In the potentiometer circuit shown in the figure, the potentiometer wire AB is $10\ \text{m}$ long and has a resistance of $20\ \Omega$. It is connected in series with a driver cell of emf $4\ \text{V}$ (with negligible internal resistance) and a rheostat of resistance $R$. A cell of emf $1.2\ \text{V}$ is joined, through a galvanometer, between end A and a sliding contact J. The galvanometer shows no deflection when AJ is $6.0\ \text{m}$. The resistance $R$ of the rheostat is

Fig. 1: A potentiometer circuit: a 4 V driver cell and a rheostat R in series with a 10 m wire AB, and a 1.2 V cell with a galvanometer connected from A to a sliding contact J on the wire.