State the principle of working of a galvanometer. A galvanometer of resistance $G$ is converted into a voltmeter to measure upto $V$ volts by connecting a resistance $R_1$ in series with the coil. If a resistance $R_2$ is connected in series withit, then it can measure upto $\;\frac{V}{2}$ volts. Find the resistance, in terms of $R_1$ and $R_2$ required to be connected to convert it into a voltmeter that can read upto $2V$ . Also find the resistance $G$ of the galvanometer in terms of $R_1$ and$R_2$.