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The plates of a parallel capacitor are given charges +4Q and -2QThe capacitor is then connected across an uncharged capacitor of same capacitance C. What is the final potential difference between plates of first capacitor. I considered trying to distribute charge in form of algebraic variables and then apply Kirchoff's loop law. But i am not sure how the distribution of charge should be,and there are not sufficient equations getting framed to take out variables. Some help is appreciated!

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The charge on the two plates will get distributed in such a manner: (+1C)|||(+3C) (-3C)|||(+1C). There is a particular behaviour that I noticed(while doing many questions of the same type) in which the charges on the outer surface of the plates is equal to the sum of all the charges present on the combination of plates... This is what I have used to find the charge distribution on plates I. E. Net charge on combination of plates = (+4C - 2C)/2 = 1C. Now the charge on the capacitor is the charge on the inner plates... I. E. 3C. I hope now you will be able to solve the problem.

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It's not entirely clear from your question, but it appears you have 6 coulombs charge on a capacitor C, which is then distributed to be on a capacitor 2C. The rest should be obvious application of the voltage on a capacitor equation.

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