notes prepared by subhankar Karmakar
Alternating current:
An alternating current is that current whose magnitude changes continuously with time and direction reverses periodically.
When a coil is rotated in a magnetic field, an alternating EMF is induced in it which is given by the relation
ℰ = ℰₒ sin (ⲱt) ---------------------------- (i)
When applied to a circuit of resistance R, it will produce a current Ｉ such that
Ｉ = ℰ/R = (ℰₒ/R) sin (ⲱt) = Ｉₒ sin (ⲱt)--------(ii)
Therefore, the current in the circuit varies sinusoidally with time and it is called alternating current.
Ｉ = Instantaneous Current
Ｉₒ = ℰₒ/R = Maximum or peak value of current. It is also called current amplitude.
Amplitude: The maximum value attained by an alternating current in either direction is called its amplitude or peak value and is denoted by Ｉₒ.
Time Period: The time taken by an alternating current to complete one cycle of its variations is called its time period and is denoted by T.
This time is equal to the time taken by the coil to complete one rotation in the magnetic field.
T = 2π/ⲱ ; where ⲱ = angular velocity of the coil.
Frequency: The number of cycles completed per second by an alternating current is called its frequency and is denoted by f. It is equal to the frequency of rotation of the coil in the magnetic field.
f = 1/T = ⲱ/(2π)
∴ Ｉ = Ｉₒ sin (ⲱt) = Ｉₒ sin (2πft) = Ｉₒ sin (2πt/T) -------- (iii)
• In India AC supply has a frequency of 50 Hz
Mean / Average Value of AC over a half cycle:
Average value of AC : It is defined as that value of direct current which sends the same charge in a circuit in the same time as is sent by the given alternating current in its half time period. It is denoted by Ｉₘ or Ｉₐᵥ.
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