# Capacitors in parallel

#### Gondo

Joined Mar 26, 2007
3
Having some trouble with this one, hoping that you can help me,

Two capacitors have the capacities C1 and C2. One of them has the charge Q while the other one is uncharged. Now they are set in parallel.

a) Show that when equilibrium is reached, each capacitor has a charge that is equal to the original charge multiplied by the ratio of the observed capacitors capacitance and the sum of capacities.

b) Determine an expression for the energy loss expressed by the given operators. Explain the reason for this energy loss.

in a)
So far we've been juggling around with some formulas:

Q[tot]=Q+Q=(C1+C2)*V
Q=C*V

and the fact that V is the same for both capacitors after equilibrium. We do think we need an expression for V[before] though.
We are not quite sure how to set up expressions for the situation before... We're not sure whether we need to do some energy-considerations or not.

Any ideas as for how to move on from here would be greatly appreciated.

Sincerely yours,
Gondo

#### thingmaker3

Joined May 16, 2005
5,083
Which part of the problem do you need help with, and what have you done so far toward a solution?

#### Dave

Joined Nov 17, 2003
6,969
Having some trouble with this one, hoping that you can help me,

Two capacitors have the capacities C1 and C2. One of them has the charge Q while the other one is uncharged. Now they are set in parallel.

a) Show that when equilibrium is reached, each capacitor has a charge that is equal to the original charge multiplied by the ratio of the observed capacitors capacitance and the sum of capacities.

b) Determine an expression for the energy loss expressed by the given operators. Explain the reason for this energy loss.

Sincerely yours,

Gondo
As thinkmaker3 has stated you need to post up what you have done thus far, it is easier to give advice to your existing work. Please read.

We can help you with the necessary equations but need to know where you are currently at. I would start by considering the parallel capacitors as a voltage source (the charge capacitor) in series with the uncharged capacitor, and the equation C = Q/V. Also refer to this post. Think qualitatively about what is happening when you bring the two capacitors together - there is a charge migration from C1 to C2.

Dave

#### Gondo

Joined Mar 26, 2007
3
Post have now been updated with our thought on the matter so far... Hope that helped, thanks...

#### kender

Joined Jan 17, 2007
264
Q[tot] = Q + Q
Q / C = Q / C

2 simultaneous equations with 2 unknowns. this can be solved for Q and Q

#### Gondo

Joined Mar 26, 2007
3
that's not really the problem... I think. hehe...

#### thingmaker3

Joined May 16, 2005
5,083
Formula for energy of a charged capacitor:

U = 0.5*C*V^2 = 0.5*Q*V^2 = 0.5*(Q^2)/C

Prior to being put in parallel:

1) one capacitor has charge Q and the other has charge = 0.

2) The capacitor with charge Q has V=Q/C, and the capacitor with charge = 0 has V = 0

After being put in parallel and achieving equilibrium:

1) Q[tot]=Q+Q=(C1+C2)*V as previously noted, therefore

2) V = Q[tot]/(C1+C2)