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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.dS

Faraday'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/dt

Where

= 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 :

= BLV

This 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/dt

For a Solenoid of n turns,

= -n d/dt B.dS

Self Inductance of a long solenoid is:

L = _r₀n²LA

Where

_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

Where M is the Mutual Inductance of coils 1 2

M = N₂₂/i₁ = N₁₁/i₂

₁ = -M di₁/dt

₂= -M di₂/dt

Alternating Current and Voltage:

Current and Voltage varying Sinusoidally are called as AC

and AV (Alternating Current and Voltage)

V = V₀Sint

i = i₀Sint

Mean Values of Voltage and Current:

(a)In one complete cycle:

V = 0 , i = 0

(b)In Half Cycle:

V = 2V₀/ , i = 2i₀/

(c)Root mean square Values:

V_rms= V₀/2

i_rms = i₀/2

Where V₀and i₀ are peak Voltage and current.

AC Circuit with a Resistor:

E = E₀Sint = E₀Sint/R

AC Circuit with a capacitor:

V = E₀Sint

i = E₀/(1/C) [ Sin(t+/2) ]

X_c = 1/C is capacitive Reactance.

i = i₀Sin(t + /2)

AC Circuit with an inductor:

V = E₀Sint

i = i₀Sin(t - /2) {Voltage Leading}

X_L = L Inductive Reactance.

LCR Circuit (Inductor,capacitor,Resistor Circuit in series):

Impedance , Z = (L - 1/C)² + R²

The above Expressino can be very well be given as:

Z = (X_L-X_C)² + R²

For Phase angle ,

Tan = X_L-X_C/R

Resonance:

L = 1/C

The Impedance of the circuit is equal to R only.

₀ = 1/LC

f₀ = 1/2LC (Resonance Frequency)

Power:

Average Power ,

P_avg = E_rms.I_rms.Cos

P_avg = 1/2*E₀I₀Cos

Where Cos is the power factor.

Cos = R/Z

Choke 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 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!!!!!!!!!!!!@@@@@@!!!!!!!!!!!

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