Question

There are six parallel plates of equal area $A$ arranged as shown in figure $\left(d < < A\right)$ . The equivalent capacitance between points $2$ and $5$ is $\alpha \frac{\epsilon _{0} A}{ d}$ . Then, find the value of $\alpha $ .

Answer 1

Recall the feature of balanced meter bridge.

The above combination of capacitance is the example of a balanced meter bridge,
$C_{AB}=C$ .
Recall the formula of capacitance in terms of cross-sectional area and separation between the capacitors,
$C=\frac{\epsilon _{0} A}{ d}=\alpha \frac{\epsilon _{0} A}{ d}$
$\alpha =1$ .