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ELECTRO MAGNETIC INDUCTION AND ALTERNATING CURRENT
- Magnetic Flux Density
(a) Definition: Magnetic flux density or
magnetic induction or magnetic field vector B at a point in a magnetic field is generally defined as the number of magnetic lines of induction passing through a unit area around that point placed normal to the lines of induction. The tangent to the line of induction at a point gives the direction of magnetic induction B at that point.
- Magnetic Flux
(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].
- Faraday’s law of Electromagnetic Induction
(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
- Lenz’s law 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.
- Production of induced e.m.f.: Induced electromotive force can be produced
(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)
- Fleming’s right hand rule: 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.
- Eddy Currents: 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.
- Reduction of Eddy currents: Eddy currents can be reduced by taking laminated iron core.
- Eddy currents are used in:
(a) induction furnace
(b) dead beat galvanometer
(c) a.c. induction motor
(d) electrical brake etc.
- Eddy currents harmful: Eddy currents are harmful as it increases energy loss and increase wear and tear.
Eddy currents are analogous to friction in mechanics.
- Self induction: It is the property of an electric
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
OR E= -L.(dk/dt).
- Self inductance or coefficient of self induction:
(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.
- Mutual Induction: 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)
- Mutual Inductance or coefficient of mutual induction
(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.
- Transformer: 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.
- In transformer
Vs/Vp= Es/Ep =ns/np= K
k is known as transformation ratio.
- For step up transformers value of transformation ratio k is more than one but for step down transformers k has a value less than one.
- In transformers power output in secondary = power input in primary
Es Is= EpIp
Ip _Es ns ×K
Is Ep np ×K
Efficiency of a transformer
ñ=(Power output/Power input)100%
In ideal transformation n is 100% but practically it is between 95%-98%.
- Main sources of energy loss in transformer are
(A) Eddy current losses
(B) Hysteresis losses
(C) Magnetic losses (leakage of flux)
(D) Copper losses
(E) Sound losses
- Uses of Transformer:
(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.
- Electric Generator or Dynamo: It is a device which converts mechanical energy into electrical energy. It works on the principle of electromagnetic self-induction.
- Alternating Current: It is that current which continuously changes in magnitude and periodically reverses its direction. E = E⁰ sin or and I = I⁰ sin wt.
- Virtual Ampere: 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
- Virtual Volt: 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.
- Phase relation between Voltage and Current in A.C. circuits:
(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
- Power in A.C. circuit: 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
- the A.C. circuit is purely resistive then ∅ = 0 and True power= Apparent power
- If the A.C. 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.
34: Circuit Elements:
(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: 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
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