Question

In the following figure is shown a system of four capacitors connected across a $10V$ battery. Charge that will flow from switch $S$ when it is closed is

• A. 5 $\mu C$ from $b$ to $a$
• B. 20 $\mu C$ from $a$ to $b$
• C. 5 $\mu C$ from $a$ to $b$
• D. $zero$

Answer 1

Answer: (A)

Using Kirchoff's law $-\frac{q_1}{2}+\frac{q_2}{3}=0$
$q_1=\frac{2}{3}{q}_2;10-\frac{q_1}{2}-\frac{q_2}{3}=0$
$\Rightarrow 60=3q_1+2q_2$
$\Rightarrow 60=3\left(\frac{2}{3}{q}_2\right)+2q_2$
$\Rightarrow 4q_2=60$
$\Rightarrow q_2=15\mu c$
$\Rightarrow q_1=10\mu c$
Therefore, charge through the switch
$q_1-q_2=-5\mu c(a\to b)=5\mu c(b\to a)$