Question

When $30\mu C$ charge is given to an isolated conductor of capacitance $5\mu F$ . If this conductor is now connected to another isolated conductor by a conducting wire (at very large distance) of total charge $50\mu C$ and capacity $10\mu F$ then find out the ratio of final charges on conductors.

Answer 1

The common potential is given as,

$V_c=\frac{q_1+q_2}{C_1+C_2}$

$=\frac{30+50}{5+10}$

$=\frac{16}{3}V$

The ratio of the final charges is given as,

$\frac{q_5}{q_{10}}=\frac{C_1{V}_c}{C_2{V}_c}$

$\frac{q_5}{q_{10}}=\frac{5}{10}$

$\frac{q_5}{q_{10}}=\frac{1}{2}$

The ratio of the final charges is $1:2$.