# ch25_p22 - V 1 = 2.0 V The above expression consequently...

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22. Initially the capacitors C 1 , C 2 , and C 3 form a combination equivalent to a single capacitor which we denote C 123 . This obeys the equation 1 C 1 + 1 C 2 + C 3 = 1 C 123 . Hence, using q = C 123 V and the fact that q = q 1 = C 1 V 1 , we arrive at V 1 = C 2 + C 3 C 1 + C 2 + C 3 V . (a) As C 3 this expression becomes V 1 = V . Since the problem states that V 1 approaches 10 volts in this limit, so we conclude V = 10 V. (b) and (c) A t C 3
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Unformatted text preview: V 1 = 2.0 V. The above expression consequently implies C 1 = 4 C 2 . Next we note that the graph shows that, at C 3 = 6.0 µ F, the voltage across C 1 is exactly half of the battery voltage. Thus, 1 2 = C 2 + 6.0 µ F C 1 + C 2 + 6.0 µ F = C 2 + 6.0 µ F 4 C 2 + C 2 + 6.0 µ F which leads to C 2 = 2.0 µ F. We conclude, too, that C 1 = 8.0 µ F....
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