Question) Find the potential difference between points X and Y of the circuit shown in the figure. Given that $C1=2?F, C2=3?F, C3=4?F, C4=5?F and E=5V.$

 Dear Student,

Assumptions :  mentioned capacitors are in micro farad.




We have to find V_x -V_y = V_x  -V_A+V_A-V<sub>y

​</sub>As  point 'A'  is at higher potential therefore

 V_x  -V_A+V_A-V_y = -V_C1+ V_C3

Now we have to find V_C1 and V_C3



Applying KVL in loop 1 and loop 2

$$\begin{gathered} In loop 1 \\ let q be charge on C1 and C2 \\ then \\ \frac{q}{\hspace{0.17em}C1}+\frac{q}{C2} =E \\ \frac{q}{2}+\frac{q}{3} =5 \\ q=6\mu C \\ therefore \\ voltage across C1 =V_{C1}= \frac{q}{\hspace{0.17em}C1} =3 V \\ Similarly applyin KVL in loop 2 gives \\ q\text{'} =\frac{100}{9}\mu C (q\text{'} =charge on capacitor C3 and C4) \\ therefore V_{C3} =\frac{25}{9} V \\ hence -V_{C1} +V_{C3} =-3 +\frac{25}{9} =\frac{-2}{9}V =V_x -V_y \end{gathered}$$

Regards