Question

A parallel plate capacitor of capacitance c, a metal sheet is inserted between the plates, parallel to them. If the thickness of the sheet is half of the separation between the plates. The capacitance will be

Answer 1

Let cross sectional area of parallel plate capacitor is A, seperation between plates is d then, capacitance of capacitor is C = $\frac{\epsilon_0A}{d}$.......(1)

now a metal sheet of thickness d/2 is inserted between the plates. then, capacitance of capacitor is given by, $C'=\frac{\epsilon_0A}{d-d/2}=\frac{2\epsilon_0A}{d}$.....(2)

from equations (1) and (2),

we can say that C' = 2C

hence, after inserting metal sheet of thickness half of seperation between plates , capacitance of capacitor becomes double.