Alternating current

Alternating current is the current whose magnitude changes with time periodically.
Instantaneous value of alternating current is given by,
                   I= I○ sinωt or I= I○cos ωt.

Where I○= peak or maximum value of A.C. or amplitude of A.C.; I= value of current at instant t.
ω= 2π/T =2πf = angular frequency of A.C. ; T= time period I.e. time taken to complete one full cycle.
F= frequency of A.C.
Similarly, alternating e.m.f. changes in magnitude continuously with time and reverses it's direction periodically.
Instantaneous value of alternating e.m.f. is given by
E= E○ sin ωt or E= E○cos ωt. 

The Average ,RMS, and peak value of alternating current and Alternating Voltage

Mean or average value of an alternating current and voltage
It is defined as that value of steady current which would sent same amount of charge through a circuit in the time of half cycle (π/2)as is sent by the A.C. throudh the same circuit when passed for the same time.

I(mean)=2I○/π , E(mean)= 2E○/π
Here, I○ and E○ are peak current and voltage.

Root mean square or effective value of an Alternating Current and Voltage
It is the steady current which when passed through a given resistor for a certain time, shall produce the same heat as given A.C. shall do when passed for the same time.

I(RMS)= I○/√2= 0.707I○, E(RMS)= E○/√2= 0.707 E○
br /> Representation of A C. Circuit and voltage by phasor diagrams
In order to show phase relationship between voltage and current in an AC circuit, we use phasors. the analysis of an AC circuit is facilitated by the use of phasor diagram. Phasor

Animated representation of a rotating vector

is a diagram which rotates about the origin with an angular speed omega. The vertical components of the phasors U and I represent sinusoidally varying quantities voltage and current.