P26_021 - q is the original charge, conservation of charge...

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21. The charges on capacitors 2 and 3 are the same, so these capacitors may be replaced by an equivalent capacitance determined from 1 C eq = 1 C 2 + 1 C 3 = C 2 + C 3 C 2 C 3 . Thus, C eq = C 2 C 3 / ( C 2 + C 3 ). The charge on the equivalent capacitor is the same as the charge on either of the two capacitors in the combination and the potential diFerence across the equivalent capacitor is given by q 2 /C eq . The potential diFerence across capacitor 1 is q 1 /C 1 ,whe re q 1 i sthecha rgeonth i s capacitor. The potential diFerence across the combination of capacitors 2 and 3 must be the same as the potential diFerence across capacitor 1, so q 1 /C 1 = q
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Unformatted text preview: q is the original charge, conservation of charge yields q 1 + q 2 = q = C 1 V , where V is the original potential diFerence across capacitor 1. Solving the two equations q 1 C 1 = q 2 C eq and q 1 + q 2 = C 1 V for q 1 and q 2 , we nd q 2 = C 1 V q 1 and q 1 = C 2 1 V C eq + C 1 = C 2 1 V C 2 C 3 C 2 + C 3 + C 1 = C 2 1 ( C 2 + C 3 ) V C 1 C 2 + C 1 C 3 + C 2 C 3 . The charges on capacitors 2 and 3 are q 2 = q 3 = C 1 V q 1 = C 1 V C 2 1 ( C 2 + C 3 ) V C 1 C 2 + C 1 C 3 + C 2 C 3 = C 1 C 2 C 3 V C 1 C 2 + C 1 C 3 + C 2 C 3 ....
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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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