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

Answer: 1

We can express this arrangement as circuit

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

$C_1=\frac{2C}{3}+C=\frac{5C}{3}$
When equivalent capacitance calculated between $2$ and $4.$

Hence $C_2=\frac{2C}{3}+C=\frac{5C}{3}$
So $C_1:C_2$ equal to $1:1$.