Initially, the switch in FIGURE is in position A and capacitors and are uncharged. Then the switch is flipped to position . Afterward, what are the charge on and the potential difference across each capacitor?
The charge on is , and the charge on and is . The potential difference on is , the potential difference on is and the potential difference on is .
We need to find the charge on and the potential difference across each capacitor.
The equivalent circuit when the switch is in the position A is given in the figure bellow. In this case we have only one capacitor connected to the battery. Its plates are charged by where
The piece of wire that connects with a plate of with plate of carries the charge .Some of this charge will be transferred to the upper plate of and we will have
The charge of will be induced on the opposite plate of . This in turn will induce on the neighboring plate of (since that piece of wire is neutral in total), and the induced charge on the opposite plate will be . The capacitors and are oriented in different differently than . Since there is no electromotive force in this circuit, the potential difference on must be equal to the sum of potential differences on and i.e.
Now, we have two equations for and . From equation we have . Substitute this into the second equation to get
This further yields
Now, the potential differences are
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