Question

Three capacitors of $2\mu F,3\mu F$ and $5\mu F$ are independently charged with batteries of emf's 5V, 20V, and 10V respectively. After disconnecting from the voltage sources. These capacitors are connected as shown in figure with their positive polarity plates are connected to $S$ and negative polarity is earthed. Now a battery of $20V$ and an uncharged capacitor of $4\mu F$ capacitance are connected to the junction $S$ as shown with a switch $S$. When switch is closed, find:
(a) the potential of the junction $A$
(b) final charges on all four capacitors

Answer 1

Initial charges on $2\mu F$, $5\mu F$, $3\mu F$ are $10\mu C$, $50\mu C$, $60\mu C$

total initial charge $=12\mu C$

Since charge is conserved in loop

$(V-0)2\mu F+(V-0)5\mu F+(V-0)3\mu F+(V-20)4\mu F=120$

$=14V-80=120$

$V=100/7$

b) (i) charge on $2\mu F=\left(\frac{100}{7}\right)2=\frac{200}{7}\mu F$

(ii) charge on $5\mu F=\left(\frac{100}{7}\right)5=\frac{500}{7}\mu F$

(iii) charge on $3\mu F=\left(\frac{100}{7}\right)3=\frac{300}{7}\mu F$

(iv) charge on $4\mu F=(\frac{100}{7}-20)4=\frac{-160}{7}\mu F$