Generation of AC Single Phase Sinusoidal.

(A) GENERATION OF AC SINGLE PHASE SINUSOIDAL VOLTAGE

                                                                AC circuits widely used in domestic and industrial applications, When applied voltage is alternating nature means the flow of electrons forward and reverse both the direction. In DC circuit only resistance will oppose the flow of electrons but in AC circuit resistance, capacitance and inductance oppose the flow of electrons. Firstly we talk about generating of alternating sinusoidal voltage single phase three phases discussed later. In this image any rectangular coil having turn (N) kept in uniform magnetic field (B) and the coil rotating anticlockwise at uniform angular velocity ω red/sec at vertical position (A) flux φ linking the coil is zero because it is parallel to the magnetic field at this position angle is 0 degree between the magnetic field and the coil.   

Rectangular coil in
magnetic field B

When the coil starts moves anticlockwise direction some angle increase the flux linking hence the EMF (voltage) induced in figure (B). In figure (C) the coil moved from 0 to 90 degree at this position flux linking maximum because the line of magnetic field and the coil perpendicular to each other maximum value EMF and linking flux φ max .Again the coil moved from 90 to 180 degree flux linking reduced figure (D) at 180 degree flux φ linking the coil is zero because it is parallel to the magnetic field at this electrons completed half cycle. Next the same cycle flow of electrons reverses from 180 to 270 degree maximum flux linking  but negative value but the coil achieved 270 to 360 value of flux linking zero and completed a cycle.  

(B) ALTERNATING QUANTITY SINUSOIDAL WAVE FORM

AC sinusoidal wave form 

The amplitude alternating EMF varies at w.r.t. time means at point A less than at point B they are instantaneous value. The maximum value (+Em) attends by EMF at 90 degree called a peak or maximum value. Time period (T) is the time taken in second to complete one cycle. The number of cycle completed in one second called frequency measured in (Hz)

In this figure maximum flux 𝚽 in downward direction at any angle θ the flux divided in two component   𝚽m sin⍵t along with the coil and 𝚽m cos⍵t perpendicular to coil mention in image. Along a the coil flux not induced  perpendicular component 𝚽m cos⍵t EMF induced in the coil .when no of turn in the coil is N then value of EMF is

e= -N *d𝚽 / dt (rate of change of flux wrt time)

the value of  𝚽 = 𝚽m cos⍵t 

e= -N *d𝚽 / dt 

Kept value of  𝚽  in above equation become

e= -N *d  / dt *( 𝚽m cos⍵t)

e=N*𝚽m ⍵sin⍵t(after differentiating)

e=Em sin⍵t where Em= N*𝚽m*⍵ induced emf and induced current is i=Im sin⍵t the are the induced emf and current in sinusoidal  AC wave.