P28_055 - 55. (a) At t = 0 the capacitor is completely...

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55. (a) At t = 0 the capacitor is completely uncharged and the current in the capacitor branch is as it would be if the capacitor were replaced by a wire. Let i 1 be the current in R 1 and take it to be positive if it is to the right. Let i 2 be the current in R 2 and take it to be positive if it is downward. Let i 3 be the current in R 3 and take it to be positive if it is downward. The junction rule produces i 1 = i 2 + i 3 , the loop rule applied to the left-hand loop produces E− i 1 R 1 i 2 R 2 =0 , and the loop rule applied to the right-hand loop produces i 2 R 2 i 3 R 3 =0 . Since the resistances are all the same we can simplify the mathematics by replacing R 1 , R 2 ,and R 3 with R . The solution to the three simultaneous equations is i 1 = 2 E 3 R = 2(1 . 2 × 10 3 V) 3(0 . 73 × 10 6 Ω) =1 . 1 × 10 3 A and i 2 = i 3 = E 3 R = 1 . 2 × 10 3 V 3(0 . 73 × 10 6 Ω) =5 . 5 × 10 4 A . At
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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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