Connected Capacitors: Charge & Potential Diffrences

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In summary, connecting an isolated capacitor C1 with charge Q0 to an uncharged capacitor C2 will result in both capacitors carrying a charge of 1/2 Q0. The potential difference across each capacitor will be zero. However, this answer is incorrect as it violates Kirchhoff's loop rule. To satisfy KVL, the charge must be distributed in a way that the sum of the charges in the plates is equal to Q0, resulting in the correct answer.
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andrewdavis23
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Homework Statement


An isolated capacitor C1 carries a charge Q0. Its wires are then connected to those of a second capacitor C2, previously uncharged. What charge will each carry now? What will be the potential difference across each?

Homework Equations


C=Q/V

The Attempt at a Solution


I figured the charge would eventually become evenly distributed (no measure of time was given). So, I figured...

Q1=Q2=1/2 Q0

The potential difference (voltage) would be zero because the charges are equal. ?
 
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  • #2
Are you sure?

Lets see what happens if we take your first answer as correct. You said (from a very obvious perspective) that charge gets equally distributed, but then if you apply Kirchhoff's loop rule (KVL) across the closed circuit, doesn't it get violated?? The total voltage difference across the loop turns out to be:

Q0/2C1-Q0/2C2

which is not equal to zero... which means that you answer isn't correct. Any any case you can't violate KVL!

Indeed you try to distribute the charge in such a way that KVL is satisfied, and since the sum of the charges present in the plates has to be Q0... you will get the correct answer!
 

FAQ: Connected Capacitors: Charge & Potential Diffrences

What are connected capacitors?

Connected capacitors refer to two or more capacitors that are connected in a circuit, either in series or in parallel. This allows them to share a common voltage or charge, resulting in changes in their individual charge and potential differences.

What is charge in capacitors?

Charge in capacitors refers to the electric charge that is stored in the capacitor due to the separation of positive and negative charges on its plates. This charge is measured in coulombs (C) and is directly related to the voltage and capacitance of the capacitor.

How do connected capacitors affect potential difference?

Connected capacitors can either increase or decrease the potential difference, depending on whether they are connected in series or in parallel. In series, the potential difference across each capacitor is divided among them, resulting in a smaller overall potential difference. In parallel, the potential difference across each capacitor remains the same, resulting in a larger overall potential difference.

How does capacitance affect the charge and potential difference in connected capacitors?

Capacitance is a measure of a capacitor's ability to store charge. In connected capacitors, the total capacitance is affected by the arrangement of the capacitors (in series or parallel), and this in turn affects the charge and potential difference across each capacitor. Higher capacitance will result in a larger charge and potential difference.

What happens to the charge and potential difference when capacitors are connected and disconnected?

When capacitors are connected, their charges and potential differences are affected by the circuit arrangement. In series, the charges on each capacitor are the same, but the potential difference is divided among them. In parallel, the potential difference is the same, but the charges are divided among the capacitors. When capacitors are disconnected, their charges and potential differences remain the same as before they were connected.

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