The plates of a parallel plate capacitor are charged up to 100 volt. A 2mm thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by 1.6mm . The dielectric constant of the plate is :

Question

The plates of a parallel plate capacitor are charged up to 100 volt. A 2mm thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by 1.6mm . The dielectric constant of the plate is : (A) 5 (B) 1.25 (C) 4 (D) 2.5

Tardigrade Admin · Accepted Answer

Since, the potential difference between the plates of capacitor remains same and charge on the capacitor is also same. Therefore, the capacitance of parallel plate capacitor should remain same after insertion of dielectric slab and increasing the separation between the plates.
Initial capacitance of capacitor,

C = \frac{ϵ _{0} A}{d}

.
Final capacitance of capacitor,

C = \frac{( ϵ ) _{0} A}{D - t ( 1 - \frac{1}{k} )} = \frac{( ϵ ) _{0} A}{d + 1.6 - 2 ( 1 - \frac{1}{k} )}

From above equations,

\frac{( ϵ ) _{0} A}{d + 1.6 - 2 ( 1 - \frac{1}{k} )} = \frac{( ϵ ) _{0} A}{d} \Rightarrow d = d + 1.6 - 2 + \frac{2}{k} \Rightarrow k = 5

Q. The plates of a parallel plate capacitor are charged up to $100$ volt. A $2 mm$ thick plate is inserted between the plates, then to maintain
the same potential difference, the distance between the capacitor plates is increased by $1.6 mm$ . The dielectric constant of the plate is :

$5$

$1.25$

$4$

$2.5$

Q. The plates of a parallel plate capacitor are charged up to 100 volt. A 2mm thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by 1.6mm . The dielectric constant of the plate is :

5

1.25

4

2.5

Q. The plates of a parallel plate capacitor are charged up to $100$ volt. A $2 mm$ thick plate is inserted between the plates, then to maintain
the same potential difference, the distance between the capacitor plates is increased by $1.6 mm$ . The dielectric constant of the plate is :

$5$

$1.25$

$4$

$2.5$