Question

Two insulated conductors are charged by transferring electrons from one conductor to the other. A potential difference of $100\text{V}$ was produced by transferring $6.25\times {10}^{15}$ electrons from one conductor to the other. The capacitance of the system will be

• A. $20\mu \text{F}$
• B. $10\mu \text{F}$
• C. $40\mu \text{F}$
• D. $5\mu \text{F}$

Answer 1

The correct option is B $10\mu \text{F}$

The total amount of charge $Q$, transferred from one plate to the another can be found by using,
$$Q=ne$$Where,
$n=6.25\times {10}^{15}$, is the number of electrons and
$e=1.6\times {10}^{-19}\text{C}$, is the charge on a electron.

$\Rightarrow Q=6.25\times {10}^{15}\times 1.6\times {10}^{-19}$

$\therefore Q={10}^{-3}\text{C}$

We know the formula for capacitance as$$C=\frac{Q}{V}$$Given, potential differnec, $V=100\text{V}$

$\Rightarrow C=\frac{{10}^{-3}}{100}\text{F}$

$\Rightarrow C=10\mu \text{F}$

Hence, option (b) is the correct answer.

Key Concept: $Q=ne$ and $Q=CV$