question_answer

If the equivalent capacitance between P and Q of the combination of the capacitors shown in figure below is \[30\text{ }\mu \text{F}\], the capacitor C is

A)  \[60\,\mu F\]

B)  \[30\,\mu F\]

C)  \[10\,\mu F\]

D)  \[5\,\mu F\]

Correct Answer: A

Solution :

\[C'={{C}_{1}}+{{C}_{2}}+{{C}_{3}}\] \[=20+20+20\] \[=60\mu F\] \[\frac{1}{C''}=\frac{1}{C'}+\frac{1}{60}\] \[\frac{1}{30}=\frac{1}{C'}+\frac{1}{60}\] \[\frac{1}{C'}=\frac{1}{30}-\frac{1}{60}\] \[\frac{1}{C'}=\frac{2-1}{60}\] \[\frac{1}{C'}=\frac{1}{60}\] \[\Rightarrow \] \[C'=60\]