Alternating currents (ac) are currents that alternate in direction (usually many times per second).

Alternating currents

• Alternating currents (ac) are currents that alternate in direction (usually many times per second).
• Such currents are produced by voltage sources whose polarities alternate between positive and negative.
• By convention, alternating currents are called ac currents and alternating voltages are called ac voltages.
• One complete variation is referred to as a cycle.
• If a waveform repeats itself at regular intervals, it is called a periodic waveform.

Generation of AC Signal:

• Alternating voltage may be generated by rotating a coil in a magnetic field.
• The value of the voltage generated depends on the (a)number of turns in the coil, (b)strength of the field and (c)the speed at which the coil or magnetic field rotates.
• Michael Faraday discovered the fundamental relationship between the voltage and magnetic flux in a circuit.
• If the flux linking a conductor changes with time, a voltage is induced at its terminal.
• The magnitude of the induced voltage is proportional to the rate of change in the magnetic flux.
• The arrangement of coil & magnet can be understood by the following figure.

• The generated emf is always in the form of sinusoidal voltage.

Fundamental quantities of Sinusoidal Waveform:

• Cycle: One complete set of positive and negative values of alternating quantity is known as cycle.
• one complete cycle is said to spread over 360 degree.
• 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).
• frequency is given by the reciprocal of the time period of the alternating quantity.(f=1/T)
• Amplitude: The maximum value, positive or negative, of an alternating quantity is known as its amplitude
• Peak to Peak Value: It is measured between minimum and maximum peak.

• Angular Velocity: The rate at which the coil of generator rotates to produce the AC signal is known as Angular Velocity.

• Phase: Phase of an alternating current means the fraction of the time period of that alternating current which has elapsed since the current last passed through the zero position of reference.
• If a sinewave does not pass through zero at t=0, it has a phase shift.
• Waveforms can be shifted to left or right.
• Waveform shifted left can be understood as given. It is also known as leading wave with respect to reference zero point.
  
• Waveform shifted right can be understood as given. It is also known as lagging wave with respect to reference zero point.
  
• When we compare two different wave forms, then a leading alternating quantity is one which reaches its maximum (or zero) value earlier as compared to the other quantity.
• Similarly a lagging alternating quantity is one which reaches its maximum or zero value later than the other quantity.
• A plus sign when used in connection with phase difference denotes lead whereas a minus sign denotes lag.

Root Mean Square (RMS) Value:

• The r.m.s. value of an alternating current is given by that steady (d.c.) current which when flowing through a given circuit for a given time produces the same heat as produced by the alternating current when flowing through the same circuit for the same time.
• It is also known as the effective or virtual value of the alternating current.
• The r.m.s. value of a complex current wave is equal to the square root of the sum of the squares of the r.m.s. values of its individual components.
• Irms=I=I_m / √2 or Vrms=V=V_m / √2

Average Value:

• The average value of an alternating current is expressed by that steady current which transfers across any circuit the same charge as is transferred by that alternating current during the same time.
• In the case of a symmetrical alternating current (i.e. one whose two half cycles are exactly similar, whether sinusoidal or non sinusoidal), the average value over a complete cycle is zero.
• Hence, in their case, the average value is obtained by adding or integrating the instantaneous values of current over one half cycle only.
• But in the case of an unsymmetrical alternating current (like half wave rectified current) the average value must always be taken over the whole cycle.
• Vavg=2V_m/π or Iavg=2I_m/π

Form Factor:

• It is the ratio of RMS value of alternating signal to the average value is known as Form factor.
• For a sinusoidal signal the value is 1.11.
• FF=Vrms/Vavg=V_m / √2/2V_m/π = 1.11

Crest or Peak or Amplitude Factor:

• It is defined as the ratio of maximum value to the r.m.s. value of an alternating signal.
• For a sinusoidal signal the value is 1.414.
• The information of this factor helps to find dielectric stress and iron loss as they both are proportional to maximum value.
• PF=Vm/V_m / √2=√2=1.414

Representation of sinusoidal signal in Phasor form:

• The alternating voltages and currents are represented by phasors rotating counter clockwise with the same frequency as that of the alternating quantity.
• A sine wave can be represented by a phasor with the phase angle amount shifted from reference axis and the radius being the rms value of the signal.
• The angle shift of radius from reference is considered as clockwise if phase angle is positive & anticlockwise if phase angle is negative.