Question

In the circuit given below, what is the amount of maximum power transfer to R? (a) 56 W (b) 76 W (c) 60 W (d) 66 W The question was asked in a national level competition. Origin of the question is Advanced Problems on Millman’s Theorem and Maximum Power Transfer Theorem in division Useful Theorems in Circuit Analysis of Network Theory Select the correct answer from above options network theory questions and answers, network theory questions pdf, network theory question bank, network theory gate questions and answers pdf, mcq on network theory pdf, gate network theory questions and solutions, network theory mcq Test , ies network theory questions, Network theory Questions for GATE EC Exam, Network Theory MCQ (Multiple Choice Questions)

Answer 1

Right option is (d) 66 W Best explanation: Drop across V1Ω = 5 × 1 = 5V Also, \frac{V-V_{1Ω}}{10} + \frac{V-20-V_{1Ω}}{2} + \frac{V-V_{OC}}{5} = 2 Or, 0.1 V – 0.1V1Ω + 0.5V – 10 – 0.5V1Ω + 0.2 – 0.2VOC = 2 Or, 0.8V – 0.6V1Ω = 12 + 0.2VOC Or, 0.8 V – 0.2VOC = 12 +3=15 (Putting V1Ω = 5) Again, \frac{V_{OC}-V}{5} + 2 = 5 Or, 0.2VOC – 0.2V = 3 Again, RTH = {(10||2) + 1} + 5 = (\frac{20}{12+1}) + 5 = 7.67 Ω Following the theorem of maximum power transfer, R = RTH = 7.67 Ω And PMAX = \frac{V_{OC}^2}{4R} = \frac{45^2}{4×7.67} = 66 W.