Question

Find the charges on the three capacitors shown

Answer 1

let us assume leftside is loop1 and right side is loop2

applying kirchoff law for loop1

$\frac{q_1}{2}+\frac{q_3}{6}-10=0⟹3q_1+q_3=60$ this is eq$1$

applying kirchofflaw for loop2

$\frac{q_2}{4}+20-\frac{q_3}{6}=0⟹3q_2-2q_3=-240$ this is eq$2$

also$-q_1+q_2+q_3=o$(isolated system)

from1 $3(q_2+q_3)+q_3=60$

$3q_2+4q_3=60$ this is eq$3$

now solving $2$ and$3$

$q_3=50c$

$3q_1+q_3=60$

$q_1=\frac{10}{3}C$

$-q_1+q_2+q_3=0$

$-\frac{10}{3}+50+q_2=0$

$q_2=\frac{10}{3}-50=\frac{10-150}{3}=\frac{-140}{3}C$