sum or the total energy is constant in time.
A transformer consists of an iron core on which are bound a primary coil of Np turns and a secondary coil of Ns turns. If the secondary coil has a greater number of turns than the primary, the voltage is stepped-up. This type of arrangement is called a step-up transformer. If the secondary coil has turns less than the primary, we have a step-down transformer.