1. L-11 ELECTROMAGNETISM ELE 1001: Basic Electrical Technology
Dept. of E&E, MIT, Manipal

2. ELE1001: Basic Electrical Technology
Objective
Find self and mutual inductance of magnetically coupled coils.
Apply dot rule to find the sign of mutually induced emf in series and parallel magnetic circuits.
Dept. of E&E, MIT, Manipal

3. Contents Self Induced emf Mutually induced emf
ELE 1001: Basic Electrical Technology
Contents
Self Induced emf
Mutually induced emf
Self & mutual inductance
Coupling coefficient
Dot rule
Coils in series-aiding
Coils in series-opposing
Coils in parallel
Dept. of E&E, MIT, Manipal

4. Self Induced EMF Statically induced emf can be further divided into:
ELE 1001: Basic Electrical Technology
Self Induced EMF
Statically induced emf can be further divided into:
Mutually induced emf
Self induced emf
Self Induced EMF : The induced emf in a coil is proportional to the rate of the change of the magnetic flux passing through it due to its own current. This proportionality constant is called the self inductance, L.
The negative sign indicates that induced emf is opposing the cause producing it.
Dept. of E&E, MIT, Manipal

5. ELE 1001: Basic Electrical Technology
Mutually Induced emf
Mutually induced EMF: The induced emf in a coil due to the change of flux produced by the change of current in the nearby coil . This proportionality constant is called the mutual inductance, M
Dept. of E&E, MIT, Manipal

6. Self & Mutual Inductance
ELE 1001: Basic Electrical Technology
Self & Mutual Inductance
Current flow i1, in coil ‘C1’ produces self induced emf e1 in it and mutually induced emf e2 in nearby coil ‘C2’
ɸ1:Total flux developed due to i1
ɸ11:flux linking with C1
ɸ12:flux linking with C2
Dept. of E&E, MIT, Manipal

7. Self & Mutual Inductance
ELE 1001: Basic Electrical Technology
Self & Mutual Inductance
Self induced emf, e1 in ‘C1’ or
Mutual induced emf, e2 in ‘C2’ or
Hence,
(If µr is constant,
is constant)
Unit: Henry (H)
Dept. of E&E, MIT, Manipal

8. ELE 1001: Basic Electrical Technology
Coupling Coefficient
Gives idea about the magnetic coupling between the two coils.
when the entire flux in one coil links with the other, the coupling coefficient is its maximum value i. e. 1.
Dept. of E&E, MIT, Manipal

9. Coupling Coefficient ELE 1001: Basic Electrical Technology
Dept. of E&E, MIT, Manipal

10. Dot Rule Polarity of mutually induced voltage depends on-
ELE 1001: Basic Electrical Technology
Dot Rule
Polarity of mutually induced voltage depends on-
The current directions
The physical construction of the coils
Dot rule helps to determine the sign of mutually induced voltage without going into the details of physical construction.
Dept. of E&E, MIT, Manipal

11. Dot Rule Additive Coupling Fluxes are aiding Can be represented as :
ELE 1001: Basic Electrical Technology
Dot Rule
Additive Coupling →
Can be represented as :
Current enters (or leaves) the dotted terminal on two coils.
Sign of M terms same as sign of L terms
Fluxes are aiding
Dept. of E&E, MIT, Manipal

12. Dot Rule Subtractive coupling Fluxes are opposing
ELE 1001: Basic Electrical Technology
Dot Rule
Subtractive coupling
Current enters the dotted terminal in one coil and leaves the dotted terminal in other coil:
Sign of M terms opposite to sign of L terms
Fluxes are opposing
Dept. of E&E, MIT, Manipal

13. Coils in Series – Aiding
ELE 1001: Basic Electrical Technology
Coils in Series – Aiding +  M L1 L2 →
L1 + L2 + 2M
Dept. of E&E, MIT, Manipal

14. Coils in Series – Opposing
ELE 1001: Basic Electrical Technology
Coils in Series – Opposing +
Equivalent circuit  M L1 L2
L1 + L2 - 2M
Dept. of E&E, MIT, Manipal

15. ELE 1001: Basic Electrical Technology
Exercise
1. The total inductance of two coils A and B, when connected in series is 0.5 H or 0.2 H, depending on the relative directions of the currents in the coils. Coil A, when isolated from coil B, has a self–inductance of 0.2 H. Calculate (a) the mutual inductance between two coils, (b) the self inductance of the coil B , (c) the coupling coefficient between the two coils , and (d) the two possible values of the emf induced in coil A when the current in the series combination decreases at 1000 A/s.
Ans: (a) H; (b) 0.15 H ; (c) ; (d) 275 V ,125 V
Dept. of E&E, MIT, Manipal

16. ELE 1001: Basic Electrical Technology
Exercise
2. Two coils with inductances in the ratio 1:4 have a coupling coefficient k=0.6. When these coils are connected in series aiding the equivalent inductance is 44.4mH. Find L1, L2, and M.
Ans:
L1 =6mH L2 =24mH M =7.2mH
Dept. of E&E, MIT, Manipal

17. ELE1001: Basic Electrical Technology
Summary
Magnetically coupled coils will have self and mutual inductances.
Sign of mutually induced emf can be represented using dot rule without going into the details of physical construction.
Dept. of E&E, MIT, Manipal