Question

Four identical plates $1,2,3$ and $4$ are placed parallel to each other at equal distance as shown in the figure. Plates $1$ and 4 are joined together and the space between $2$ and $3$ is filled with a dielectric of dielectric constant $k=2$. The capacitance of the system between $1$ and $3$ and $2$ and $4$ are $C_{1}$ and $C_{2}$, respectively. The ratio $\frac{C_{1}}{C_{2}}$ is ______

Answer 1

We can express this arrangement as circuit

When equivalent capacitance is calculated between $1$ and $3$ then

$C_{1}=\frac{2 C}{3}+C=\frac{5 C}{3}$
When equivalent capacitance calculated between $2$ and $4 .$

Hence $C_{2}=\frac{2 C}{3}+C=\frac{5 C}{3}$
So $C_{1}: C_{2}$ equal to $1: 1$.