let it is $=\mathrm{q}$

and let current in resistance branch $=\mathrm{i}$

$\therefore \mathrm{V}_{\mathrm{C}_{1}}=\mathrm{i} \mathrm{R}_{1} \Rightarrow \frac{\mathrm{q}}{\mathrm{C}_{1}}=\mathrm{i} \mathrm{R}_{1} \Rightarrow \mathrm{q}=\mathrm{ir}_{1} \mathrm{C}_{1}$

similarly $\mathrm{V}_{\mathrm{C}_{2}}=\mathrm{i} \mathrm{R}_{2} \Rightarrow \frac{\mathrm{q}}{\mathrm{C}_{2}}=\mathrm{i} \mathrm{R}_{2} \Rightarrow \mathrm{q}=\mathrm{i} \mathrm{R}_{2} \mathrm{C}_{2}$

$\therefore \quad \mathrm{iR}_{1} \mathrm{C}_{1}=\mathrm{i} \mathrm{R}_{2} \mathrm{C}_{2}$

$\Rightarrow \frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}=\frac{\mathrm{C}_{2}}{\mathrm{C}_{1}}$