(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 network of resistors each of resistance r as shown in the Fig. Obtain the expression for (a) the current draw from the cell and (b) the power consumed in the network.

Explanation

(ii) The circuit diagram of network of resistors can be redrawn as shown 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) `