ch27-p111 - 111. (a) Placing a wire (of resistance r) with...

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111. (a) Placing a wire (of resistance r ) with current i running directly from point a to point b in 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, i s goes toward the lower right through R s and i x goes toward the upper right through R x ), then the currents must be related as follows: 01 1 2 20 , , s sx x ii i i iiiiii = += + + =+ = 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 ir iR iR iR ss x xx = −− = −−− = 11 2 00 0 0 0 ε . We incorporate the current relations from above into these loop equations in order to
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