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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 1)
Option 2)
Option 3)
Option 4)

Answers (1)

best_answer

Series Grouping -

$\frac{1}{C_{eq}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\cdots$

- wherein

Parallel Grouping -

$C_{eq}=C_{1}+C_{2}+\cdots$

- wherein

$C=2\mu F$ for all capacitor.

$C_{eq}=\left ( \frac{6}{13} \right )\mu F$

For (3 capacitor in parallel) with series with 4 capacitor

$C_{1}=3C\: \: \: \: \: \: \: \: \; \; \; \; C_{2}=\frac{C}{4}$

$C_{AB}=\frac{3C\cdot \frac{C}{4}}{3C+\frac{C}{4}}=\frac{\frac{3}{4}C}{\frac{13}{4}}=\frac{3}{13}C$

$C_{AB}=\frac{3}{13}\times 2\mu F=\frac{6}{13}\mu F$

Option 1)
Option 2)

Option 3)

Option 4)

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