P28_027 - note that the current is the same in every...

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27. Let the resistors be divided into groups of n resistors each, with all the resistors in the same group connected in series. Suppose there are m such groups that are connected in parallel with each other. Let R be the resistance of any one of the resistors. Then the equivalent resistance of any group is nR , and R eq , the equivalent resistance of the whole array, satisFes 1 R eq = m X 1 1 nR = m nR . Since the problem requires R eq = 10 Ω = R , we must select n = m . Next we make use of Eq. 28-13. We
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Unformatted text preview: note that the current is the same in every resistor and there are n · m = n 2 resistors, so the maximum total power that can be dissipated is P total = n 2 P , where P = 1 . 0 W is the maximum power that can be dissipated by any one of the resistors. The problem demands P total ≥ 5 . P , so n 2 must be at least as large as 5 . 0. Since n must be an integer, the smallest it can be is 3. The least number of resistors is n 2 = 9....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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