Three capacitors \( C_1 \), \( C_2 \) and \( C_3 \) are connected to a 6 V battery, as shown in figure. The charge on the capacitor \( C_1 \) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 24\,\mu\mathrm{C} \)
Capacitors in parallel add, and capacitors in series carry the same charge. In the figure \( C_2 \) and \( C_3 \) are connected between the same two points (the middle node and the lower wire), so they are in parallel, and this pair is in series with \( C_1 \) across the battery.
\( C_{23} = C_2 + C_3 = 4 + 4 = 8\,\mu\mathrm{F} \)
\( \displaystyle C_{\mathrm{eq}} = \frac{C_1C_{23}}{C_1 + C_{23}} = \frac{8\times8}{8+8} = 4\,\mu\mathrm{F} \)
\( Q = C_{\mathrm{eq}}V = 4\,\mu\mathrm{F}\times6\,\mathrm{V} = 24\,\mu\mathrm{C} \)
The series combination carries one common charge, and \( C_1 \) is one of its two parts, so the charge on \( C_1 \) is \( 24\,\mu\mathrm{C} \).