SATHEE: Electrostatic Potential and Capacitance

Electrostatic Potential and Capacitance - Result Question 22

24. The capacitance of a parallel plate capacitor with air as medium is $6 μ F$ . With the introduction of a dielectric medium, the capacitance becomes $30 μ F$ . The permittivity of the medium is :

[2020]

$(\in_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2})$

(a) $1.77 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$

(b) $0.44 \times 10^{- 10} C^{2} N^{- 1} m^{- 2}$

(d) $0.44 \times 10^{- 13} C^{2} N^{- 1} m^{- 2}$

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Answer:

Correct Answer: 24. (b)

Solution:

(b) Capacitance of a parallel plate capacitor with air is

$\begin{matrix} (i) & C = \frac{ε_{0} A}{d} \end{matrix}$

Here, $A =$ area of plates of capacitor,

$d =$ distance between the plates

Capacitance of a same parallel plate capacitor with introduction of dielectric medium of dielectric constant $K$ is

$\begin{matrix} (ii) & C^{'} = \frac{K ε_{0} A}{d} \end{matrix}$

Dividing (ii) by (i)

$\Rightarrow \frac{C^{'}}{C} = K \Rightarrow \frac{30}{6} = K \Rightarrow K = 5$

$\Rightarrow K = \frac{ε}{ε_{0}}$

$\Rightarrow ε = K ε_{0} = 5 \times 8.85 \times 10^{- 12}$

Electrostatic Potential and Capacitance - Result Question 22

24. The capacitance of a parallel plate capacitor with air as medium is $6 μ F$ . With the introduction of a dielectric medium, the capacitance becomes $30 μ F$ . The permittivity of the medium is :

Answer:

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Electrostatic Potential and Capacitance - Result Question 22

24. The capacitance of a parallel plate capacitor with air as medium is 6μF. With the introduction of a dielectric medium, the capacitance becomes 30μF. The permittivity of the medium is :

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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24. The capacitance of a parallel plate capacitor with air as medium is $6 μ F$ . With the introduction of a dielectric medium, the capacitance becomes $30 μ F$ . The permittivity of the medium is :