Question

Find the charges on the four capacitors of capacitance 1$\mu F$ , 2$\mu F$ , 3$\mu F$ and 4$\mu F$ shown in the figure

Answer 1

At steady state no current flows through the capacitor.

$R_{eq}=\frac{3\times 6}{3+6}=2\Omega$

$i=\frac{6}{2}=3$.

Since current is divided in the inverse ratio of the resistance in each branch, thus $2A$ will pass through $1\Omega ,2\Omega$ branch and $1A$ through $3\Omega ,3\Omega$ branch

$V_{AB}=2\times 1=2V$.

$Q$ on $1\mu F$ capacitor $=2\times 1\mu c=2\mu C$

$V_{BC}=2\times 2=4V$.

$Q$ on $2\mu F$ capacitor $=4\times 2\mu c=8\mu C$

$V_{DE}=1\times 3=2V$.

$Q$ on $4\mu F$ capacitor $=3\times 4\mu c=12\mu C$

$V_{FE}=3\times 1=V$.

$Q$ across $3\mu F$ capacitor $=3\times 3\mu c=9\mu C$