question_answer

The equivalent capacitance between points A and B in the given figure, is

A)  \[\frac{36}{13\mu F}\]                                 

B)  \[2\mu F\]

C)  \[1\mu F\]                                        

D)  \[3\mu F\]

Correct Answer: D

Solution :

\[{{C}_{1}}\] and \[{{C}_{2}}\] are in series \[\therefore \]  \[\frac{1}{C'}=\frac{1}{{{C}_{1}}}+\frac{1}{{{C}_{2}}}=\frac{1}{3}+\frac{1}{6}\] \[\Rightarrow \]               \[C'=2\mu F\] Similarly, \[{{C}_{3}}\] and \[{{C}_{4}}\]are in series                 \[\frac{1}{C''}=\frac{1}{{{C}_{3}}}+\frac{1}{{{C}_{4}}}=\frac{1}{2}+\frac{1}{2}\] Now, \[C'\] and \[C''\] are in parallel \[\therefore \]  \[{{C}_{comb}}=C'+C''\]                 \[=2\mu F+1\mu F=3\mu F\]