Mutual Inductance

Mutual Inductance is the ratio between induced Electro Motive Force across a coil to the rate of change of current of another adjacent coil in such a way that two coils are in possibility of flux linkage.Mutual induction is a phenomenon when a coil gets induced in EMF across it due to rate of change current in adjacent coil in such a way that the flux of one coil current gets linkage of another coil. Mutual inductance is denoted as ( M ), it is called co-efficient of Mutual Induction between two coils. mutual inductance Mutual inductance for two coils gives the same value when they are in mutual induction with each other. Induction in one coil due to its own rate of change of current is called self inductance (L), but due to rate of change of current of adjacent coil it gives mutual inductance (M).

From the above figure, first coil carries current i1 and its self inductance is L1. Along with its self inductance it has to face mutual induction due to rate of change of current i2 in the second coil. Same case happens in the second coil also. Dot convention is used to mark the polarity of the mutual induction. Suppose two coils are placed nearby. mutual inductance Coil 1 carries I1 current having N1 number of turn. Now the flux density created by the coil 1 is B1. Coil 2 with N2 number of turn gets linked with this flux from coil 1. So flux linkage in coil 2 is N2 . φ2121 is called leakage flux in coil 2 due to coil 1].

Consider φ21 is also changing with respect to time, so an EMF appears across coil 2. This EMF is called mutually induced EMF. Now it can be written from these equations, Again, coil 1 gets induced by flux from coil 2 due to current I2 in the coil 2. mutual inductance In same manner it can be written that for coil 1. However, using the reciprocity theorem which combines Ampere’s law and the Biot-Savart law, one may show that the constants are equal. i.e. M12 = M21 = M. M is the mutual inductance for both coil in Henry. The value of mutual inductance is a function of the self-inductances Suppose two coils are place nearby such that they are in mutual induction. L1 and L2 are co-efficient of self induction of them. M is the mutual inductance. Here, ƙ is called co-efficient of coupling and it is defined as the ratio of mutual inductance actually present between the two coils to the maximum possible value. If the flux due to first coil completely links with second coil, then ƙ = 1, then two coils are tightly coupled. Again if no linkage at all then ƙ = 0 and hence two coils are magnetically isolated. Merits and demerits of mutual inductance: Due to mutual inductance, transformer establishes its operating principle. But due to mutual inductance, in any circuit having inductors, has to face extra voltage drop.

How to find out Leq in a circuit having mutual inductance with dot convention Suppose two coils are in series with same place dot. mutual inductance Mutual inductance between them is positive. Suppose two coils are in series with opposite place dot. mutual inductance When a few numbers of inductors are in series with mutual inductances. mutual inductance


Closely Related Articles Self InductanceMore Related Articles Electric Current and Theory of Electricity | Heating and Magnetic EffectNature of ElectricityDrift Velocity Drift Current and Electron MobilityElectric Current and Voltage Division RuleRMS or Root Mean Square Value of AC SignalWorking Principle of a CapacitorQuality Factor of Inductor and CapacitorTransient Behavior of CapacitorCylindrical CapacitorSpherical CapacitorCapacitors in Series and ParallelHow to Test Capacitors?Electrical Conductance Conductivity of Metal Semiconductor and Insulator | Band TheoryWhat is Electrical Resistance?Resistivity and Laws of ResistanceProperties of Electric ConductorTemperature Coefficient of ResistanceResistance Variation with TemperatureSeries ResistanceActive and Passive Elements of Electrical CircuitElectrical DC Series and Parallel CircuitOhm's Law | Equation Formula and Limitation of Ohm's LawKirchhoff Current Law and Kirchhoff Voltage LawSingle and Multi Mesh AnalysisSuperposition TheoremThevenin Theorem and Thevenin Equivalent Voltage and ResistanceNorton Theorem | Norton Equivalent Current and ResistanceReciprocity TheoremNodal Analysis in Electric CircuitsMaximum Power Transfer TheoremDelta - Star transformation | Star - Delta TransformationMagnetic FieldMagnetic FluxMagnetic PermeabilityHysteresis LoopMagnetic Field and Magnetic Circuit | Magnetic MaterialsMagnetic SaturationEnergy Stored in a Magnetic FieldStatic Electric Field | Electrostatic Induction A Current Carrying Conductor Within A Magnetic FieldMagnetic SusceptibilityHard Magnetic MaterialsSoft Magnetic MaterialsMagnetic Circuit with Air GapElectric ChargeCoulombs Law | Explanation Statement Formulas Principle Limitation of Coulomb’s LawElectric Lines of ForceWhat is Electric Field?Electric Field Strength or Electric Field IntensityWhat is Flux? Types of Flux?Electric FluxElectric PotentialCapacitor and Capacitance | Types of CapacitorsEnergy Stored in CapacitorCharging a CapacitorDischarging a CapacitorFourier Series and Fourier TransformTrigonometric Fourier SeriesAnalysis of Exponential Fourier SeriesParity GeneratorElectric Circuit and Electrical Circuit ElementsSeries Parallel Battery CellsRL Series CircuitWhat is Inductor and Inductance | Theory of InductorRLC CircuitThree Phase Circuit | Star and Delta SystemRL Parallel CircuitRL Circuit Transfer Function Time Constant RL Circuit as FilterConstruction of AC Circuits and Working of AC CircuitsSeries RLC CircuitParallel RLC CircuitResistances in Series and Resistances in ParallelResonance in Series RLC CircuitPlanar and Non Planar Graphs of CircuitClipping CircuitSI System of UnitsElectrical International SymbolElectric Power Single and Three Phase Power Active Reactive ApparentVector Algebra | Vector DiagramRelationship of Line and Phase Voltages and Currents in a Star Connected SystemVector Diagram | Three Phase Vector DiagramTypes of Resistor Carbon Composition and Wire Wound ResistorVaristor Metal Oxide Varistor is Nonlinear ResistorCarbon Composition ResistorWire Wound ResistorVariable Resistors | Defination, Uses and Types of Variable ResistorsLight Dependent Resistor | LDR and Working Principle of LDRSource of Electrical EnergyVoltage SourceIdeal Dependent Independent Voltage Current SourceVoltage or Electric Potential DifferenceVoltage in SeriesVoltage in ParallelVoltage Drop CalculationVoltage DividerVoltage MultiplierVoltage DoublerVoltage RegulatorVoltage FollowerVoltage Regulator 7805Voltage to Current ConverterNew Articles Collecting Oil Sample from Oil Immersed Electrical EquipmentCauses of Insulating Oil DeteriorationAcidity Test of Transformer Insulating OilMagnetic FluxRing Counter