Capacitance of four metal plates

In summary, The problem from Irodov involves four parallel metal plates with equal area and distance between them. The external plates are connected by a wire and the objective is to find the equivalent capacitance between point A and B. The solution involves recognizing three capacitors (12), (23), and (34) and their arrangement in the circuit. Each node (A, B, and C) has capacitance between them, with C being the wire connecting the outer plates.
  • #1
Patrikp
23
0

Homework Statement


Four identical parallel metal plates with area $$S$$ and distance between each two $$d$$ are located in air. The external plates are connected by wire. What is the equivalent capacitance between A and B?
This is problem from Irodov.

Homework Equations


$$q=UC$$[/B]

The Attempt at a Solution


Plates 1 and 4 are always on same potential which I am not sure how to use.
I tried to simplify as on the picture but that turns out to be wrong(why?).

[/B]
 

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  • #2
As I see it there are three nodes, A, B and C (the wire connecting the outer plates 1 and 4).

Draw the three nodes on paper. There is capacitance between...

A and B
A and C
B and C
 
  • #3
CWatters said:
As I see it there are three nodes, A, B and C (the wire connecting the outer plates 1 and 4).

Draw the three nodes on paper. There is capacitance between...

A and B
A and C
B and C
Can you explain how did you get that? Thanks
 
  • #4
You have to recognize the 3 capacitors, its easier if you number them, say capacitor plate 1,2,3 and 4 , so the 3 capacitors are (12),(23) and (34), now try figuring out the the arrangement of these capacitors, by considering which are connected and which are not.
Patrikp said:
Can you explain how did you get that?
If you want to know how to recognize the 3 capacitors try giving the plates charges, imagine A is the +ve terminal and see which all plates should have +ve and which -ve, once you figure that out, i think you'll be able to get the answer.
 
  • #5
Patrikp said:
Can you explain how did you get that? Thanks

Try..

image.jpg


PS the colours don't mean anything they are just to highlight the three nodes.
 

Related to Capacitance of four metal plates

1. What is capacitance?

Capacitance is the ability of a system to store electrical charge. It is measured in units of Farads (F).

2. How is capacitance calculated for four metal plates?

The capacitance of four metal plates can be calculated using the formula C = εA/d, where C is capacitance, ε is the permittivity of the material between the plates, A is the area of each plate, and d is the distance between the plates.

3. How does the distance between the plates affect capacitance?

The closer the plates are to each other, the higher the capacitance. This is because the electric field between the plates is stronger, allowing for more charge to be stored.

4. Does the size of the plates affect capacitance?

Yes, the larger the plates, the higher the capacitance. This is because there is more surface area for charge to accumulate on, thus increasing the overall capacitance.

5. Can the material of the plates affect capacitance?

Yes, the material of the plates can affect capacitance. Materials with a higher permittivity, such as metals, will have a higher capacitance compared to materials with a lower permittivity, such as air.

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