A potentiometer is supplied a constant voltage of 5 V. A cell of emf 1.4 V is balanced by the voltage drop across 280 cm of the potentiometer wire. The total length of the potentiometer wire will be:

10 m

Let Potential drop per unit length across potentiometer wire is V . 

Since 1.4V is balanced by 280cm = 2.8 m.

$\Rightarrow V = \frac{1.4}{2.8} = 0.5 V/m$

Length required to balance 5V potential difference is $ L = \frac{5}{0.5}= 10m$