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 $
Show Answer
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 $
