Electrostatics Question 275
Question: In the given circuit if point C is connected to the earth and a potential of $ +2000V $ is given to the point A, the potential at B is [MP PET 1997; Pb. PET 2003]
Options:
A) 3 : 1
B) 5 : 1
C) 3 : 5
D) 5 : 3
Show Answer
Answer:
Correct Answer: C
Solution:
Initially potential difference across both the capacitor is same hence energy of the system is $ U _{1}=\frac{1}{2}CV^{2}+\frac{1}{2}CV^{2}=CV^{2} $ ..(i)
In the second case when key K is opened and dielectric medium is filled between the plates, capacitance of both the capacitors becomes 3C, while potential difference across A is V and potential difference across B is $ \frac{V}{3} $
hence energy of the system now is $ U _{2}=\frac{1}{2}(3C)V^{2}+\frac{1}{2}(3C){{( \frac{V}{3} )}^{2}} $
$ =\frac{10}{6}CV^{2} $ ..(ii) So, $ \frac{U _{1}}{U _{2}}=\frac{3}{5} $
