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} $



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