The formula of the capacitance is
[tex]C=\dfrac{q}{V}[/tex]
If you half the potential difference, you'll have the new capacity
[tex]C_1 = \dfrac{q}{\frac{V}{2}}=\dfrac{2q}{V} = 2\cdot\dfrac{q}{V}=2C[/tex]
So, if you half the potential difference, the capacitance doubles.
