Electrostatics Question 526
Question: A parallel plate capacitor with air as medium between the plates has a capacitance of $ 10\mu F $ . The area of capacitor is divided into two equal halves and filled with two media having dielectric constant $ k _{1}=2 $ and $ k _{2}=4 $ . The capacitance of the system will now be [MP PMT 1987; RPET 2001]
Options:
A) x$ 10\mu F $
B) $ 20\mu F $
C) $ 30\mu F $
D) $ 40\mu F $
Show Answer
Answer:
Correct Answer: C
Solution:
$ C _{R}=C _{1}+C _{2}=\frac{k _{1}{\varepsilon _{0}}A _{1}}{d}+\frac{k _{2}{\varepsilon _{0}}A _{2}}{d} $
$ =\frac{2\times {\varepsilon _{0}}\frac{A}{2}}{d}+\frac{4\times {\varepsilon _{0}}\frac{A}{2}}{d} $
$ =2\times \frac{10}{2}+4\times \frac{10}{2}=30\mu F $
