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Question 16

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

Option (A): 5 parallel capacitors in series with 2 capacitors $$\implies C_{\text{eq}} = \frac{1}{\frac{1}{5 \times 2} + \frac{2}{2}} = \frac{10}{11}\,\mu\text{F}$$

Option (B): 3 parallel capacitors in series with 4 capacitors $$\implies C_{\text{eq}} = \frac{1}{\frac{1}{3 \times 2} + \frac{4}{2}} = \frac{6}{13}\,\mu\text{F}$$

Option (C): 4 parallel capacitors in series with 3 capacitors $$\implies C_{\text{eq}} = \frac{1}{\frac{1}{4 \times 2} + \frac{3}{2}} = \frac{8}{13}\,\mu\text{F}$$

Option (D): 2 parallel capacitors in series with 5 capacitors $$\implies C_{\text{eq}} = \frac{1}{\frac{1}{2 \times 2} + \frac{5}{2}} = \frac{4}{11}\,\mu\text{F}$$

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