Magnetic Flux Density Definition:

(a) Definition: Magnetic flux (0) through a surface is defined as the total number of magnetic lines of induction passing through the surface B.A = BA cos ∅.
(b) Unit: Unit of ∅ is weher in S.I. and maxwell in C.G.S. system.
I weber = 10⁸ maxwell.
(C) Dimensional Formula: Dimension of o is [ML² A –¹T–²].

I) First law: Whenever the magnetic flux linked with a circuit changes, an induced electromotive force is set up in it. The induced e.m.f. lasts so long as the change in magnetic flux persists.
(ii) Second law: The magnitude of the induced e.m.f. is directly proportional to the time rate of change of the magnetic flux do linked with the circuit ie.
|M| ≤ d∅/dt
Combining E = -(∅²-∅¹)/t= d∅/dt

It states that the direction of the induced e.m.f. is always such that it opposes the very cause producing it. It obey’s law of conservation of energy. It is also known as 3rd law of electromagnetic induction.

(a) by changing B.
(b) by changing area A, E = B/V
(c) by changing the relative orientation of the
coil and the field E =nBAw sin Wt
= E⁰ sin wt (E = nBAw)

Stretch the thumb, the forefinger and the central finger of your right hand mutually perpendicular to one another. If the forefinger points towards the direction of the magnetic field and the thumb points towards the direction of motion of the conductor then the central finger will always points towards the direction of induced e.m.f. or induced current.

These are closed loops or whirls of induced current set up in a metal body circulating in a plane perpendicular to the magnetic lines of induction. It is also known as Foucault current.

Eddy currents can be reduced by taking laminated iron core.

(a) induction furnace
(b) dead beat galvanometer
(c) a.c. induction motor
(d) electrical brake etc.

Eddy currents are harmful as it increases energy loss and increase wear and tear. Eddy currents are analogous to friction in mechanics.

circuit e.g a coil by virtue of which it opposes the change (i.e. growth or decay) in strength of the current flowing through the circuit by inducinga current upon itself
∅=LI
OR E= -L.(dk/dt).

(a) Definition : The self inductance of a circuit is numerically equal to the induced electromotive force in the circuit when rate of change of current in the circuit is unity.
(b) Unit Henry : It is the unit of self inductance. The self inductance of a coil 1s said to be 1 henry when a current changing at the rate of 1 ampere per second induces an induced e.m.f. ofl volt in it.
(c) Expression: Self inductance of a long solenoid is given by L =H All
where n = number of turns/length
l= total length of solenoid
A = cross section area
The analog of self inductance in mechanics is mass.

It is the phenomenon of production of an induced e.m.f. (or current) in a circuit by changing the current flowing in a neighbouring circuit ∅² = MI¹ or E² =- M(dl/dt)

(a) Definition: The mutual inductance of a pair of coils is numerically equal to the induced e.m.f. in the secondary coil by a unit rate of change of current in the primary coil.
(b) Unit: Unit of mutual inductance is henry (H). The mutual inductance of a given pair of coils is 1 henry when a current changing at the rate of one ampere per second in the primary coil produced an e.m.f. of 1 volt in the secondary coil.
(c) Expression: The mutual inductance for the given pair of concentric solenoids, M= μ⁰n¹A/l where n¹ and n² are the number of turns/length in two coils.

A transformer is an clectrical machine for converting a large A.C. current at low voltage into a small A.C. current at high voltage or vice-versa. It works on the principle of mutual induction.

Vs/Vp= Es/Ep =ns/np= K
k is known as transformation ratio.

value of transformation ratio k is more than one but for step down transformers k has a value less than one.

power input in primary
Es Is= EpIp
Ip _Es ns ×K
Is Ep np ×K

ñ=(Power output/Power input)100%
In ideal transformation n is 100% but practically it is between 95%-98%.

(A) Eddy current losses
(B) Hysteresis losses
(C) Magnetic losses (leakage of flux)
(D) Copper losses
(E) Sound losses

(a) It is used in telephone, telegraph, television, radio receiving sets, electrical welding machine, electric furnace and in wireless transmitting and receiving sets.
(b) Commonly it is used in transmitting a.c. power from the power generating station to distant places.

Step up transformers are used for transmission of electrical energy over long distances with less power loss.

It is a device which converts mechanical energy into electrical energy. It works on the principle of electromagnetic self-induction.

It is that current which continuously changes in magnitude and periodically reverses its direction. E = E⁰ sin or and I = I⁰ sin wt.

One virtual ampere is that alternating current which produces the same heat as is produced by a steady current of one ampere through the same resistance for the same time. The A.C. ammeter records the effective value of alternating measured in terms of virtual ampere.

One virtual volt is that alternating potential difference which when applied across a certain resistance produces the same heat as done by steady potential difference of l volt across the same resistance for the same time. The A.C. voltmeter records the effective value of alternating voltage measured in terms of virtual volt.

(a)s When the circuit contains resistance only: For a pure resistance A.C. circuit the current is in phase with voltage and Ohm’s law is obeyed by the circuit.
(b) A.C. circuits containing induction
only: In case of a pure inductive circuit the current lags behind the voltage by π/2 or alternatively the voltage leads the current by π/2
(c) A.C. circuit containing capacitance only: In case of a pure capacitive circuit the current leads the voltage by π/2 or alternatively the voltage lags behind the current by π/2

Rate of doing electrical work, is called power in A.C. circuit and is equal VI . Average (true) power = Veff COS VerIen is known as apparent power and cos ∅ known as power factor.
Power factor, cos ∅ = Apparent power/True power

∅ = 0 and True power= Apparent power
=Veff Ieff

circuit is purely inductive or purely capacitive then ∅= 90° and average power = 0. Current in such a circuit is commonly called “Wattless current’ because it does not contribute anything towards power (watts) consumed.

(a) Resistor: It opposes the flow of current. It offers equal resistance to d.c. as well as upon a.c. Its symbol is Its S.I. unit is ohm.
(b) Inductor : It is a few turns of conducting wires wound over a metallic or non-metallic frame.
It opposes to a.c. This opposition to a.c. is known as inductive reactance. Its S.I. unit is ohm. Symbol of inductor is
(c) Capacitor: It consists of two metal plates,one +vely charged and the other -vely charged.
It opposes to a.c. This opposition to a.c. is known as capacitive reactance. Its S.I. unit is ohm. Symbol of capacitor

Form factor is ratio of r.m.s., value to average value of current or voltage.
In case of a.c., form factor = Irms/Ia= I⁰√2/ 2I⁰π = π / 2√2 = 1.11