question_answer

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

A)                 \[60\mu F\]                                       

B)  \[30\mu F\]

C)                 \[10\mu F\]                                       

D) \[5\mu F\]

Correct Answer: A

Solution :

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