Question

A metal ball of radius $R$ has a charge $Q$ and capacitance $C$.The charge is changed from $q$ to $2q$. The capacitance changes to

• A. $2C$
• B. $\frac{C}{2}$
• C. $C$
• D. $4C$

Answer 1

The correct option is C $C$

A metal ball behaves as an isolated spherical capacitor.

The capacitance of a spherical capacitor (isolated) is given by
$C=4\pi {\epsilon }_{0}R$

Thus, $C$ only depends on the radius of the shell . So, $C$ remains unchanged upon changing the charge.

Hence, option (c) is the correct answer.