Electrostatics Question 604

Question: Consider a parallel plate capacitor of $ 10\mu F $ (micro-farad) with air filled in the gap between the plates. Now one half of the space between the plates is filled with a dielectric of dielectric constant 4, . The capacity of the capacitor changes to [AFMC 2001; MP PET 2001]

Options:

A) $ 25\mu F $

B) $ 20\mu F $

C) $ 40\mu F $

D) $ 5\mu F $

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Answer:

Correct Answer: A

Solution:

$ C _{1}=\frac{{\varepsilon _{0}}( \frac{A}{4} )}{d},C _{2}=\frac{K{\varepsilon _{0}}( \frac{A}{2} )}{d},C _{3}=\frac{{\varepsilon _{0}}( \frac{A}{4} )}{d} $

$ C _{eq}=C _{1}+C _{2}+C _{3}=( \frac{K+1}{2} )\frac{{\varepsilon _{0}}A}{d} $

$ =( \frac{4+1}{2} )\times 10=25\mu F $



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