1Thevenin’s TheoremIntroduction• Thevenin’s Theorem is a very important and useful theorem.• It is a method for the reduction of a portion of a complex circuit into a simple one.• It reduces the need for repeated solutions of the same sets of equations.Thevenin Equivalent CircuitAny two-terminal linear network, composed of voltage sources, current sources, and resistors, can be replaced by an equivalent two-terminal network consisting of an independent voltage source in series with a resistor.Network ofSourcesandResistorsArbitraryNetworkArbitraryNetworkVThRTh....aabb+v-+v-iiV-I Characteristic of Thevenin EquivalentVThRTh..ab+v-iviVTh..iscv = VTh-RThi02Finding VThand RTh• Open circuit across terminalsCalculate the open-circuit voltage in the original network, vocThoc ,0 vvvi ===VThRTh..ab+-ivoc=VTh..abNetwork ofSourcesandResistors+voc-ocTh vV =Finding VThand RTh– Cont’d..abiscNetwork ofSourcesandResistorsscocThivR =• Short circuit across terminalsCalculate the short-circuit current in the original network, iscThThsc ,0Rviiv ===VThRTh..abiisc=VTh/RThThevenin Equivalent - Example25 V3 A20 Ω5 Ω 4 Ωab..Find the Thevenin equivalent with respect to terminals a,b.Alternative Method of finding RTh-- for circuits containing only independent sources..abCircuit withallindependentsources setequal tozeroReq1.Set all independent sources to zero2.Find equivalent resistance Reqof the dead circuit between the terminalseqTh RR=3Alternative Method of finding RTh-- for circuits containing dependent sources1. Set all independent sources to zero2. Apply either a test voltage source v0(or a test current source i0) to the terminals3. Calculate i0 (or v0 ) 00ThivR =..abCircuitwith allindependent sourcesset equalto zerov0i0..abCircuitwith allindependent sourcesset equalto zero+v0-i0Thevenin Equivalent - Example- +10 A4 Ω6 Ω3 Ω2i1 i1abooFind the Thevenin equivalent of the following circuit. If a 10Ω resistor is connected between the terminals, what current will flow in