A.C FUNDAMENTALS * Friend's law of electromagnetic induction * first law:- sates that whenever there is changed in magnetic flux passing through or coil. A voltage is induced in the coil.
* Second law:-
It states that the magnetic of induced voltage is proportional to the rate of change of flux passing i.e, e directly proportional to Q/ dt => e= - d/dt.
Negative sing indicator that direct of induce voltage is in such way that it opposes the cause which has induced it. Then is also known as lenz law.
* Concept of generation of alternative voltage voltage.
Diagram:- (figure.1)
• an alternative voltage can be generated in a coil rotating in a stationary magnetic field. Alternative voltage can also be Generated in a stationary coil placed in a rotating magnetic field.
• In fact voltage is generated in the coil so long as there is relative motion between the coi and magnetic field.
*
Equation of generated alternative voltage:- (figure.2) (figure.2)
• let we are consider a coil A,B having "N" number of turns is placed initial along the region having magnetic field directed along top to bottom.
•Let Q be the magnetic flux passing through the surface of the coil which is the plane of the coil.
•Let w (omega) be the angular speed with which the coil is rotated in anti- clockwise direction. (figure.3)
According to the fraday's law of electromagnetic induction.
the induced voltage in the coil.(figure.4)
Similarly, the instantaneous value of alternative current given by the equivalent, I= I= Ion Sin'w' t.
Where I'm = peak or Max^m value of current.
•A.C--> It is the current whose magnitude remains constant & independent of time is called Direct current.
*Complete cycle of A.C--> It is the one set of position (+ve) and (- ve) Negative value of alternative quantity is called complete cycle.
* Lime period:- it is the time of taken to complete one cycle of the alternative quantity [ time period,
T=2π/w]
*Frequency:--> It is the number of [ frequency=1/time] cycle per second. The frequency is numerically equal to the
Omega= w=2πf.
I= ImSin'w' t
@
question no#1> the instructions value of A.C is given by the equation i= 12 sin 314t, then determine:-
(1.) Peak current
(2.) Frequency
(3.) Time period
Solution:- The given equation of A.C
I= Im sin'w't ('w'=omega)
By Comparing
1.> Peak current Im= 12A
2.> w=314
= 2πf= 314
= f= 314/2π
=314×100/2× 3.14 = 50Hz. Ans.
* Average value of alternative current (Iav g).
• The avarage value of alternative current is the study current that sends the same ammount of sent by alternative current through the same circuit in the same time interval.
Note:- The avarage value of complete cycle of alternating current is zero because charge transfer during the cycle is equal to the charge received during the next - ve cycle.
• Therefore the avarage value of A.C is determine only for half time period means one cycle .
--> Mathmatical expression:- let the instructions value of A.C be i= I'm sin wt. Then avarage value of A.C :-- (figure.5)
note:- hence avarage value of A.C is equal to the 0.637 time the maximum value of current.
*Form factor:- it is the ratio of RMS value to the average value of or an alternating quality.
i.e, form factor= RMS value/Avarage value
For sinusoidal A.C. Form factor= R.M.S current/Avarage current
Form factor= 0.707IM/0.637IM= 1.11
* Peak factor:- It is the ratio of maximum value to the RMS value of an alternating quality.
i.e peak factor = maximum current/RMS = Tim/0.707im
1/0.707= 1.414
Peak factor=1.414(v.v.i)
*
Vector alternative current:- (figure.6)
(figure.6)
•An alternating current can be represented in the form of a rotating vector. The factor has same magnitude equal to the magnitude of the current and rotates with same angular speed omega.
• The magnitude at any instant of time is equal to the vertical component of the vector at that instant.
Thank you. Written by. Abhishek Singh (E.E)
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