Quantrex Academy · Free JEE Advanced PYQ solutions
JEE Advanced Physics Capacitance 2023 JEE Advanced 2023 (Paper 1)

JEE Advanced Physics Question (2023) — Solution

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   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 × 10 − 12   C 2   N − 1   m − 2 , the effects of the non-conducting walls on the capacitance are negligible]

Options

  1. A. 27   pF
  2. B. 63   pF
  3. C. 81   pF
  4. D. 135   pF

Answer

B. 63   pF

Step-by-step solution

Height of the liquid column  = volume base area ⇒ h = 250   cm 3   s - 1 × 10   s 50   cm × 5   cm = 10   cm Now capacitance of the upper part can be written as, C 1 = A 1 ε 0 d = 0 . 50 - 0 . 10 × 0 . 50 × 9 × 10 - 12 5 × 10 - 2 = 0 . 36 × 10 – 10   F Capacitance for the lower part can be written as, C 2 = K A 2 ε 0 d = 3 × 0 . 10 × 0 . 5 × 9 × 10 - 12 5 × 10 - 2 ⇒ C 2 = 0 . 27 × 10 – 10   F Both part of the capacitor can be considered as connected in parallel, C e f f = C 1 + C 2 = 63   pF

Practice more on Quantrex App →

Related: Physics — Capacitance · All PYQ Banks