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 $

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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 $



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