Two circular plates each of radius '$r$' are kept parallel to each other distance '$d$' apart. The capacitance of the capacitor formed is '$C_1$'. If the radius of each of the plates is increased to $\sqrt{3}$ times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes '$C_2$'. The ratio $C_1 : C_2$ is

A capacitor of capacitance C has charge Q and energy stored in it is W. If the charge is increased to 3Q, the energy stored in the capacitor W' will be

A potentiometer wire of length $4\ \text{m}$ and resistance $5\ \Omega$ is connected in series with a resistance of $992\ \Omega$ and a cell of e.m.f. $4\ \text{V}$ with internal resistance $3\ \Omega$. The length of $0.75\ \text{m}$ on potentiometer wire balances the e.m.f. of

By connecting a resistance of $980\ \Omega$ in series with a galvanometer, it is converted into a voltmeter of a certain range. When the resistance of $470\ \Omega$ is connected in series, the range is halved. The resistance of the galvanometer is