The charge on the capacitor C_3 in the segment AB is:

The correct answer is Option (2) → \( \displaystyle\frac{250}{3}\,\mu\mathrm{C} \)

Read the circuit loop by loop. The top loop contains \( C_1 \), \( C_2 \) and \( C_3 \) one after another, connected across the 50 V battery, so these three are in series and carry the same charge. \( C_4 \) and the pair \( C_5 \)-\( C_6 \) are separate branches connected directly across the same battery, so they do not affect the charge on \( C_3 \).

    \( \displaystyle \frac{1}{C_s} = \frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{3}{5}\,\mu\mathrm{F}^{-1} \Rightarrow C_s = \frac{5}{3}\,\mu\mathrm{F} \)

    \( \displaystyle Q = C_sV = \frac{5}{3}\,\mu\mathrm{F}\times50\,\mathrm{V} = \frac{250}{3}\,\mu\mathrm{C} \)

Capacitors in series carry equal charge, so the charge on \( C_3 \) is \( 250/3\,\mu\mathrm{C} \approx 83\,\mu\mathrm{C} \).