Question

Three uncharged capacitors of capacitance $C_{1},C_{2}$ and $C_{3}$ are connected as shown in the figure to one another at point $O$ and to points $A,B$ and $D$ at potentials $V_{A},$ $V_{B}$ and $V_{D}.$ Then the potential at $O$ will be, :

• A. $\frac{V_{A} + V_{B} + V_{D}}{C_{1} + C_{2} + C_{3}}$
• B. $\frac{V_{A} C_{1} + V_{B} C_{2} + V_{D} C_{3}}{C_{1} + C_{2} + C_{3}}$
• C. $\frac{V_{A} V_{B} + V_{B} V_{D} + V_{D} V_{A}}{C_{1} + C_{2} + C_{3}}$
• D. $\frac{V_{A} V_{B} V_{D}}{C_{1} C_{2} + C_{2} C_{3} + C_{3} C_{1}}$

Answer 1

Answer: (B)

$V_{A}-V=\frac{q_{1}}{C_{1}}$
$V_{B}-V=\frac{q_{2}}{C_{2}}$
$V_{D}-V=\frac{q_{3}}{C_{3}}$
$q_{1}+q_{2}+q_{3}=0$
$\frac{C_{1} V_{A} + C_{2} V_{B} + V_{D} C_{3}}{C_{1} + C_{2} + C_{3}}=V$