A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1\,μ F when the space between the plates is filled with an insulating material of resistivity 1× 10^ 13 \, m and

Question

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Correct answer: 0

The resistance of the insulating material is given by

R = \dfrac{\rho d}{A}

.

The capacitance of the parallel plate capacitor is given by

C = \dfrac{\epsilon_0 \epsilon_r A}{d}

.

Multiplying the expressions for

R

and

C

, we get:

RC = \rho \epsilon_0 \epsilon_r

Rearranging for relative permittivity

\epsilon_r

:

\epsilon_r = \dfrac{RC}{\rho \epsilon_0}

Substituting the given values:

\epsilon_r = \dfrac{17.7 \times 10^{14} \times 10^{-6}}{10^{13} \times 8.85 \times 10^{-12}}

\epsilon_r = \dfrac{17.7 \times 10^8}{8.85 \times 10^1}

\epsilon_r = 2 \times 10^7

Comparing this with the given expression

\epsilon_r = \alpha \times 10^7

, we get:

\alpha = 2

Answer:

2

A parallel plate capacitor is having separation between plates...

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