Question

A container has a base of 50 cm × 5 cm and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area 50 cm × 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 cm3s−1. What is the value of the capacitance of the container after 10 seconds? [Given: Permittivity of free space 𝜖0 = 9 × 10−12 C2N−1m−2, the effects of the non-conducting walls on the capacitance are negligible]

• A. 27 pF
• B. 63 pF
• C. 81 pF
• D. 135 pF

Answer 1

Answer: (B)

63 pF

Answer 2

$h = \frac {250*10}{50*5} = 10 cm$

$C1 = \frac{(0.40 * 0.50) * 9 * 10}{5 * 10}$

= 0.36 * 10-10 F

$C2 = \frac {3*0.10*0.5*9*10-12}{5*10-2}$

C2 = 0.27 * 10-10 F

C = C1 + C2

= 63pF