Question

A parallel-plate capacitor is connected to a battery as shown in the figure. A conducting plate is inserted mid-way between the two plates. Take the plate area as A. The distance between each plate in the new configuration is d.

What is the capacitance of the system after the plate is inserted?

• A. $\frac{{\epsilon }_{0}A}{d}$
• B. $\frac{{\epsilon }_{0}A}{2d}$
• C. $\frac{2{\epsilon }_{0}A}{d}$
• D. Cannot say anything

Answer 1

The correct option is B $\frac{{\epsilon }_{0}A}{2d}$

From given,

and we can the redraw circuit as
$C_{eq}=\frac{C^2}{2C}=\frac{C}{2}=\frac{{\epsilon }_{0}A}{2d}$
$C_{eq}=\frac{{\epsilon }_{0}A}{2d}$