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problem24_75

# University Physics with Modern Physics with Mastering Physics (11th Edition)

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24.75: a) We are to show the transformation from one circuit to the other: From Circuit 1: y ac C q q V 3 1 - = and = bc V , 3 2 x C q q + where 3 q is derived from : ab V - - + + = - - - = = x y x y z y x z y x x y z ab C q C q K C q C q C C C C C C q C q q C q q C q V 2 1 2 1 3 3 2 3 1 3 From Circuit 2: 3 2 3 1 1 3 2 1 1 1 1 1 1 C q C C q C q q C q V ac + + = + + = and . 1 1 1 3 2 2 3 1 3 2 1 2 2 + + = + + = C C q C q C q q C q V bc Setting the coefficients of the charges equal to each other in matching potential equations from the two circuits results in three independent equations relating the two sets of capacitances. The set of equations are: - - = - - = x y x x y y KC KC C C KC KC C C 1 1 1 1 1 , 1 1 1 1 1 2 1 and . 1 1 3 x y C KC C = From these, subbing in the expression for , K we get: . ) ( . ) ( . ) ( 3 2 1 z x z z y y x y x z z y y x x x z z y y x C C C C C C C C C C C C C C C C C C

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problem24_75 - 24.75 a We are to show the transformation...

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