Electrostatics Question 607
Question: A parallel plate capacitor has capacitance C. If it is equally filled with parallel layers of materials of dielectric constants $ {K _{\text{1}}} $ and $ {K _{\text{2}}} $ its capacity becomes $ {C _{\text{1}}} $ . The ratio of $ {C _{\text{1}}} $ to C is [MP PMT 2001]
Options:
A) $ K _{1}+K _{2} $
B) $ \frac{K _{1}K _{2}}{K _{1}-K _{2}} $
C) $ \frac{K _{1}+K _{2}}{K _{1}K _{2}} $
D) $ \frac{2K _{1}K _{2}}{K _{1}+K _{2}} $
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Answer:
Correct Answer: D
Solution:
$ C _{A}=\frac{K _{1}{\varepsilon _{0}}A}{d/2},C _{B}=\frac{K _{2}{\varepsilon _{0}}A}{d/2} $
$ C _{eq}=\frac{C _{1}}{C _{2}}=\frac{2K _{1}K _{2}}{K _{1}+K _{2}} $
$ =\frac{C _{A}C _{B}}{C _{A}+C _{B}}=( \frac{2K _{1}K _{2}}{K _{1}+K _{2}} )\frac{{\varepsilon _{0}}A}{d} $
$ ( \because c=\frac{{\varepsilon _{0}}A}{d} ) $
