Question

In between the plates of parallel plate capacitor of plate separation ‘d’ a dielectric plate of thickness ‘d’ is inserted. The capacitance becomes one-third of the original capacity without dielectric. The dielectric constant of the plate is ______.

Options

• `t/(2d - t)`

• `t/(2d + t)`

• `(3t)/(d - t)`

• `(3t)/(d + t)`

Answer 1

In between the plates of parallel plate capacitor of plate separation ‘d’ a dielectric plate of thickness ‘d’ is inserted. The capacitance becomes one-third of the original capacity without dielectric. The dielectric constant of the plate is `bbunderline(t/(2d + t))`.

Explanation:

Given: C' = `C/3`

⇒ `(A epsilon_0)/(d - t + t/k)`

= `1/3 (A epsilon_0)/d`

Without a dielectric slab, the capacitance is:

C = `(A epsilon_0)/d`

On the introduction of a dielectric, the capacitance becomes:

C' = `(A epsilon_0)/(d - t + t/k)`

k = `t/(2d + t)`