hw14 - homework 14 LEE BENJAMIN Due Oct 6 2007 4:00 am...

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homework 14 – LEE, BENJAMIN – Due: Oct 6 2007, 4:00 am 1 Question 1, chap 28, sect 4. part 1 of 3 10 points Twelve resistors, each of equal value 75 Ω, are connected so that each is along one edge of a cube, as shown in the Fgure below. A current of 13 . 3 A is introduced at point “a”. The current will be allowed to exit only along a wire at point “e”, as drawn. a d e h g b c f 6 12 10 7 3 5 8 1 2 4 11 9 I I Which one of the following conditions is correct concerning the electric potential at the various nodes in the circuit above? 1. V c = V d and V g = V h correct 2. V b = V g and V d = V f 3. V c = V g and V d = V h 4. V b = V f and V c = V g 5. V h = V b and V f = V d 6. V c = V h and V d = V g 7. V b = V d and V f = V h 8. V d = V b and V f = V g 9. V b = V f and V d = V g 10. V f = V b and V d = V h Explanation: Consider the Fgure in the question. The current I is introduced into node “a”. Three independent resistors of equal value are acces- sible via this node, namely, resistor R 1 , R 2 , and R 3 . Neglect resistor R 3 for the moment, which is parallel with the rest of the resistors in the network. Because resistors R 1 and R 2 are equal and the remainder of the circuit is symmetric, the current will split equally between these two paths. Thus, the electric potential across each of the resistors R 1 and R 2 is equal and V c = V d . The same argument can be made for R 5 and R 6 , thus V g = V h Question 2, chap 28, sect 4. part 2 of 3 10 points What is the equivalent resistance of the resistor network shown in the Fgure? Correct answer: 43 . 75 Ω (tolerance ± 1 %). Explanation: Let : R = 75 Ω . We wish to calculate the equivalent resis- tance of our cubic setup. To assist in this endeavor, recall the following facts derived in Part 1. Since I 1 = I 2 and I 4 = I 5 , we have V c = V d and V g = V h . Note: We can achieve the identical cur- rent distribution if we re-arrange the twelve resistors in the following conFguration let- ting nodes “c” and “d” be one node and nodes “g” and “h” be one node.

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homework 14 – LEE, BENJAMIN – Due: Oct 6 2007, 4:00 am 2 7 9 11 12 5 4 8 10 6 3 1 2 a e f b
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hw14 - homework 14 LEE BENJAMIN Due Oct 6 2007 4:00 am...

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