Question

Three uncharged capacitors of capacitance $1\mu \text{F}$, $2\mu \text{F}$ and $3\mu \text{F}$ are connected as shown in figure. If potentials at $\text{P,Q}$ and $\text{R}$ are $1\text{V},2\text{V}$ and $3\text{V}$ respectively. Then potential at $\text{O}$ is

• A. $\frac{7}{5}\text{V}$
• B. $\frac{18}{11}\text{V}$
• C. $\frac{11}{18}\text{V}$
• D. $\frac{7}{3}\text{V}$

Answer 1

The correct option is D $\frac{7}{3}\text{V}$



Let potential at point $\text{V\_0}$ be $x$, then using KCL at the junction $\text{O}$ we get,

$q_1+q_2+q_3=0$

$C_1(V_0-V_1)+C_2(V_0-V_2)+C_3(V_0-V_3)=0$

$3(V_0-3)+2(V_0-2)+1(V_0-1)=0$

$6V_0=14$

$V_0=\frac{14}{6}=\frac{7}{3}\text{V}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (d) is the correct answer.