question_answer

The equivalent capacitance of the network (with all capacitors having the same capacitance c) is:

A)        \[\alpha \]                                         

B)  zero

C)  \[C\left( \frac{\sqrt{3}-1}{2} \right)\]                    

D)  \[C\left( \frac{\sqrt{3}+1}{2} \right)\]

Correct Answer: C

Solution :

As from the figure,                 \[\frac{1}{{{C}_{\infty }}}=\frac{1}{{{C}_{\infty }}+C}+\frac{2}{C}\]                 \[=\frac{3C+2{{C}_{\infty }}}{C({{C}_{\infty }}+C)}\] Here, circuit is splitted into two parts as shown in the figure,             \[2C_{\infty }^{2}+2C{{C}_{\infty }}-{{C}^{2}}=0\] \[\Rightarrow \]               \[{{C}_{\infty }}=C\left( \frac{-1+\sqrt{3}}{2} \right)\]