MHTCET 15 May 2024 Shift 2 Paper

Concept:For capacitors in series, the charge on each capacitor is the same, and the net voltage is the algebraic sum of the battery EMFs.Explanation:The two batteries of $20 \, \mathrm{V}$ and $4 \, \mathrm{V}$ are connected in opposition, so the net potential difference is:$$V_{\mathrm{eq}} = 20 - 4 = 16 \, \mathrm{V}$$The $3 \, \mu\mathrm{F}$ and $5 \, \mu\mathrm{F}$ capacitors are in series, so their equivalent capacitance is:$$C_{\mathrm{eq}} = \frac{3 \times 5}{3 + 5} = \frac{15}{8} \, \mu\mathrm{F}$$The total charge stored in the series combination is:$$Q = C_{\mathrm{eq}} \times V_{\mathrm{eq}} = \frac{15}{8} \times 16 = 30 \, \mu\mathrm{C}$$Since the charge is the same on each series capacitor, the voltage across the $3 \, \mu\mathrm{F}$ capacitor is:$$V_3 = \frac{Q}{C_3} = \frac{30}{3} = 10 \, \mathrm{V}$$Answer:The potential difference across the $3 \, \mu\mathrm{F}$ capacitor is $10 \, \mathrm{V}$. Hence, the correct option is C.