Electrostatics Question 270

Question: Two condensers of capacities $ 2C $ and C are joined in parallel and charged upto potential V. The battery is removed and the condenser of capacity C is filled completely with a medium of dielectric constant K. The p.d. across the capacitors will now be [IIT 1988]

Options:

A) $ {{x}^{\text{2}}} $

B) x

C) $ {{x}^{\text{1}}} $

D) $ {{x}^{\text{2}}} $

Show Answer

Answer:

Correct Answer: A

Solution:

$ U=\frac{1}{2}CV^{2}=\frac{1}{2}( \frac{{\varepsilon _{0}}A}{x} )V^{2} $ $ \frac{dU}{dt}=\frac{1}{2}{\varepsilon _{0}}AV^{2}( -\frac{1}{x^{2}}\frac{dx}{dt} ) $

therefore $ \frac{dU}{dt}\propto {{x}^{-2}} $



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