EEE Active Learning Assignment Topics:- Statically and Dynamically Induced EMF

1. EEE Active Learning Assignment • Topics:- Statically and Dynamically Induced EMF • Group Members:- Shyam Patel, Shubham Raval, Prince Jain, Kiran Panchal

2. What is EMF? EMF is acronym for electromotive force. The amount of work or energy required to bring 1 coulomb positive charge from negative pole to positive pole through the electrolyte of cell is called EMF of the cell. Unit of EMF is Volt.

3. What Is Induced EMF? Whenever a conductor cuts or is cut by magnetic flux, an EMF is induced in the coil or the conductor. Magnitude of induced EMF e = Rate of change of flux linkage, where flux linkage = flux * number of turns in coil

5. There are 2 methods available for deciding the direction of induced EMF • Fleming’s Right Hand Rule • Lenz’s Law

6. Fleming’s Right Hand Rule Thumb indicates the direction of conductor movement. First finger indicates the direction of flux. Induced current I coming out of the conductor is indicated by the second finger.

8. Lenz’s Law The direction of induced EMF produced due to electromagnetic induction is such that, it will set up a current to oppose the basic cause responsible for its production. e = -N(dϕ/dt), where – sign indicates that EMF opposes the cause producing t.

9. There are 2 types of EMF: • Statically Induced EMF • Dynamically Induced EMF

10. Statically Induced EMF

11. Definition: • Usually the conductor or the coilremains stationary • Flux or magnetic field linked with conductor is changed by simply change in current producing the flux. • Example: Transformers

13. Statically Induced EMF can be sub-divided into: • Self Induced EMF • Mutually Induced EMF

14. Self Induced EMF: • Current through the coil is changed • Flux linked with its own turns also changes, which will produce in it what is called self induced EMF. • The direction of this induced EMF would be according to Lenz’s law such as to oppose its very cause of production.

15. Due to its reason of opposing its very cause of product, it is also called opposing or counter EMF of selfinduction.

16. Magnitude of self induced EMF: • Induced EMF = e = -N (ϕ/I) * (dI/dt) • e = -L * (dI/dt) volts, where L = (N*ϕ/I) is called Inductance or self inductance. • Unit of inductance is : (Weber turn)/Ampere or Henry. • EMF induced in volt when the current in coil is changing uniformly as 1 ampere per second is called inductance. • Magnitude of self induced EMF: • Induced EMF = e = -N (ϕ/I) * (dI/dt) • e = -L * (dI/dt) volts, where L = (N*ϕ/I) is called Inductance or self inductance. • Unit of inductance is : (Weber turn)/Ampere or Henry. • EMF induced in volt when the current in coil is changing uniformly as 1 ampere per second is called inductance.

17. Other equations for self inductance(L): • L = (N * flux)/I Henry, where flux = NI/S and S is called reluctance. • L = N2/S Henry • S can be written as S = l/μa • So L = (N2 * μa)/l Henry where, l = length of magnetic circuit, a = cross section area of magnetic circuit μ = permittivity N = number of turns

18. Mutually Induced EMF: • Consider 2 coils A and B lying close to one another. • Coil A is joined to a battery, a switch and a variable resistance R whereas coil B is connected to a sensible voltmeter V. When current through A is established by closing the switch, its magnetic field is partly linked with the coil B. • As current through A is changed the, the flux linked with B is also changed. Hence mutually induced EMF is produced in B whose magnitude can be given by Faraday’s Law and direction by Lenz’s Law.

19. Now, if the battery is connected to coil B and voltmeter to coil A then the situation is reversed and change of current in B will produce mutually induced EMF in coil A.

20. There is no movement of any conductor, also the flux variations has been brought by the change in current only. • Such an EMF induced in one coil due the influence of the other coil is called mutually induced EMF.

21. Concept of Mutual Inductance (M): • Mutually induced EMF is given by: E2 = -M (dI1/dt) volts, where M is called mutual inductance (M), and is given by M = N2 * ϕ2/I1 . • EMF induced in second coil when a uniform current of 1 Amp/sec takes place in the first coil. • It is the flux linkage of the second coil per ampere current flowing in the first coil. • Unit is : Henry

22. Expression for Mutual Inductance: • M = (N1 * N2 * μ * a2)/l2 , where N1, N2 are number of turns in the respective coils, a1 , a2 are the respective cross sectional areas, l1 , l2 are the lengths of the coils

24. Dynamically induced E.M.F.

25. Definition • When EMF is induced in coil by virtue of movement of either the conductor or the magnetic field ,the EMF is called dynamicallyinduced EMF .

26. Here coil having two sides is rotated in uniform magnetic field ,flux linkage by the coil changes. Because of the change of flux linkage ,EMF is induced in coil.

28. Expression for the Magnitude • From fig (a), flux cut by conductor = BA = B*l*dx The rate of change of flux dϕ/dt = B*l*(dx/dt) = B*l*v volts =e (Induced EMF) • From fig.(b), flux cut by the conductor dϕ = B*A = B*l*dx*sinθ e = dϕ/dt = B*l*dx/dt*sinθ = B*l*v*sinθ

29. Source:- edurite score more , J. S. Katre, B. L. Theraja