Capacitance of an isolated conducting sphere of radius R _ 1...

Capacitance of isolated conducting sphere $C = 4\pi{ε}_{0}{R}_{1}$

By enclosing inside another sphere of radius ${R}_{2}$, new capacitance ${C}^{'} = \dfrac{4\pi{ε}_{0}{R}_{1}{R}_{2}}{\left({R}_{2} - {R}_{1}\right)}$

Given: $\dfrac{4\pi{ε}_{0}{R}_{1}{R}_{2}}{\left({R}_{2} - {R}_{1}\right)} = n \times 4\pi{ε}_{0}{R}_{1}$

$⇒ \dfrac{{R}_{2}}{\left({R}_{2} - {R}_{1}\right)} = n ⇒ \dfrac{\dfrac{{R}_{2}}{{R}_{1}}}{\left(\dfrac{{R}_{2}}{{R}_{1}} - 1\right)} = n$

$⇒ \dfrac{{R}_{2}}{{R}_{1}} = n\dfrac{{R}_{2}}{{R}_{1}} - n ⇒ \dfrac{{R}_{2}}{{R}_{1}} = \dfrac{n}{\left(n - 1\right)}$