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(i) State the two Kirchhoff's laws. Explain briefly how these rules are justified.(ii) The current is drawn from a cell of emf E and internal resistance r connected to the networkof resistors each of resistance r as shown in the Fig.Obtain the expression for (a) thecurrent draw from the cell and (b) the power consumed in the network. |
Answer» Solution :(ii) The circuit diagram of network of resistors can be redrawn asshown in Fig.  Obviously, here RESISTANCE of branch ACB is : `R. = (1)/((1/r + 1/r)) + (1)/((1/r + 1/r)) = r/2 + r/2 = r` Thus, effectively between A and B, we have three resistors each of value r. Hence effective resistance R between A and B will be `1/R = 1/r + (1)/(r.) + 1/r = 1/r + 1/r + 1/r = 3/r rArr R = r/3` As INTERNAL resistance of CELL is also r, hence (a)the current DRAWN from the cell `I = (E )/(R + r) = (E )/(r/3 + r) = (3E)/(4r)` and (b) power consumed in the network `P = I^2 R ( (3E)/(4r))^2 xx r/3 = (3E^2)/(16r) ` |
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