Capacitors in Series and Parallel

Problems from IIT JEE

Problem (IIT JEE 1990): Seven capacitors each of capacitance ${2}\;\mathrm{\mu F}$ are connected in a configuration to obtain an effective capacitance ${\frac{10}{11}}\;\mathrm{\mu F}$. Which of the following combination will achieve the desired result?

  1. Capacitors in Series and Parallel
  2. Capacitors in Series and Parallel
  3. Capacitors in Series and Parallel
  4. Capacitors in Series and Parallel

Solution: In option A, equivalent capacitance of five capacitors in parallel is $C_1={10}\;\mathrm{\mu F}$ and that of two capacitors in series is $C_2={1}\;\mathrm{\mu F}$. The $C_1$ and $C_2$ in series give equivalent capacitance $C_\text{eq}=\frac{C_1C_2}{C_1+C_2}={\frac{10}{11}}\;\mathrm{\mu F}$.