Why Do Capacitors in Parallel Share the Same Voltage?

[oneplusone]

Homework Statement

C1 = 6.00 uF
C2 = 3.00 uF
$\Delta V = 20.0$ V

Capacitor c1 is first charged by the closing of s_1. Switch S_1 is then opened and the carved capacitor is connected to the uncharged capacitor b the closing of S_2. Calculate the initial charge acquired by C_1 and the final charge on each capacitor.

Homework Equations

C=Q/V

The Attempt at a Solution

See attached.

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I get everything in this solution besides when they set Q_1/C_1 = Q_2/C_2.
Is it ALWAYS true that the voltage across two points are the same?

 

[Chronum]

If you connected 2 capacitors, remember that their plates are connected by a conductor.

Now what happens when you connect two points with a conductor?

 

[oneplusone]

Current is formed, so there is a voltage?
And since there is no loss of electrons (charge) and the intensity (current) is the same, the voltage is the same?
Is that correct?

 

[Chronum]

Well, as long as there is current flowing, you can't really make a problem out of it, at least not here, because it's not in a steady state.

But yes, when current does stop flowing in the circuit, the voltages are the same on both capacitors.

Now, there are formulae for the final charge/voltage in such an arrangement. I'd suggest you go through your textbook or look through the forums. I've forgotten the formulae myself, but I do remember that they exist.

 

[NascentOxygen]

Current is formed, so there is a voltage?
And since there is no loss of electrons (charge) and the intensity (current) is the same, the voltage is the same?
Is that correct?

You could include the resistance of the wire as a resistor in your crcuit, making it 3 elements. Current will flow through the resistor until the voltage across the resistor falls to zero. At the start, there are different voltages on each side.

 

[rude man]

Homework Statement

C1 = 6.00 uF
C2 = 3.00 uF
$\Delta V = 20.0$ V

Capacitor c1 is first charged by the closing of s_1. Switch S_1 is then opened and the carved capacitor is connected to the uncharged capacitor b the closing of S_2. Calculate the initial charge acquired by C_1 and the final charge on each capacitor.

Homework Equations

C=Q/V

The Attempt at a Solution

See attached.

===============


I get everything in this solution besides when they set Q_1/C_1 = Q_2/C_2.
Is it ALWAYS true that the voltage across two points are the same?

When S2 is closed the two capacitors are in parallel so by definition their voltage drops must be the same.