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 $
Show Answer
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 $
