Question

Capacitor $A$ is charged to a potential of $100 \,V$ and capacitor $B$ is charged to a potential of $75\, V$. What are the charges on $A$ and $B$ after key $K$ is closed, as shown in figure?

• A. $\frac{250}{3}\, \mu C ; \frac{500}{3} \,\mu C$
• B. $\frac{250}{4}\, \mu C ; \frac{250}{3} \,\mu C$
• C. $\frac{500}{4}\, \mu C ; \frac{500}{3}\, \mu C$
• D. $\frac{1250}{4}\, \mu C ; \frac{1250}{3} \,\mu C$

Answer 1

Answer: (A)

$ Q_{A}=5 \times 100=500\, \mu C $,
$ Q_{B}=10 \times 75=750\, \mu C$
As negative plate of $A$ is connected to positive plate of $B$,
Therefore, net charge $=750-500=250 \,\mu C$
$\therefore $ Common potential
$V=\frac{\text { net charge }}{\text { total capacity }}$
$=\frac{250}{5+10}=\frac{250}{15}$ volt.
$Q_{A}'=C_{1} V=5 \times \frac{250}{15}=\frac{250}{3} \mu C$
$Q_{B}' =C_{2} V=10 \times \frac{250}{15}=\frac{500}{3} \mu C$