Question

Condensers with capacities C,2C,3C and 4C are charged 10 the voltage, V,2 V,3 V and 4 V correspondingly. The circuit is closed. Find the voltage on all condensers in the equilibrium.

Answer 1

Let +q charge rotates in the loop in clockwise direction for achieving equilibrium state. In final steady state, charges on the capacitors will be as shown below:

Now applying Kirchhoff's loop law we have,

$\left(\frac{CV-q}{C}\right)+\left(\frac{4CV-q}{2C}\right)+\left(\frac{9CV-q}{3C}\right)+\left(\frac{16CV-q}{4C}\right)=0$

or $q=4.8CV=\frac{24}{5}CV$

Now $V_1=V-\frac{q}{C}=V-\frac{24}{5}V=-\frac{19}{5}V$

$V_2=2V-\frac{q}{2C}=2V-\frac{24}{10}V=-\frac{2}{5}V$

$V_3=3V-\frac{q}{3C}=3V-\frac{24}{15}V=\frac{7}{5}V$ and

$V_4=4V-\frac{q}{4C}=4V-\frac{6}{5}V=\frac{14}{5}V$