State the principle of working of a galvanometer. A galvanometer of resistance $\mathit{G}$ is converted into a voltmeter to measure upto $\mathrm{V}$ volts by connecting a resistance ${\mathit{R}}_1$ in series with the coil. If a resistance ${\mathit{R}}_2$ is connected in series withit, then it can measure upto $\frac{\mathit{V}}{2}$ volts. Find the resistance, in terms of ${\mathit{R}}_1$ and ${\mathit{R}}_2$ required to be connected to convert it into a voltmeter that can read upto $2\mathrm{V}$ . Also find the resistance $\mathit{G}$ of the galvanometer in terms of ${\mathit{R}}_1$ and${\mathit{R}}_2$.