Electrostatics Question 567
Question: . A capacitor $ 4\mu F $ charged to 50 $ V $ is connected to another capacitor of $ 2\mu F $ charged to 100 $ V $ with plates of like charges connected together. The total energy before and after connection in multiples of $ ({{10}^{-2}}J) $ is [MP PMT 1992]
Options:
A) 1.5 and 1.33
B) 1.33 and 1.5
C) 3.0 and 2.67
D) 2.67 and 3.0
Show Answer
Answer:
Correct Answer: A
Solution:
The total energy before connection
$ =\frac{1}{2}\times 4\times {{10}^{-6}}\times {{(50)}^{2}}+\frac{1}{2}\times 2\times {{10}^{-6}}\times {{(100)}^{2}} $
$ =1.5\times {{10}^{-2}}J $
When connected in parallel $ 4\times 50+2\times 100=6\times V $
therefore $ V=\frac{200}{3} $ Total energy after connection
$ =\frac{1}{2}\times 6\times {{10}^{-6}}\times {{( \frac{200}{3} )}^{2}}=1.33\times {{10}^{-2}}J $
