## ALTERNATING CURRENT

 Alternating current Mention of expression for instantaneous current Peak and rms values of alternating current and voltage. AC voltage applied to a resistor Expression for current Phase relation between voltage and current Phasor representation AC voltage applied to an inductor Expression for current Phase relation between voltage and current Phasor representation AC voltage applied to a capacitor Current amplitude Average power Phasor diagram AC voltage applied to series LCR circuit Impedance Phasor diagram solution Analytical solution Electrical resonance : resonant frequency, sharpness of resonance Power in AC circuit Power factor Inductive and capacitive circuit Meaning of wattles current LC oscillations Qualitative explanation Frequency of LC oscillations and total energy of LC circuit LC oscillators Transformer Principle, construction and working Step up and step down transformers Sources of energy losses Numericals Concept based problems
An alternating voltage v = vm sinωt applied to a resistor R drives a current i = im sinωt in the resistor. where, The current is in phase with the applied voltage.
For an alternating current i = im sinωt passing through a resistor R, the average power loss P (averaged over a cycle) due to joule heating is
(1/2) im2R .To express it in the same form as the dc power (P = I2R), a special value of current is used. It is called root mean square (rms) current and is denoted by I: Similarly, the rms voltage is defined by, We have, P = IV = I2R

## Inductive reactance:

An ac voltage v = vm sinωt applied to a pure inductor L, drives a current in the inductor i = im sin (ωt – π/2),
where im = vm /XL.
• XL = ωL is called inductive reactance. The current in the inductor lags the voltage by π/2.
• The average power supplied to an inductor over one complete cycle is zero.

## Coulomb’s Law:

An ac voltage v = vm sinωt applied to a capacitor drives a current in the capacitor: i = im sin (ωt + π/2).
Here, it is called capacitive reactance.
The average power supplied to a capacitor over one complete cycle is zero.
For a series RLC circuit driven by voltage v = vm sinωt, the current is given by I = im sin (ωt + φ) where and where  is the phase difference between voltage across the source and current in the circuit is, is called the impedance of the circuit. The average power loss over a complete cycle is given by, P = V I cosφ.
The term cosφ is called the power factor
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 defined by is an indicator of the sharpness of the resonance, the higher value of Q indicates sharper peak in the current.

## Simple harmonic motion:

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: and therefore, the frequency ω of free oscillation is ## Transformer:

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 primary coil is connected to an ac source, the primary and secondary voltages are related by and the currents are related by If the secondary coil has a greater number of turns than the primary, the voltage is stepped-up (Vs > Vp). This type of arrangement is called a stepup transformer.
If the secondary coil has turns less than the primary, we have a step-down transformer.