Circuits with capacitators connected parallel

[mbkau00]

doesn't V need to be solved for? substituting q1 into the last equation and solving for q2 will equal 0.

so to clarify:

c1 = 0.05uF
c2 = 0.1uF
q1 = 2x10^-8

V is unknown
q2 is unknown

 

[gneill]

doesn't V need to be solved for? substituting q1 into the last equation and solving for q2 will equal 0.

so to clarify:

c1 = 0.05uF √
c2 = 0.1uF √
q1 = 2x10^-8 X
Qtotal = 2x10^-8

V is unknown
q1 is unknown
q2 is unknown

You do not know what q1 will be when the capacitors are connected. You only know what it is BEFORE they are connected, and it happens to be the total charge available. q1 and q2 are your unknowns that represent the charges AFTER connection.

 

[mbkau00]

rearranging:

V=Q1/C1
V=Q2/C2
q1+q2= 2x10^(-8)

rearranging and substituting:

V=q1/0.05uF, 0.05uF*V=q1
V=q2/0.1uF, 0.1uF*V=q2

0.05uF*V+0.1uF*V = 2x10^-8

 

[gneill]

rearranging:

V=Q1/C1
V=Q2/C2
q1+q2= 2x10^(-8)

rearranging and substituting:

V=q1/0.05uF, 0.05uF*V=q1
V=q2/0.1uF, 0.1uF*V=q2

0.05uF*V+0.1uF*V = 2x10^-8

I'm not sure why you keep bringing V back into play. You're looking for the percentage of the charge that ends up being transferred from C1 to C2. So you only need the charges Q1 and Q2.

Eliminate V as you did earlier:

(1) Q1/C1 = Q2/C2
(2) Q1 + Q2 = Q

From (2): Q2 = Q - Q1

Replace Q2 in (1): Q1/C1 = (Q - Q1)/C2

solve for Q1.

Do the same for Q2. You should do this with the symbols because dragging around a lot of numbers through a derivation is both tiring and prone to error. Also, when done, you'll find that the equations are particularly elegant and easy to remember for similar problems in the future.

 

[mbkau00]

Thanks for your help and persistence.

Unfortunately I don't get an answer near 70% which is the correct answer. I think i must admit defeat, considering time spent.
Thanks again :)

 

[gneill]

Thanks for your help and persistence.

Unfortunately I don't get an answer near 70% which is the correct answer. I think i must admit defeat, considering time spent.
Thanks again :)

Well, you're very close to the final formulas now. What did you arrive at for the charge on C2?

 

[mbkau00]

1.5*10^-7Q1 = 1*10^-15 - 5*10^-8Q1
Q1 = 6.67*10^-9

2*10^-15 - 1*10^-7Q2 = 5*10^-8Q2
Q2 = 1.33*10^-8

I am honestly as lost as when I started as I don't have a definitive approach in why certain variables are, or aren't related.

 

[gneill]

1.5*10^-7Q1 = 1*10^-15 - 5*10^-8Q1
Q1 = 6.67*10^-9

2*10^-15 - 1*10^-7Q2 = 5*10^-8Q2
Q2 = 1.33*10^-8

I am honestly as lost as when I started as I don't have a definitive approach in why certain variables are, or aren't related.

Well, your values for Q1 and Q2 look fine!

Perhaps a crude analogy would help. You have two containers with different dimensions (capacities). One contains a certain volume of water (charge) while the other is empty. You want to know how much of the water needs to end up in each container so the water will reach to the same height (voltage) in each. Water volume is conserved -- it doesn't disappear when you move it around. Charge is likewise conserved.

For the capacitor the underlying relationship is Q = C*V. For the containers you'd have something like Volume = A*h, where A is the area of the base of the container and h the height of the fluid.

For the fluid case, if the heights of the fluid is the same then V1/A1 = V2/A2 and V1 + V2 = V, the total volume of fluid you're working with. The similar equations you arrived at for the capacitors are Q1/C1 = Q2/C2 and Q1 + Q2 = Q.

When solved the expressions for Q1 and Q2 have the simple form:

$Q1 = \frac{C1}{C1 + C2} Q$

$Q2 = \frac{C2}{C1 + C2} Q$

So each capacitor gets a fraction of Q that is equal to that capacitor's portion of the total capacitance.

 

[mbkau00]

Your analogy definitely adds a great perspective. Thanks so much.

I still can't see how the answer is 70% of charge went from C1 to C2.

 

[gneill]

Your analogy definitely adds a great perspective. Thanks so much.

I still can't see how the answer is 70% of charge went from C1 to C2.

Remember that C1 started out with charge Q (it ended up with charge Q1). Make sure that you're comparing Q2 with Q.

 

[mbkau00]

Thank you.