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 WThe 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

In the circuit given below, what is the amount of maximum power transf

1.	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 WThe 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
Answer» 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.

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