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}} $
