Question

Which of the following combinations of seven identical capacitors each of 2$\mu$F gives a capacitance of 10/11 $\mu$F?

• A. 5 in parallel with 2 in series
• B. 4 in parallel with 3 in series
• C. 3 in parallel with 4 in series
• D. 2 in parallel with 5 in series

Answer 1

The correct option is A 5 in parallel with 2 in series

A) $\frac{1}{C_{eq}}=\frac{1}{5C}+\frac{1}{C}+\frac{1}{C}=\frac{11}{5C}=\frac{11}{5\times 2}=11/10\Rightarrow C_{eq}=10/11\mu F$
B) $\frac{1}{C_{eq}}=\frac{1}{4C}+\frac{1}{C}+\frac{1}{C}+\frac{1}{C}=\frac{13}{4C}=\frac{13}{4\times 2}=13/8\Rightarrow C_{eq}=8/13\mu F$
C) $\frac{1}{C_{eq}}=\frac{1}{3C}+\frac{1}{C}+\frac{1}{C}+\frac{1}{C}+\frac{1}{C}=\frac{13}{3C}=\frac{13}{3\times 2}=13/6\Rightarrow C_{eq}=6/13\mu F$
D) $\frac{1}{C_{eq}}=\frac{1}{2C}+\frac{1}{C}+\frac{1}{C}+\frac{1}{C}+\frac{1}{C}+\frac{1}{C}=\frac{11}{2C}=\frac{11}{2\times 2}=11/4\Rightarrow C_{eq}=4/11\mu F$