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

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

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

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

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

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

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

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

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

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

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

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

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

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

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) 0.075 H; (b) 0.15 H ; (c) 0.433 ; (d) 275 V ,125 V Dept. of E&E, MIT, Manipal

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

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