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Wires go between Boston, Chicago, and Seattle. Those cities are at voltages xB, xC, xS

Chapter 1, Problem 1.6.61

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QUESTION:

Wires go between Boston, Chicago, and Seattle. Those cities are at voltages xB, xC, xS. With unit resistances between cities, the three currents are in y: y = Ax is yBC yCS yBS = 1 1 0 0 1 1 1 0 1 xB xC xS (a) Find the total currents AT y out of the three cities. (b) Verify that (Ax)T y agrees with x T (ATy)six terms in both.

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QUESTION:

Wires go between Boston, Chicago, and Seattle. Those cities are at voltages xB, xC, xS. With unit resistances between cities, the three currents are in y: y = Ax is yBC yCS yBS = 1 1 0 0 1 1 1 0 1 xB xC xS (a) Find the total currents AT y out of the three cities. (b) Verify that (Ax)T y agrees with x T (ATy)six terms in both.

ANSWER:

Step 1 of 3

Given that the voltages of the cities are . With unit resistances between the cities, the three currents are in y given as

With unit resistances between the cities, the three currents are in y given as

 as

         

Here the matrix A is

         

The transpose of A is

         

 

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