Capacitor combination Question

In summary, the conversation discusses adding a single capacitor to a circuit containing a 250 pF capacitor in order to store three times as much energy in a combination of two capacitors. The equation PE = (1/2) CV^2 is used to determine the value of the added capacitor, with the final potential energy being three times the initial potential energy. By adding the capacitance of the initial capacitor (C1) to the added capacitor (C2), a value of 500 pF is determined for C2.
  • #1
sunflowerzz
25
0

Homework Statement



A circuit contains a single 250 pF capacitor hooked across a battery. It is desired to store three times as much energy in a combination of two capacitors by adding a single capacitor to this one. How would you hook it up, and what would its value be?

Homework Equations



PE = (1/2) CV^2

The Attempt at a Solution



PE(final) = 3PE(initial)

so then:

(1/2)CV^2 = 3 * (1/2) CV^2

Not sure where to go from here? I would think that if it is three times as much energy, then it should be 3 times the capacitance 3C = 3 * 250 pF = 750 pF but this isn't correct
 
Physics news on Phys.org
  • #2
sunflowerzz said:

Homework Statement



A circuit contains a single 250 pF capacitor hooked across a battery. It is desired to store three times as much energy in a combination of two capacitors by adding a single capacitor to this one. How would you hook it up, and what would its value be?

Homework Equations



PE = (1/2) CV^2

The Attempt at a Solution



PE(final) = 3PE(initial)

so then:

(1/2)CV^2 = 3 * (1/2) CV^2

Not sure where to go from here? I would think that if it is three times as much energy, then it should be 3 times the capacitance 3C = 3 * 250 pF = 750 pF but this isn't correct

I would call the initial capacitor C1, and the cap you add could be C2. That will make your equation make more sense.

And you have the right idea, but the question asks what size capacitor should you *add* to make the total energy storage 3x the initial storage on C1. How does that change your answer? :smile:
 
  • #3
berkeman said:
I would call the initial capacitor C1, and the cap you add could be C2. That will make your equation make more sense.

And you have the right idea, but the question asks what size capacitor should you *add* to make the total energy storage 3x the initial storage on C1. How does that change your answer? :smile:

Ok so then it's:

(1/2)C2V^2 = 3 * (1/2)C1V^2

When you say "add", does this mean C2 will be in parallel with C1?

OOH...so if it's parallel, then It's C1 + C2 but is C1 = C2? If it is, then C = C1 + C2 = 250 + 250 = 500 pF

But how do you know that both capacitors are 250 pF?
 
  • #4
sunflowerzz said:
Ok so then it's:

(1/2)C2V^2 = 3 * (1/2)C1V^2

When you say "add", does this mean C2 will be in parallel with C1?

OOH...so if it's parallel, then It's C1 + C2 but is C1 = C2? If it is, then C = C1 + C2 = 250 + 250 = 500 pF

But how do you know that both capacitors are 250 pF?

If you add C2 in parallel, what should you have written instead on the lefthand side (LHS) of your equation:

"(1/2)C2V^2 = 3 * (1/2)C1V^2"

Your LHS is incorrect as written.
 
  • #5
berkeman said:
If you add C2 in parallel, what should you have written instead on the lefthand side (LHS) of your equation:

"(1/2)C2V^2 = 3 * (1/2)C1V^2"

Your LHS is incorrect as written.

Do you mean LHS for C2 = C1 + C2?
 
  • #6
sunflowerzz said:
Do you mean LHS for C2 = C1 + C2?

Yes, the LHS should be the sum of C1+C2, not just C2. Your intuition has been correct all along. What value do you now get for C2?
 
  • Like
Likes 1 person
  • #7
berkeman said:
Yes, the LHS should be the sum of C1+C2, not just C2. Your intuition has been correct all along. What value do you now get for C2?

Ok I got it:

(1/2)*(C1 + C2)*V^2 = 3 * (1/2)C1V^2

C1 + C2 = 3C1
C2 = 3C1 - C1 = 2C1 = 2 * 250 = 500 pF

Thanks! :)
 

1. How do you calculate the total capacitance of a series combination of capacitors?

To calculate the total capacitance of a series combination of capacitors, you simply add up the reciprocal of each individual capacitance. In other words, if you have three capacitors with capacitance values of C1, C2, and C3, the total capacitance would be 1/Ctotal = 1/C1 + 1/C2 + 1/C3.

2. What is the formula for calculating the total capacitance of a parallel combination of capacitors?

The formula for calculating the total capacitance of a parallel combination of capacitors is simply the sum of all the individual capacitances. In mathematical terms, it would look like Ctotal = C1 + C2 + C3 + ... + Cn.

3. How does the total capacitance change when capacitors are connected in series compared to parallel?

When capacitors are connected in series, the total capacitance decreases because the effective distance between the plates increases, reducing the overall capacitance. On the other hand, when capacitors are connected in parallel, the total capacitance increases because the effective distance between the plates decreases, increasing the overall capacitance.

4. What is the effect of adding a dielectric material in a capacitor combination?

Adding a dielectric material in a capacitor combination increases the capacitance of the system. This is because the dielectric material reduces the effective distance between the plates, thus increasing the capacitance. The amount of increase in capacitance depends on the dielectric constant of the material used.

5. Can capacitors be combined in both series and parallel in a single circuit?

Yes, it is possible to have a combination of capacitors in both series and parallel in a single circuit. This can be useful in creating complex circuits that require a specific capacitance value. In such cases, the total capacitance can be calculated using a combination of the series and parallel formulas.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
898
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
861
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
16
Views
3K
  • Introductory Physics Homework Help
Replies
16
Views
1K
Back
Top