ONLINE ELECTRICAL ENGINEERING STUDY SITE

Norton Theorem | Norton Equivalent Current and Resistance

Norton Theorem

Any active network can be represented as an equivalent current source with an impedance connected in parallel across it. Simplifying any network by converting the active part of that network to an equivalent current source with an impedance connected in parallel is called Norton Theorem.
Norton Theorem is just alternative of Thevenin Theorem. In this theorem, the circuit network is reduced into a single constant current source in which, the equivalent internal resistance is connected in parallel with it. Every voltage source can be converted into equivalent current source.
Suppose, in a complex network we have to find out the current through a particular branch. If the network has one or more active sources, these will supply current to the said branch.

As in the said branch current comes from rest of the network, it can be considered that the network itself is a current source. The equivalent impedance of the network across the branch is nothing but the impedance of the equivalent current source, and hence it is connected in parallel. The equivalent resistance of a network is the equivalent electrical resistance of the network when someone looks back into the network from the terminals where said branch is connected. During calculating this equivalent resistance, all sources are removed leaving their internal resistances in the network. Actually, in Norton Theorem, the branch of the network through which we have to find out the current, is removed from the network. After removing the branch, we short circuit the terminals where the said branch was connected. Then we calculate the short circuit current that flows between the terminals. This current is nothing but Norton equivalent current IN of the source. The equivalent resistance between the said terminals with all sources removed leaving their internal resistances in the circuit is calculated and say, it is RN. Now we will form a current source that's current is IN A and internal shunt resistance is RN Ω.
For getting a clearer concept of this theorem, we have explained it by the following example.

In the example, two resistances R1 and R2 are connected in series and this series combination is connected across one voltage source of emf E with internal resistance Ri as shown. Series combination of one resistive branch of RL and another resistance R3 is connected across the resistance R2 as shown. Now we have to find out the current through RL by applying Norton Theorem.
First, we have to remove the resistance RL from terminals A and B and make the terminals A and B short circuited by zero resistance.
Second, we have to calculate the short circuit current or Norton equivalent current IN through the points A and B. The equivalent resistance of the network, To determine internal resistance or Norton equivalent resistance RN of the network under consideration, remove the branch between A and B and also replace the voltage source by its internal resistance. Now the equivalent resistance as viewed from open terminals A and B is RN,  As per Norton Theorem, when resistance RL is reconnected across terminals A and B, the network behaves as a source of constant current IN with shunt connected internal resistance RN and this is Norton equivalent circuit.

Norton Equivalent Circuit

norton theorem 04




Comments/Feedbacks






Closely Related Articles Active 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 ResistanceReciprocity TheoremNodal Analysis in Electric CircuitsMaximum Power Transfer TheoremDelta - Star transformation | Star - Delta TransformationMore 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 ResistanceMagnetic 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 CircuitMutual InductanceSelf InductanceSI 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 Principle of Water Content Test of Insulating OilCollecting Oil Sample from Oil Immersed Electrical EquipmentCauses of Insulating Oil DeteriorationAcidity Test of Transformer Insulating OilMagnetic Flux