SINGLE PHASE A.C CIRCUITS ELECTRICAL ENGG SCIENCE CHAPTER - 6

CONTENT 1. Generation of alternating voltage and current 2. Different forms of E.M.F equations. 3. A.C through R, L and C and power factor 4. A.C through R,R-C and R-L series and parallel circuits 5. Active and reactive components of circuit & Active, reactive and apparent power.

What is A.C? An alternating current (a.c) is the current which changes periodically both in magnitude and direction.

Different A.C. waveforms

Cycle One complete set of positive and negative values of alternating quantity is known as cycle.

Time Period The time taken by an alternating quantity to complete one cycle is called its time period T.

Frequency The number of cycles/second is called the frequency of the alternating quantity. Its unit is hertz(Hz) f= 𝑃𝑁 120 Also f= 1 𝑇 or T= 1 𝑓

Amplitude The maximum value, positive or negative, of an alternating quantity is known as its amplitude.

Generation of alternating voltage and current The machine which are used to generate electrical voltages are called generators. The generators which generate purely sinusoidal a.c. voltages are called ALTERNATORS.

Generation of alternating voltage and current Basic principle of an alternator is the principle of electromagnetic induction. The sine wave is generated according to FARADAY’S LAW OF ELECTROMAGNETIC INDUCTION.

Faraday’s Law of Electromagnetic Induction Whenever there is a relative motion between the conductor and the magnetic field in which it is kept, an e.m.f. gets induced in the conductor. The relative motion may exist because of movement of conductors with respect to magnetic field or movement of magnetic field with respect to conductor.

Let us see how an alternator produces a sine wave, with the help of simplest form of an alternator called single turn or single loop alternator.

Different forms of E.M.F equations The standard form of an alternating voltage is given by,

Different forms of E.M.F equations

R.M.S Value The r.m.s value of an alternating current is given by that steady current (d.c) which, when flowing through a given time, produces the same amount of heat as produced by the alternating current, which when flowing through the same circuit for the same time.

R.M.S Value

Average Value The average value of an alternating quantity is defined as that value which is obtained by averaging all the instantaneous values over a period of half cycle.

Form Factor (Kf)

Peak Factor (KP)

Phase The phase of an alternating quantity at any instant is the angle Ф (in radians or degrees) travelled by the phasor representing that alternating quantity upto the instant of consideration, measured from the reference.

Phase

Phase Difference (In Phase)

Phase Difference (Lag)

Phase Difference (Lead)

Phasor Diagram In phase

Apparent Power (S) It is defined as the product of r.m.s value of voltage (V) and current (I). It is denoted by S. It is measured in unit volt-amp (VA) or kilo volt-amp (kVA).

Real or True Power (P) It is defined as the product of applied voltage and active component of the current. It is real component of the apparent power. It is measured in unit watts (W) or kilo watts (kW).

Reactive Power (Q) It is defined as product of the applied voltage and the reactive component of the current. It is represented by Q. It is measured in unit Volt-Amp Reactive (VAR) or kilo Volt-Amp Reactive (kVAR)

Power Factor It is defined as factor by which the apparent power must be multiplied in order to obtain the true power. It is the ratio of true power to apparent power.

Power Factor It is also defined as the ratio of resistance to the impedance. KEYPOINT: Nature of power factor is always determined by position of current with respect to the voltage.

Power Factor If current lags voltage power factor is said to be lagging. If current leads voltage power factor is said to be leading.

A.C through R

Current

Phasor Diagram

Power

A.C through L

Current

Phasor Diagram

Power

A.C through C

Current

Phasor Diagram

Power

AC through RL series circuit

Impedance

Power

AC through RC series circuit

Power