Question

A parallel-plate capacitor is constructed with circular plates of radius 5.10×10−2 m . The plates are separated by 0.23 mm , and the space between the plates is filled with a dielectric with dielectric constant κ. When the charge on the capacitor is 1.3 μC the potential difference between the plates is 1120 V . Part A Find the value of the dielectric constant, κ. Express your answer using two significant figures.

Answer 1

Answer:

3.7

Explanation:

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

r = Radius = $5.1\times 10^{-2}\ m$

A = Area = $\pi r^2$

V = Voltage = 1120 V

d = Distance of plate seperation = 0.23 mm

Charge is given by

$Q=CV\\\Rightarrow Q=\dfrac{k\epsilon_0 A}{d}\times V\\\Rightarrow k=\dfrac{Qd}{\epsilon_0 AV}\\\Rightarrow k=\dfrac{1.3\times 10^{-6}\times 0.23\times 10^{-3}}{8.85\times 10^{-12}\times \pi (5.1\times 10^{-2})^2\times 1120}\\\Rightarrow k=3.69164\\\Rightarrow k=3.7$

The value of dielectric constant is 3.7