DC CIRCUIT METHODS Problem 1 Use source transformation to find vo in the circuit in Fig. 4.17. Solution: Problem 2 Find io in the circuit of Fig. 4.19 using source transformation. Answer: 1.78 A. Thevenin’s Theorem THEOREM Thevenin’s theorem states that “a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTh in series with a resistor RTh where VTh is the open circuit voltage at the terminals and RTh is the input or equivalent resistance at the terminals when the independent source are turn off”. 8 of 20 DEVELOPED BYIn 1883 the theorem was developed by LÉON CHARLES THÉVENIN (1857-1926), an electrical engineer with France’s NATIONAL POSTES ET TÉLÉGRAPHES TELECOMMUNICATIONS organization. 9 of 20 THEVENIN’S EQUIVALENT CIRCUIT Fig 1: A linear two-terminal circuit by its Thevenin equivalent: (a) Original circuit (b) Thevenin equivalent circuit. 10 of 20 HOW TO FIND THEVENIN’S VOLTAGE Remove the component of interest- normally called the load resistance (𝑅𝐿 ) Mark the terminals as 𝑉𝑇𝐻 where the load was removed from Calculate the Thevenin voltage 𝑉𝑇𝐻 by finding the open circuit voltage across the load terminals Here, VTh voc : open circuit voltage at a b Fig 2: Finding 𝑉𝑇𝐻 11 of 20 HOW TO FIND THEVENIN’S RESISTANCE CASE 1: (No dependent sources) Turn off all independent source. RTH: can be obtained via simplification of either parallel or series connection seen from a-b Fig 3: Finding 𝑅𝑇𝐻 (No dependent source) 12 of 20 HOW TO FIND THEVENIN’S RESISTANCE (cont.) CASE 2: (With dependent sources) Turn off all independent sources. Apply a voltage source vo at a-b terminal and determining the resulting current io .Then, RTh vo io Alternatively, apply a current source io at a-b terminal and find the terminal voltage vo . RTh vo io Fig 4: Finding 𝑅𝑇𝐻 when circuit has dependent sources 13 of 20 SIMPLIFIED CIRCUIT VTh IL RTh RL RL VL RL I L VTh RTh RL Fig 5: A circuit with a load: (a) Original circuit (b) Thevenin equivalent circuit 14 of 20 EXAMPLE:1 Find the Thevenin’s equivalent circuit of the circuit shown in Fig 6 to the left of the terminals a-b. Then find the current through RL = 6 , 16 , and 36 . Fig 6 15 of 20 FIND RTH RTh : 32V voltage source short 2A current source open 4 12 RTh 4 || 12 1 1 4 16 Fig 7: Finding 𝑅𝑇𝐻 16 of 20 FIND VTH VTh : (1) Mesh analysis 32 4i1 12(i1 i2 ) 0 , i2 2A i1 0.5A VTh 12(i1 i2 ) 12(0.5 2.0) 30V (2) Alternatively, Nodal Analysis (32 VTh ) / 4 2 VTh / 12 VTh 30V Fig 8: Finding 𝑉𝑇𝐻 17 of 20 EQUIVALENT CIRCUIT To get iL : VTh 30 iL RTh RL 4 RL RL 6 I L 30 / 10 3A RL 16 I L 30 / 20 1.5A RL 36 I L 30 / 40 0.75A Fig 9: Thevenin equivalent circuit 18 of 20 EXAMPLE: Using Thevenin’s theorem, find the equivalent circuit to the left of the terminals in the circuit in Fig. Then find i. Answer: VTh = 6 V, RTh = 3 , i = 1.5 A. 19 of 20 20 of 20 21 of 20 Problem 1 Find the Norton equivalent circuit of the circuit in Fig. 4.39. 22 of 20 Solution: 23 of 20 REFERENCES 1. Fundamental of Electric Circuit by Alexander & Sadiku. 2. Introductory Circuit Analysis by Robert L. Boyelstead. 24 of 20