111. (a) Placing a wire (of resistance r) with current irunning directly from point ato point bin Fig. 27-61 divides the top of the picture into a left and a right triangle. If we label the currents through each resistor with the corresponding subscripts (for instance, isgoes toward the lower right through Rsand ixgoes toward the upper right through Rx), then the currents must be related as follows: 011220,,ssxxiiiiiiiiii=+=++=+=where the last relation is not independent of the previous three. The loop equations for the two triangles and also for the bottom loop (containing the battery and point b) lead to iR iR iriR iR iRssxxx−−=−−=−−−=11200000ε.We incorporate the current relations from above into these loop equations in order to
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