Question

Three uncharged capacitors of capacities $C_1,C_2$ and $C_3$ are connected as shown in the figure to one another and the points A, B and C are at potentials $V_1,V_2$ and $V_3$ respectively. Then the potential at O will be:

• A. $\frac{V_1{C}_1+V_2{C}_2+V_3{C}_3}{C_1+C_2+C_3}$
• B. $\frac{V_1+V_2+V_3}{C_1+C_2+C_3}$
• C. $\frac{V_1(V_2+V_3)}{C_1(C_2+C_3)}$
• D. $\frac{V_1{V}_2{V}_3}{C_1{C}_2{C}_3}$

Answer 1

The correct option is A $\frac{V_1{C}_1+V_2{C}_2+V_3{C}_3}{C_1+C_2+C_3}$

The net charge in the encircled portion is zero.
Therefore,
$C_1(-V_1+V_o)+C_2(V_o-V_2)+C_3(V_o-V_3)=0$

$\Rightarrow V_o=\frac{C_1{V}_1+C_2{V}_2+C_3{V}_3}{C_1+C_2+C_3}$