E-StoreElectromagnetic Induction and AC Current
16 Sep 2007 14:55:33 IST
Electromagnetic Induction and AC Current
electromagnetic Induction:
The Production of Electromotive force in a conductor when
there is a change in the magnetic flux linkage with coil or
when there is a relative motion of the conductor across a
magnetic field.
Magnetic Flux:
Magnetic Flux through an area dS in a magnetic Field B is
= 
B.dSFaraday's Law:
When the Flux of a magnetic field through a loop changes,
an emf is induced in the loop which is given by :
= -d/dtWhere
= B.dS is the Flux through the loop.The EmF lasts as long as the magnetic Field changes.
Lenz's Law:
It states that the polarity of the induced Emf and the
direction of the induced current is such tat it opposes the
change that has induced it.
Motional Emf:
When a conducting rod of length L moves with a velocity V
in a magnetic field B such that B,V & L are mutually per-
-pendicular to each other then the induced Emf is :
= BLVThis is called as motional Emf.If the circuit is completed
the direction of the current can be worked out by Lenz's
Law.
Induced Electric Field:
A time varying Magnetic field induces an electric field.If
a conductor is placed in this field , an induced Emf is
produced :
= E.dL (Here is Cyclic Integral)
= - d/dt
E.dL = - d/dt (Cyclic Integral)Self Induction:
A Current Carying loop produces a magentic Flux Through
the area.
= Li Where L is the Self Inductance.If Current Changes in the loop the Induced Emf is given
by:
= - d/dt = -L di/dtFor a Solenoid of n turns,
= -n d/dt B.dSSelf Inductance of a long solenoid is:
L = 
r0n2LA
r0n2LAWhere
r is the relative magnetic permeability of the core , n is no. of turns per unit length , L is the length of solenoid.
and A is the cross-sectional area of the solenoid.
Mutual Inductance:
A changing current in one circuit causes a changing Flux &
hence an induced Emf in a neighbouring circuit.
N22 = Mi1
2 = Mi1Where M is the Mutual Inductance of coils 1 2
M = N22/i1 = N11/i2
2/i1 = N11/i2
1 = -M di1/dt
2 = -M di2/dtAlternating Current and Voltage:
Current and Voltage varying Sinusoidally are called as AC
and AV (Alternating Current and Voltage)
V = V0Sin
t
ti = i0Sint
tMean Values of Voltage and Current:
(a)In one complete cycle:
V = 0 , i = 0
(b)In Half Cycle:
V = 2V0/
, i = 2i0/
, i = 2i0/
(c)Root mean square Values:
Vrms = V0/
2
2irms = i0/2
2Where V0 and i0 are peak Voltage and current.
AC Circuit with a Resistor:
E = E0Sint = E0Sint/R
t = E0Sint/RAC Circuit with a capacitor:
V = E0Sint
ti = E0/(1/C) [ Sin(t+/2) ]
C) [ Sin(t+/2) ]Xc = 1/C is capacitive Reactance.
C is capacitive Reactance.i = i0Sin(t + /2)
t + /2)AC Circuit with an inductor:
V = E0Sint
ti = i0Sin(t - /2) {Voltage Leading}
t - /2) {Voltage Leading}XL = L Inductive Reactance.
L Inductive Reactance.LCR Circuit (Inductor,capacitor,Resistor Circuit in series):
Impedance , Z = (L - 1/C)2 + R2
(L - 1/C)2 + R2The above Expressino can be very well be given as:
Z = (XL-XC)2 + R2
(XL-XC)2 + R2
For Phase angle ,
,Tan = XL-XC/R
= XL-XC/RResonance:
L = 1/CThe Impedance of the circuit is equal to R only.
0 = 1/LCf0 = 1/2LC (Resonance Frequency)
LC (Resonance Frequency)Power:
Average Power ,
Pavg = Erms.Irms.Cos
Pavg = 1/2*E0I0Cos
Where Cos is the power factor.
is the power factor.Cos = R/Z
= R/ZChoke Coil:
A Coil with low resistance and high inductance used to reduce current in AC Circuit without much heat loss is
called as a Choke Coil.
Power factor , Cos = R / (L - 1/C)2 + R2
= R / (L - 1/C)2 + R2R is Low and L is High thus is Reducing current.
Hope you all find it useful.
I have typed this whole thing the third time as before this two times I by mistake pressed (ctrl+w) , Press it
and you will find it out what happens.
plZ rate me if useful.
Cheers!!!!!!!!!!!!@@@@@@!!!!!!!!!!!
Comments (19)
Swashata Ghosh
Blazing goIITian
Joined: 20 May 2007 20:03:31 IST
Posts: 459
16 Sep 2007 15:46:06 IST
Like
0 people liked this
Nice
16 Sep 2007 15:46:47 IST
Like
0 people liked this
nice article
feeling sorry fr u(u had to rewrite it thrice :( )
feeling sorry fr u(u had to rewrite it thrice :( )
Free Sign Up!
Preparing for IIT-JEE ?
Arihant Revision Package for IIT JEE - Books, Practice Tests + Rank Predictor
@ INR 1,995/-
For Quick Info
|
|
|
|
|
| 35,229,755 Engineering Questions Attempted |
6,69,530 Visitors Monthly |
79 Engg. Exam Covered |
909 Students Currently Online |
Connect with Us  |
 |
Vriti Communities
Privacy Policy © Vriti 2011