Electrostatics Question 813

Question: An uncharged parallel plate capacitor having a dielectric of dielectric constant K is connected to a similar air cored parallel plate capacitor charged to a potential $ V _{0}. $ The two share the charge, and the common potential becomes V. The dielectric constant K is

Options:

A) $ \frac{V _{0}}{V}-1 $

B) $ \frac{V _{0}}{V}+1 $

C) $ \frac{V}{V _{0}}-1 $

D) $ \frac{V}{V _{0}}+1 $

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Answer:

Correct Answer: A

Solution:

[a] $ C _{1}=C,V _{1}=V _{0},C _{2}=KC,V _{2}=0 $

And $ V _{common}=V $

We know that $ V _{common}=\frac{C _{1}V _{1}+C _{2}V _{2}}{C _{1}+C _{2}} $

$ \therefore V _{common}=\frac{CV _{0}+KC\times O}{C+KC} $

or $ K=\frac{V _{0}}{V}-1 $



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