## 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 = v

_{m}sinωt applied to a resistor R drives a current i = i_{m}sinωt in the resistor. where, The current is in phase with the applied voltage.
For an alternating current i = i

(1/2) i

Similarly, the rms voltage is defined by,

We have, P = IV = I

_{m}sinωt passing through a resistor R, the average power loss P (averaged over a cycle) due to joule heating is(1/2) i

_{m}^{2}R .To express it in the same form as the dc power (P = I^{2}R), 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 = I

^{2}R## Inductive reactance:

An ac voltage v = v

where i

_{m}sinωt applied to a pure inductor L, drives a current in the inductor i = i_{m}sin (ωt – π/2),where i

_{m}= v_{m}/X_{L}.- X
_{L}= 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 = v

Here,

it is called

The average power supplied to a capacitor over one complete cycle is zero.

_{m}sinωt applied to a capacitor drives a current in the capacitor: i = i_{m}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 = v

is called the

The term cosφ is called the

_{m}sinωt, the current is given by I = i_{m}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

and therefore, the

**simple harmonic motion**:and therefore, the

**frequency ω**of free oscillation is## Transformer:

A

and the currents are related by

If the secondary coil has a greater number of turns than the primary, the voltage is stepped-up (V

If the secondary coil has turns less than the primary, we have a

**transformer**consists of an iron core on which are bound a primary coil of N_{p}turns and a secondary coil of N_{s}turns. If the primary coil is connected to an ac source, the primary and secondary voltages are related byand the currents are related by

If the secondary coil has a greater number of turns than the primary, the voltage is stepped-up (V

_{s }> V_{p}). 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**.