Ce diaporama a bien été signalé.
Nous utilisons votre profil LinkedIn et vos données d’activité pour vous proposer des publicités personnalisées et pertinentes. Vous pouvez changer vos préférences de publicités à tout moment.
Gandhinagar Institute Of
Technology
Element Of Electrical Engineering
(2110014)
Active Learning Assignment
Topic:
Guided B...
Self-Inductance
When the switch is closed, the battery (source
emf) starts pushing electrons around the circuit.
The curre...
•When an electric current is passed
through an insulated conducting coil, it
gives rise to a magnetic field in the coil
so...
DEFINATION
As the strength of the current in the
coil is changed, the flux linked with the coil
also changes. Under such ...
Conducting coil
Battery
Key/Switch Rheostat
Direction of the Current
Current flows
In anti-clock
Wise direction
Current
flows
In clock
Wise
direction
Mutual induction is the phenomenon
of production of induced emf in one
coil due to a change of current in the
neighboring ...
At any instant ,
Magnetic Flux linked with the secondary coil ∝ current in the primary coil.
i.e. ᵩ ∝ I
ᵩ=MI
The proportio...
Consider two long co-axial solenoids S1 and S2, with S2 wound over S1 .
Let l= length of each solenoid
r1, r2=radii of the...
We now consider the flux linked with the outer solenoid S2 due to the
current I1 in the inner solenoid S1 . The field B1 d...
1. Number of Turns : larger the number of turns , larger the
mutual inductance.
2. Larger the common cross-sectional area ...
Multiplying equations (15) and (17),
But N1Φ1/i1 = Self induced of coil 1 = L1
N2Φ2/i2 = Self induced of coil 2 = L2
... M...
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
self inductance , mutual inductance and coeffecient of coupling
Prochain SlideShare
Chargement dans…5
×

self inductance , mutual inductance and coeffecient of coupling

10 942 vues

Publié le

self inductance , mutual inductance and coeffecient of coupling

Publié dans : Ingénierie
  • Identifiez-vous pour voir les commentaires

self inductance , mutual inductance and coeffecient of coupling

  1. 1. Gandhinagar Institute Of Technology Element Of Electrical Engineering (2110014) Active Learning Assignment Topic: Guided By: Branch: Division: Rahish Silavat
  2. 2. Self-Inductance When the switch is closed, the battery (source emf) starts pushing electrons around the circuit. The current starts to rise, creating an increasing magnetic flux through the circuit. This increasing flux creates an induced emf in the circuit. The induced emf will create a flux to oppose the increasing flux. The direction of this induced emf will be opposite the source emf. This results in a gradual increase in the current rather than an instantaneous one. The induced emf is called the self-induced emf or back emf.
  3. 3. •When an electric current is passed through an insulated conducting coil, it gives rise to a magnetic field in the coil so that the coil itself behaves like a magnet. •The magnetic flux produced by the current in the coil is linked with the coil itself.
  4. 4. DEFINATION As the strength of the current in the coil is changed, the flux linked with the coil also changes. Under such circumstances an emf is induced in the coil too. Such emf is called a self-induced emf and this phenomenon is known as self-induction.
  5. 5. Conducting coil Battery Key/Switch Rheostat Direction of the Current
  6. 6. Current flows In anti-clock Wise direction Current flows In clock Wise direction
  7. 7. Mutual induction is the phenomenon of production of induced emf in one coil due to a change of current in the neighboring coil.
  8. 8. At any instant , Magnetic Flux linked with the secondary coil ∝ current in the primary coil. i.e. ᵩ ∝ I ᵩ=MI The proportionality constant M is called th mutual inductance or coeffecient of mutual induction of the two coils. Any change in the current I sets up and induced emf in the secondary coil which is given by E= −𝑑ᵩ 𝑑𝑡 = -M −𝑑I 𝑑𝑡
  9. 9. Consider two long co-axial solenoids S1 and S2, with S2 wound over S1 . Let l= length of each solenoid r1, r2=radii of the two solenoids 𝐴 = 𝜋r1 2 = area of cross section of inner solenoid S1 N1, N2 = number of turns in the two solenoids First we pass a time varying current I2 through S2 . The magnet field setup inside S2 due to I2 B2 = µ0 n2 I2 where n2 = N2 /l =number of turns per unit length of S2. Total magnetic flux linked with the inner solenoid S1 is Φ1 = B2 A N1 = µ0 n2 I2 A N1 ∴ Mutual inductance of coil 1 w.r.t coil 2 is M12 = Φ1 / I2 = µ0 n2 A N1 = µ0 N2 A N1 / l
  10. 10. We now consider the flux linked with the outer solenoid S2 due to the current I1 in the inner solenoid S1 . The field B1 due to I1 is constant inside S1 but zero in the annular region between the two solenoids. hence. B1 = µ0 n1 I1 Where n1 = N1 /l = the number of turns per unit length of S1 The total flux linked with the outer solenoid S2 is Φ2 = B1 A N2 = µ0 n1 I1 A N2 = µ0 N2 A N1 I1 / l ∴ Mutual inductance of coil 2 w.r.t coil 1 is M21 = Φ2 / I1 = µ0 N2 A N1 / l Clearly, M12 = M21 = M ∴M= µ0 N2 A N1 / l Thus mutual inductance of two coils is the property of their combination. It does not matter which one of them functions as primary or secondary coil.
  11. 11. 1. Number of Turns : larger the number of turns , larger the mutual inductance. 2. Larger the common cross-sectional area of two solenoids , larger will be their mutual inductance. 3. Larger the distance b/w two solenoids , smaller will be the magnetic flux linked with the secondary coil due to current in the primary coil. Hence smaller will be the value of M.
  12. 12. Multiplying equations (15) and (17), But N1Φ1/i1 = Self induced of coil 1 = L1 N2Φ2/i2 = Self induced of coil 2 = L2 ... M2 = k1k2L1L2 ... M = √(k1k2) √(L1L2) Let k = √(k1k2) ... M = k √(L1L2) ............(18) where k is called coefficient of coupling. ... k = M/(√(L1L2)) .........(19)

×