Electrostatics Question 272
Question: A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V. Another capacitor of capacitance 2C is connected to another battery and is charged to potential difference 2V. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is [IIT 1995]
Options:
A) $ 1\mu F $
B) $ 2\mu F $
C) $ \frac{1}{2}\mu F $
D) $ \infty $
Show Answer
Answer:
Correct Answer: B
Solution:
This combination forms a G.P. $ S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots $
Sum of infinite G.P. $ S=\frac{a}{1-r} $
Here a = first term = 1 and r = common ratio = $\frac{1}{2}$
therefore $ S=\frac{1}{1-\frac{1}{2}}=2 $
therefore $ C _{eq}=2,\mu F $
BETA
