Algebra Problem with Capacitators

[dempster]

Homework Statement

Q0=Q1+Q2 Q1/C1 =Q2/C2 I substituted it Q1/C1=Q0-Q1/C2 then I got Q1=C1Q0-C1Q1/C2 but the answer has to be Q1=Q0C1/C1+C2 my algebra isn't good enough to solve it what are the steps that I have to take to make it to the answer

Homework Equations

The Attempt at a Solution

 

[RUber]

Please be more clear with your spacing and parentheses.
Are you saying that you have $Q_0 = Q_1 + Q_2 \frac {Q_1}{C_1} = \frac {Q_2}{C_2} ?$
$\frac{Q_1}{C_1} = Q_0 - \frac{Q_1}{C_2}?$
This is very difficult to follow and does not make much sense.

Or are you saying that $Q_0 = Q_1 + Q_2$ and $\frac {Q_1}{C_1} = \frac {Q_2}{C_2}$?
In any case, if you are solving for Q1, you should not have it in your answer as you did when you wrote:
$Q_1 = C_1Q_0 - \frac{C_1Q_1}{C_2}$.

If you have $Q_0 = Q_1 + Q_2$ and $\frac {Q_1}{C_1} = \frac {Q_2}{C_2}$, then start by solving for Q2 in terms of Q1 from the second relation. Then substitute that into the first and solve for Q1.

 

[dempster]

Q0=Q1+Q2 I made that to Q2=Q0-Q1 Then this Applies Q1/C1=Q2/C2 I substituted Q2 and did everything times C1 so I got Q1= C1(Q0-Q1)/C2 but I know that the answer should be Q1= C1Q0/C1+C2 But I can't make the steps to make that happen?

 

[RUber]

Add $\frac{C1Q1}{C2}$ to each side.
Factor out Q1 on left.
Divide to solve for Q1.

 

[epenguin]

" I know that the answer should be Q1= C1Q0/C1+C2"

You should bracket those last two terms otherwise apart from anything else it's physical nonsense, essentially a charge equal to a charge plus a capacitance. Would also have been better if you started by stating what you are looking to obtain.

It might be better to start with the equation relating two charges rather than three. Then you just get one charge in terms of the other (and the capacitances). Thus Q₂ = Q₁C₂/C₁
From which you can get
Q₀ = Q₁(1 + C₂/C₁)

Which you can throw into the form or your desired equation or else you could get that more directly.

This looks like being about how total charge distributes itself between two capacitors in parallel, so you should also think about it physically to realize the equations make sense. Your can eliminate various different parameters by choice, express all and any of the charges in terms of just one.