A container has a base of and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area . The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectr

Question

A container has a base of $50 cm \times 5 cm$ and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area $50 cm \times 50 cm$ . The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant 3 at a uniform rate of $250 {cm}^{3} s^{- 1}$ .

What is the value of the capacitance of the container after 10 seconds?

[Given: Permittivity of free space $ε_{0} = 9 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ , the effects of the non-conducting walls on the capacitance are negligible] [2023]

Smart Achievers · Accepted Answer

(2)

In $t = 10 s$ , volume of liquid

$V = 250 \times 10 = 2500 {cm}^{3}$

$∴$ $h = \frac{V}{A} = \frac{2500}{50 \times 5} = 10 cm$

Capacitance of the capacitor when filled with liquid of dielectric constant $K = 3$

$C_{d} = \frac{A_{d} ε_{0} K}{d} = \frac{50 \times 10^{- 2} \times 10 \times 10^{- 2} \times ε_{0} \times 3}{5 \times 10^{- 2}} = 3 ε_{0}$

Capacitance of the air-filled capacitor

$C_{a} = \frac{A_{a} ε_{0}}{d} = \frac{50 \times 10^{- 2} \times 40 \times 10^{- 2} \times ε_{0}}{5 \times 10^{- 2}} = 4 ε_{0}$

Equivalent capacitance, $C = C_{a} + C_{d} = 7 ε_{0}$

$= 7 \times 9 \times 10^{- 12} = 63 pF$

Solution

1 $27 pF$

2 $63 pF$

3 $81 pF$

4 $135 pF$

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Solution

1 27 pF

2 63 pF

3 81 pF

4 135 pF

Want Us to Email you About Special Offers & Updates?

1 $27 pF$

2 $63 pF$

3 $81 pF$

4 $135 pF$