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InterviewSolution
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Determine the current drawn from a 12 V supply with internal resistance 0.5Omegaby the infinite network shown in Fig. Each resistor has 1Omega resistance. |
Answer» Solution : The infinite network consists of NUMBER of RESISTANCE elementary units. Let x be the EQUIVALENTRESISTANCE of the infinite ladder. Then adding one more elementary resistance unit with the infinite ladder will not affect the total resistance of the infinite ladder. The combination, therefore, can be made equivalent to as shown in Fig. Here, x is the equivalent resistance of the given infinite network. Thus, the total resistance ` x = (1)/(1/x + 1/1) + 1 +1 = (x)/(x + 1) +2 = (2 + 3X)/(1 + x)` `rArr x + x^2 = 2 + 3x` ` rArr x^2 - 2x - 2 = 0` which gives` x = (2 pm sqrt(4 + 8) )/(2) = 1 pm sqrt3` As `x = 1 - sqrt3` is not possible, hence `x = 1+ sqrt3 = 1+1.732 = 2.732 OMEGA` The current drawn from the 12 V supply having internal resistance of 0.5 `Omega`, `I = (12)/(2.732 + 0.5) = (12)/(3.232) = 3.71 A` |
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