SATHEE: Electrostatics 5 Question 14

Electrostatics 5 Question 14

15. A parallel plate capacitor is of area $6 {cm}^{2}$ and a separation 3 $mm$ . The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants $K_{1} = 10$ , $K_{2} = 12$ and $K_{3} = 14$ . The dielectric constant of a material which give same capacitance when fully inserted in above capacitor, would be

(Main 2019, 10 Jan I)

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(a) 4

(b) 36

(d) 14

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Answer:

Correct Answer: 15. (c)

Solution:

In the given arrangement, capacitor can be viewed as threedifferent capacitors connected in parallel as shown below,

So, equivalent capacity of the system is

$\begin{aligned} C_{eq} & = C_{1} + C_{2} + C_{3} \\ \Rightarrow \frac{K ε_{0} A}{d} & = \frac{K_{1} ε_{0} A / 3}{d} + \frac{K_{2} ε_{0} A / 3}{d} + \frac{K_{3} ε_{0} A / 3}{d} \\ \Rightarrow K & = \frac{K_{1}}{3} + \frac{K_{2}}{3} + \frac{K_{3}}{3} \\ Here, K_{1} & = 10, K_{2} = 12 and K_{3} = 14 \\ So, K & = \frac{10 + 12 + 14}{3} \Rightarrow K = 12 \end{aligned}$

Electrostatics 5 Question 14

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Electrostatics 5 Question 14

Answer:

Solution:

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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