question_answer

The equivalent capacitance between points-4 and 6 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 :

(d) \[3\mu F\] \[{{C}_{1}}\] 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 \[\frac{1}{C''}=\frac{1}{{{C}_{3}}}+\frac{1}{{{C}_{4}}}=\frac{1}{2}+\frac{1}{2}\] \[\Rightarrow \,\,\,C''=1\mu F\] Now, C and C" are in parallel \[\therefore \,\,\,\,\,\,\,\,\,{{C}_{eq}}=C'+C''=2+1=3\mu F\]