Electrostatics Question 276
Question: A finite ladder is constructed by connecting several sections of $ 2\mu F,\ 4\mu F $ capacitor combinations. It is terminated by a capacitor of capacitance C. What value should be chosen for C such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between [MP PMT 1999; KCET (Engg./Med.) 1999]
Options:
A) Zero
B) $ \frac{25CV^{2}}{6} $
C) $ \frac{3CV^{2}}{2} $
D) $ \frac{9CV^{2}}{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
Total charge $ =(2C)(2V)+(C)(-V)=3CV $
Common potential $ =\frac{3CV}{3C}=V $
Energy $ =\frac{1}{2}(3C){{(V)}^{2}}=\frac{3}{2}CV^{2} $
