In the given circuit, if the potential at A is 50 V, then potential at B is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \frac{50}{3}\,\mathrm{V} \)
C is earthed, so the potential difference between A and C is 50 V. \( C_2 \) and \( C_3 \) are in parallel, and that pair is in series with \( C_1 \). Capacitors in series carry the same charge.
\( \displaystyle C_{23} = 4 + 2 = 6\,\mu\mathrm{F} \)
\( \displaystyle C_{\mathrm{eq}} = \frac{C_1 C_{23}}{C_1 + C_{23}} = \frac{3 \times 6}{3 + 6} = 2\,\mu\mathrm{F} \)
\( \displaystyle q = C_{\mathrm{eq}}\,V_{AC} = 2\,\mu\mathrm{F} \times 50\,\mathrm{V} = 100\,\mu\mathrm{C} \)
\( \displaystyle V_A - V_B = \frac{q}{C_1} = \frac{100\,\mu\mathrm{C}}{3\,\mu\mathrm{F}} = \frac{100}{3}\,\mathrm{V} \)
\( \displaystyle V_B = 50 - \frac{100}{3} = \frac{50}{3}\,\mathrm{V} \)