Infinite Ladderof Capacitors

In summary, the conversation discusses finding the equivalent capacitance of a circuit with multiple capacitors. The solution involves using the formula 1/ceq = 1/c + 1/ceq and rearranging to solve for ceq. The conversation also mentions that capacitors in series combine like resistors in parallel. The final answer for the equivalent capacitance is (c/2)((5)^(1/2)-1).
  • #1
cgjones
3
0
Arrangment as is follows a's are there as place holders to keep the diagram intact while posting, all capacitors have = capacitance C

___||______||____||____||...
aaaaaa|aaaaaaa|aaaaaa|
aaaaaa=aaaaaaa=aaaaa= ...
aaaaaa|aaaaaaa|aaaaaa|
____________________________

The question just asks for the equvilant capacitance.

The professor hinted at the solution by writing 1/ceq = 1/c + 1/ceq where ceq is the equivelent capacitance and the answeris given as (c/2)((5)^(1/2)-1)
 
Last edited:
Physics news on Phys.org
  • #2
Suppose you remove the two leftmost capacitors from the diagram.
What you have left is the same infinite network of capacitors, which should
have the same capacitance.
 
  • #3
ok I understand that, so that would leave you with 1/ceq=(2/c + 1/ceq)? because the 2 "removed" capacitors are in series
 
Last edited:
  • #4
cgjones said:
ok I understand that, so that would leave you with 1/ceq=(2/c + 1/ceq)? because the 2 "removed" capacitors are in series

They are not in series. draw a diagram with just the first 2 capacitors and the rest of the network as Ceq
 
  • #5
so 1/ceq=1/c + 1/ceq is what i got, which is insolvable, circuts are definatly not my strong point i guess
____||_________
aaaaaaaa|aaaaa|
aaaaaaaa=aaaaa= ceq
aaaaaaaa|aaaaa|
______________|
 
  • #6
cgjones said:
so 1/ceq=1/c + 1/ceq is what i got, which is insolvable, circuts are definatly not my strong point i guess
____||_________
aaaaaaaa|aaaaa|
aaaaaaaa=aaaaa= ceq
aaaaaaaa|aaaaa|
______________|

The capacity of the entire circuit Ceq is equal to the capacity of the circuit you've drawn
here, which is one capacitor of value Ceq in parallel with a capacitor of value C, and the
equivalent capacitor to that in series with another capacitor with capacitance C
 
  • #7
Just do like willem2 said, and remember: capacitors in series combine like resistors in parallel, and vice versa. I tried out the problem myself, and the answer you have quoted is correct: i.e., Ceq = (c/2)(5^0.5 - 1).
 

What is an infinite ladder of capacitors?

An infinite ladder of capacitors is a theoretical circuit made up of an infinite number of capacitors connected in series. This means that the positive plate of one capacitor is connected to the negative plate of the next capacitor, creating an unending chain of capacitors.

What is the purpose of an infinite ladder of capacitors?

The purpose of an infinite ladder of capacitors is to create a circuit with a very large capacitance. This can be useful in applications where a large amount of charge needs to be stored or where a very low impedance is required.

How is the equivalent capacitance of an infinite ladder of capacitors calculated?

The equivalent capacitance of an infinite ladder of capacitors can be calculated using the formula Ceq = C/2, where C is the capacitance of each individual capacitor. This means that the equivalent capacitance of an infinite ladder of capacitors is half the capacitance of a single capacitor.

What is the effect of adding more capacitors to an infinite ladder of capacitors?

Adding more capacitors to an infinite ladder of capacitors will increase the equivalent capacitance of the circuit. This means that the circuit will be able to store more charge and have a lower impedance. However, as the number of capacitors increases, the effect on the equivalent capacitance becomes less significant.

Are there any real-world applications for an infinite ladder of capacitors?

No, an infinite ladder of capacitors is a theoretical concept and cannot be physically built. However, circuits with multiple capacitors in series can be used in practical applications to achieve a similar effect.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
813
  • Introductory Physics Homework Help
Replies
12
Views
6K
  • Advanced Physics Homework Help
Replies
8
Views
11K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
4K
  • Introductory Physics Homework Help
Replies
10
Views
5K
Back
Top