Capacitance (Potential Difference and Energy)

[kilnvzol]

Homework Statement

In the figure C1 = 10.0 μF,C2 = 20.0 μF and C3 = 27.0 μF. If no capacitor can withstand a potential difference of more than 130 V without failure, what is (a) the magnitude of the maximum potential difference that can exist between points A and B and (b) the maximum energy that can be stored in the three-capacitor arrangement?
http://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c25/q37.jpg
Image link - http://www.webassign.net/hrw8/25-45.gif

Homework Equations

1/C_series= 1/C₁ + 1/C₂ ...
U = q²/(2C) = (0.5)CV²

The Attempt at a Solution

For part A, I know that 130V goes into C1 and I think half that goes into C2 so 65V but I'm not sure how much goes into C3.
For part B, I need the solution to part A to figure that out.

Thank you!

 

[gneill]

For part A, I know that 130V goes into C1 and I think half that goes into C2 so 65V ...

Can you justify that claim?

... but I'm not sure how much goes into C3.
For part B, I need the solution to part A to figure that out.

Consider how charge is distributed amongst series-connected capacitors (when they are charged simultaneously by the same current).

What relationship is there between voltage, charge, and capacitance?

Edit: For part (b), consider a clever way to put as much energy as possible onto the arrangement.

 

[kilnvzol]

Actually I think I got part A. C = Q/V => V=Q/C the voltage for the first one is 130 so Q = (130)(10E-6) = 1.3E-3
Then you use the Q value to find the rest? So C3 is 48.15?

For part B, I just use the equation U = q2/(2C) = (0.5)CV2?

 

[gneill]

Actually I think I got part A. C = Q/V => V=Q/C the voltage for the first one is 130 so Q = (130)(10E-6) = 1.3E-3
Then you use the Q value to find the rest? So C3 is 48.15?

That looks good.

For part B, I just use the equation U = q2/(2C) = (0.5)CV2?

Yes,... but the question as posed does not restrict you to using the charges or voltages from part A...

 

[kilnvzol]

Yes,... but the question as posed does not restrict you to using the charges or voltages from part A...

Do you just plug in each voltage with its respective capacitance to the equation and see which is higher or what is the other way?

 

[gneill]

Do you just plug in each voltage with its respective capacitance to the equation and see which is higher or what is the other way?

You want to maximize the total energy stored (while respecting the voltage tolerance of the individual components). So what would be the ideal situation?

 

[kilnvzol]

You want to maximize the total energy stored (while respecting the voltage tolerance of the individual components). So what would be the ideal situation?

Only using the potential energy from the first capacitor?

 

[gneill]

Only using the potential energy from the first capacitor?

Wouldn't that be a waste of the energy storage potential of the other two?

 

[kilnvzol]

Wouldn't that be a waste of the energy storage potential of the other two?

Add all of the potential energies together?

 

[gneill]

Add all of the potential energies together?

Sure. After all, you have three "containers" and each can store some. Otherwise it's like having three boxes to put things in and only using the smallest one.

 

[kilnvzol]

Sure. After all, you have three "containers" and each can store some. Otherwise it's like having three boxes to put things in and only using the smallest one.

Thank you i got it!