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Concept 3 : Maximum Power Transfer Theorem % Sr. No. Z s (Source Impedance) 1. Rs j 0 RL Rs 2. Rs jX s RL Rs2 ( X s X L )2 3. Rs jX s XL Xs 0 4. Rs jX s ZL Zs * 5. Rs jX s RL Rs2 X s2 I 2 RL < 50% 6. Rs j 0 RL Rs2 X L2 I 2 RL < 50% Z L (Load Impedance) Condition for MPT PL (max) [maximum power delivered to load] I 2 RL Vs2 4 Rs I 2 RL I 2 RL (efficiency) 50% < 50% Vs2 RL ( Rs RL )2 < 50% Vs2 4 Rs 50% I 2 RL Example 1 : A source Vs (t ) V cos100t has an internal impedance of (4 j 3) . If a purely resistive load is connected to this source to extract the maximum power out of the source, then its value in should be [GATE EC/EE/IN 2013, IIT-Bombay] (A) 3 (B) 4 (C) 5 (D) 7 Ans. (C) Sol. In accordance with case 2 as given in table RL Rs2 ( X s X L )2 Where Rs 4 , X s 3 , X L 0 RL 42 32 5 Ans. Example 2 : [IES EE 2010] Consider the network shown in below figure. The max power that can be transferred in the load Z L is (A) 12.25 W (B) 62.5 W (C) 24.5 W Page 1 of 2 (D) 500 W Page 2 of 2 Ans. (B) Sol. If there is no information of complex variable load. Then by default we assume case 4. That means For MPT, Z L Z s * (10 j 50) 5000 Applying KVL, I 2.500 A 10 j 50 10 j 50 I 2.5 A 2 PL (max) I RL (2.5)2 10 (6.25) 10 62.5 W Ans.