In this problem $C_{1}=2C_{2}.$Initially, the charge on $C_{1}$ is $Q_{1}=Q_{0}$ and on $C_{2}$ the charge is $Q_{2}=0.$
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In the final state,
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Writing K's loop rule with the charge and current variables defined as shown, we have:
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From charge conservation:
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and
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Thus the loop rule becomes
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Rearranging
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where
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Defining the new variable
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Then
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and thus
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and
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