Question

Three uncharged capacitors of capacitance $C_1=1\mu F,C_2=2\mu F$ and $C_3=3\mu F$ are connected as shown in the figure. The potential of point $A,B$ and $D$ are $10$ volt, $25volt$ and $20volt$ respectively. Determine the potential at point $O$.

Answer 1

$\Rightarrow q_1+q_2+q_3=0$

$\Rightarrow C_1(V_o-V_A)+C_2(V_o-V_B)+C_3(V_o-V_D)=0$

$\Rightarrow (C_1+C_2+C_3)V_o=C_1{V}_A+C_2{V}_B+C_3{V}_D$

$V_o=\frac{C_1{V}_A+C_2{V}_B+C_3{V}_D}{C_1+C_2+C_3}$

$=\frac{(1\times 10)+(2\times 25)+(3\times 20)}{1+2+3}$

$=\frac{10+50+60}{6}=20Volts$