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4 placas son conectadas entre sí como muestra la figura. Determinar
la capacidad equivalente entre los bornes A y B, si la superficie de
cada placa es S y la separación entre placas es d.

The diagram shows a system of four parallel plates. The task is to determine the equivalent capacitance between points \(A\) and \(B\), with each plate having a surface area \(S\) and a distance \(d\) between the plates.

### Steps for calculating the equivalent capacitance:

1. **Identifying the Configuration:**
   - The plates are labeled from top to bottom as \(1\), \(2\), \(3\), and \(4\).
   - The system behaves like two capacitors in series connected to points \(A\) and \(B\), since charges are shared between plates \(2\) and \(3\), with the outermost plates (\(1\) and \(4\)) connected back to each other.

2. **Capacitance Between Two Parallel Plates:**
   The capacitance \(C\) between any two plates is given by:
   \[
   C = \varepsilon_0 \frac{S}{d}
   \]
   where \( \varepsilon_0 \) is the permittivity of free space, \(S\) is the surface area of the plates, and \(d\) is the distance between them.

3. **Capacitance in Series:**
   - The configuration suggests that we have two capacitors formed between plates \(1\) and \(2\), and between plates \(3\) and \(4\), connected back to back.
   - Since the middle plates (\(2\) and \(3\)) are connected, the total system behaves like two capacitors in series.

4. **Capacitance of Each Section:**
   Each section (either between \(1\) and \(2\), or between \(3\) and \(4\)) has a capacitance:
   \[
   C_1 = C_2 = \varepsilon_0 \frac{S}{d}
   \]

5. **Capacitance of the Total System:**
   The equivalent capacitance for capacitors in series is:
   \[
   \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2}
   \]
   Since \(C_1 = C_2\), we get:
   \[
   C_{eq} = \frac{C_1}{2} = \frac{\varepsilon_0 S}{2d}
   \]

### Final Answer:
The equivalent capacitance between points \(A\) and \(B\) is:
\[
C_{eq} = \frac{\varepsilon_0 S}{2d}
\]

Would you like more details on any step? Here are some related questions:

1. How does the series connection of capacitors affect the overall capacitance?
2. What happens if the distance \(d\) between the plates is changed?
3. How would adding more plates to the system alter the equivalent capacitance?
4. What role does the surface area \(S\) of the plates play in the capacitance?
5. How can you experimentally measure the capacitance in a system like this?

**Tip:** When capacitors are connected in series, the total capacitance decreases, unlike in parallel connections where it increases.

4 placas son conectadas entre sí como muestra la figura. Determinar la capacidad equivalente entre los bornes A y B, si la superficie de cada placa es S y la separación entre placas es d.

This problem demonstrates how to calculate the equivalent capacitance between terminals A and B for a system of four connected plates. Each plate has a surface area S, and the separation between them is d. The solution uses electrostatic principles and series capacitance formulas.

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