Question

Find the charges on the four capacitors of capacitances 1$\mu F,2\mu F,3\mu F$ and $\mu F$ shown in figure (32 - E32). Figure 32 - E32

Figure 32 - E32

Answer 1

At steady state no current flows through the capacitors.

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

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

Since current is divided in the inverse ratio of resistance in each branch, $2\Omega$ will pass through 1, $2\Omega$ branch and one through 3, $3\Omega$ 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 = $2\mu f=CV$

$=2\times 4\mu c$

$=8\mu c$

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

Q on 4 = 4 $\mu f$ capacitor

= $3\times 4\mu c$

= $12\mu c$

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

Q across 3 = 3 $\mu f$ capacitor

= 3$\times 3\mu c$

= 9 $\mu c$