Question

Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand the maximum electric field of \[{{10}^{6}}\]. The plate area is \[{{10}^{-4}}{{m}^{2}}\]. What is the dielectric constant if the capacitance is 15 pF (given \[{{\varepsilon }_{o}}=8.86\times {{10}^{-12}}{{C}^{2}}/N{{m}^{2}}\])

A. 3.8

B. 4.5

C. 6.2

D. 8.5

Answer 1

Hint: In this question we have been asked to calculate the dielectric constant of the parallel plate capacitor of given specifications. We have been given the voltage rating of capacitor, area and maximum electric field. We have also been given the permittivity of free space. Therefore, we shall be using the formula for calculating the capacitance of the parallel plate capacitor as it relates all the given parameters and the dielectric constant of the capacitor.

Formula used:

 \[C=k\dfrac{{{\varepsilon }_{o}}A}{d}\]

Where,

C is the capacitance

K is the dielectric constant

A is the area 

d is the distance between the plates of the capacitor.

Complete answer:

We have been asked to calculate the dielectric constant. We know that dielectric constant is the ratio of electric permeability of material to the electric permeability of free space. Since we are not given the permeability of free space we shall use formula to calculate the capacitance of the parallel plate capacitor.

From the formula we know,

\[C=k\dfrac{{{\varepsilon }_{o}}A}{d}\]

Solving for, dielectric constant

We get,

\[k=\dfrac{Cd}{{{\varepsilon }_{o}}A}\]

It is given that capacitance is 15 picoFarad i.e. \[15\times {{10}^{-12}}\] Farad.

After substituting values in above equation 

We get,

\[k=\dfrac{15\times {{10}^{-12}}\times 500\times {{10}^{-6}}}{8.86\times {{10}^{-12}}\times {{10}^{4}}}\]

On solving

\[k=8.499\]

Therefore,

\[k\approx 8.5\]

Therefore, Option (D) is correct.

Note:

The dielectric constant of a material also known as the relative permittivity of the material is the ratio of the permittivity of material to the permittivity of free space. Capacitance can be defined as the ratio of change in electric charge over the change in its electric potential. It is the ability of a capacitor to collect and store the energy in the form of electric charge.