Question

Two spherical conductors of capacitance $3\mu \text{F}$ and $5\mu \text{F}$ are charged to potentials of $300\text{Volt}$ and $500\text{Volt}$. The spheres are then connected, then the final charge on $3\mu \text{F}$ and $5\mu \text{F}$ capacitors respectively will be:

• A. $900\mu \text{C},2500\mu \text{C}$
• B. $1200\mu \text{C},2200\mu \text{C}$
• C. $1275\mu \text{C},2125\mu \text{C}$
• D. $1000\mu \text{C},2400\mu \text{C}$

Answer 1

The correct option is C $1275\mu \text{C},2125\mu \text{C}$

The common potential of spheres after connection will be,

$V=\frac{C_1{V}_1+C_2{V}_2}{C_1+C_2}$

$\Rightarrow V=\frac{\left(3\right)\left(300\right)+\left(5\right)\left(500\right)}{3+5}=\frac{900+2500}{8}$

$\therefore V=\frac{3400}{8}=425\text{Volts}$

Therefore, final charge on the sphere is

$q_1=C_{1}V$

$q_1=\left(3\mu \text{F}\right)\left(425\text{Volt}\right)$

$\Rightarrow q_1=1275\mu \text{C}$

Similarly,
$q_2=C_{2}V$

$q_2=\left(5\mu \text{F}\right)\left(425\text{Volt}\right)$

$\Rightarrow q_2=2125\mu \text{C}$

Hence, option $\left(c\right)$ is correct.

$\begin{array}{c}\text{Why this question ?}\\ \text{Tip: Always remember that charges will}\\ \text{only get redistributed after the conductors}\\ \text{are connected. The net charge of the}\\ \text{system is constant. Hence, total initial}\\ \text{charge \& final charge on system will be equal}\end{array}$