Finding the charges on capacitors in a circuit

[nameless912]

Homework Statement

Four capacitors are connected as shown and connected to a battery to maintain a constant potential difference between points a and b. A charge Q2 = 61.6 μC is measured on capacitor 2.

What is the charge on capacitor C3?

Homework Equations

Q = CV; rules for combining capacitors (in parallel, add together; in series, take the inverse of the inverses added together) U = 1/2 C*V^2 = q^2/2C

The Attempt at a Solution

The previous problems related to this one asked for the potential energy stored in the capacitor C2 and the capacitance of the entire network. I was able to figure those out easily, but with this problem I don't even know where to begin.

I feel like without knowing the battery voltage, it's impossible to work backwards to find the voltage (and therefore the charge) over C3 and C4. I was thinking maybe trying to use some kind of modified voltage divider rule like I learned in one of my EE classes for resistor networks, and that looks something like this:

C1,2/C2 = V2/V (I used the voltage divider rule for resistors in parallel since capacitors and resistors follow opposite rules)

Solving for V (the voltage over the battery), I got 9.24 volts, but I still don't know how to use that to find the voltage over C3 and C4 (because I don't know how to find the voltage across C1) and frankly I don't feel like I'm approaching this problem in the right way anyway.

I appreciate the help in advance!

 

[SammyS]

Homework Statement

Four capacitors are connected as shown and connected to a battery to maintain a constant potential difference between points a and b. A charge Q2 = 61.6 μC is measured on capacitor 2.

What is the charge on capacitor C3?

Homework Equations

Q = CV; rules for combining capacitors (in parallel, add together; in series, take the inverse of the inverses added together) U = 1/2 C*V^2 = q^2/2C

The Attempt at a Solution

The previous problems related to this one asked for the potential energy stored in the capacitor C2 and the capacitance of the entire network. I was able to figure those out easily, but with this problem I don't even know where to begin.

I feel like without knowing the battery voltage, it's impossible to work backwards to find the voltage (and therefore the charge) over C3 and C4. I was thinking maybe trying to use some kind of modified voltage divider rule like I learned in one of my EE classes for resistor networks, and that looks something like this:

C1,2/C2 = V2/V (I used the voltage divider rule for resistors in parallel since capacitors and resistors follow opposite rules)

Solving for V (the voltage over the battery), I got 9.24 volts, but I still don't know how to use that to find the voltage over C3 and C4 (because I don't know how to find the voltage across C1) and frankly I don't feel like I'm approaching this problem in the right way anyway.

I appreciate the help in advance!

It seems to me that you have to assume that all capacitors were discharged prior to being placed in this circuit.

If so, there are several ways to solve this problem. The essential principle in play is conservation of charge.


What is the equivalent capacitance of this network of capacitors ?

 

[technician]

capacitors in series all have the same charge ! so you know the charge on C1 and the charge on the combination of C3 and C4 in parallel

 

[nameless912]

What is the equivalent capacitance of this network of capacitors ?

The equivalent capacitance is 3.415 μC, the potential energy in C2 is 95 μJ, and the voltage across C2 is 3.08 volts. That's all the information I've been able to derive.

 

[nameless912]

Ah, thanks technician. That makes sense now haha.

So I'm allowed to assume in a problem like this that all the capacitors in series have the same charge on them?

 

[SammyS]

Ah, thanks technician. That makes sense now haha.

So I'm allowed to assume in a problem like this that all the capacitors in series have the same charge on them?

That's the result of conservation of charge.

 

[technician]

It is not an 'assumption'...it is a fact about capacitors in series.
It is one of these facts that can be difficult to get your head round .
The charge on each capacitor is the same and the total charge in the circuit is the same!

 

[SammyS]

It is not an 'assumption'...it is a fact about capacitors in series.
It is one of these facts that can be difficult to get your head round .
The charge on each capacitor is the same and the total charge in the circuit is the same!

In fact, having the same charge on the capacitors is essential in deriving the expression for equivalent capacitance of capacitors in series.