Seven capacitors, each of capacitance $2 \mu \mathrm{F},$ are to be connected in a configuration to obtain an effective capacitance of $\left(\frac{6}{13}\right) \mu \mathrm{F} .$ Which of the combinations, shown in figures below, will achieve the desired value?

• A

  
• Correct answer
  B

  
• C

  
• D

  

Solution

As required equivalent capacitance should be $C_{\mathrm{eq}}=\frac{6}{13} \mu \mathrm{F}$ Therefore three capacitors must be in parallel and 4 must be in series with it. $\frac{1}{\mathrm{C}_{\mathrm{eq}}}=\left[\frac{1}{3 \mathrm{C}}\right]+\left[\frac{1}{\mathrm{C}}+\frac{1}{\mathrm{C}}+\frac{1}{\mathrm{C}}+\frac{1}{\mathrm{C}}\right]$ $C_{\mathrm{eq}}=\frac{3 \mathrm{C}}{13}=\frac{6}{13} \mu \mathrm{F} \quad[$ as $\mathrm{C}=2 \mu \mathrm{F}]$ So, desired combination will be as below:

Hence, the correct answer is option: 'B'.