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THEVENIN’S and NORTON’S THEOREMS Thevenin’s Theorem Any linear one‐port circuit which contains resistors and sources can be represented by an equivalent practical voltage source consisting of an ideal voltage source Voc which is the open‐ circuit voltage across the part,in series with an equivalent resistance RTh,which is the input resistant with independent sources killed. Norton’s Theorem Any linear one‐port circuit which contains resistors and sources can be represented by an equivalent practical current source consisting of an ideal current source Isc which is the short‐ circuit current through the part,in parallel with an equivalent resistance RTh,which is the input resistant with independent sources killed. Example 20 Voc .6 12V 46 4.6 RTh 1.6 4 46 If a load resistance of RL =6Ω is connected between A 12 and B : 1 .2 A IL 46 VL 1.2 6 7.2V PL 1.2 7.2 8.64W If RL is changed to 20 12 IL 0.5 A 4 20 VL 20 0.5 10V PL 10 0.5 5W Note : Repeated solutions of the circuit for different loads are very easy now. Example VK Vx Voc VK 20 Vx 0 4 10 10VK 200 4VK 0 VK 20 4A 4 1 100 Voc 3 25 RTh isc 4 3 isc 100 V Voc 3 Example Vx Vx 1 0 6 2 Vx 3Vx 6 0 Vx 3V 3 RTh 3 1 Example Vx 3Vx Vx 1 0 4 6 6Vx 2Vx 12 0 12 Vx 3V 4 RTh 3 Maximum Power Transfer 2 RLVs 2 Vs Rs RL Rs RL 2 To maximize PL with respect to RL PL RLiL2 RL Rs RL 2Rs RL RL 0 dPL Vs 2 dRL Rs RL 4 2 Rs RL Rs RL 2 RL 0 RL Rs In this case Vs Vs 2 VS , VL , PL iL 2 RL 2 4 RL while Vs 2 Pvs 2 RL Hence the maximum power transfer to the load is 50% of the power generated by the source.