MHTCET 10 May 2024 Shift 1 Paper

Concept:For capacitors in parallel, capacitances add directly, while for capacitors in series, the reciprocals of capacitances add.Explanation:Each capacitor has capacitance $C = 2 \mu \mathrm{~F}$.Check option C: 3 capacitors in parallel, and this group in series with 4 capacitors.For 3 capacitors in parallel:$$C_p = 3C = 3 \times 2 = 6 \mu \mathrm{~F}$$This $6 \mu \mathrm{~F}$ combination is now connected in series with four capacitors of $2 \mu \mathrm{~F}$ each.$$\frac{1}{C_{eq}} = \frac{1}{C_p} + 4 \times \frac{1}{C}$$$$\frac{1}{C_{eq}} = \frac{1}{6} + 4 \times \frac{1}{2} = \frac{1}{6} + 2$$$$\frac{1}{C_{eq}} = \frac{1 + 12}{6} = \frac{13}{6}$$$$C_{eq} = \frac{6}{13} \mu \mathrm{~F}$$This exactly matches the required effective capacitance of $\frac{6}{13} \mu \mathrm{~F}$.Therefore, the required configuration is 3 capacitors in parallel followed by 4 capacitors in series.Answer:Option C: 3 capacitors in parallel and then 4 capacitors in series.