Question

Five isolated capacitors are connected as shown in the figure. Find the potential at the junction ${}^{\prime }{O}^{\prime }$

Answer 1

Let $V_0$ be the potential at point ${}^{\prime }{O}^{\prime }$The potential at point ${}^{\prime }{O}^{\prime }$ can be given by$$V_0=\frac{C_1{V}_1+C_2{V}_2+C_3{V}_3+C_4{V}_4+C_5{V}_5}{C_1+C_2+C_3+C_4+C_5}$$From the data given in the question,

$C_1=2\mu F,C_2=5\mu F,C_3=10\mu F,C_4=5\mu F$ and $C_5=3\mu F$

$V_1=10V,V_2=15V,V_3=2V,V_4=4V$ and $V_5=5V$

Substituting the given data we get,

$V_0=\frac{2\times 10+5\times 15+10\times 2+5\times 4+3\times 5}{2+5+10+5+3}$

$\Rightarrow V_0=\frac{150}{25}$

$\Rightarrow V_0=6\text{volts}$

Accepted answers: $6,6.0,6.00$