A potentiometer circuit is set up as shown. The potential gradient, across the potentiometer wire, is k volt/cm and the ammeter, present in the…

A potentiometer circuit is set up as shown. The potential gradient, across the potentiometer wire, is $\displaystyle k$ volt/cm and the ammeter, present in the circuit, reads $\displaystyle 1.0$ A when two way key is switched off. The balance points, when the key between the terminals (i) $\displaystyle 1$ and $\displaystyle 2$ (ii) $\displaystyle 1$ and $\displaystyle 3$, is plugged in, are found to be at lengths $\displaystyle l_1 \mathrm{~cm}$ and $\displaystyle l_2 \mathrm{~cm}$ respectively. The magnitudes, of the resistors R and X, in ohms, are then, equal, respectively, to :