A standard cell of 1.08 V is balanced by the potential difference across 90 c m of a 1 meter, long wire supplied by a cell of emf 2 V through a series resistor of resistance 2 Ω . If the internal resistance of cell in the primary circuit is zero then the resistance per unit length (in Ω m - 1 ) of potentiometer wire is

Step-by-step solution

E = X . l       ( X = Potential   gradient ) E   = E o L × R w R w + r + R h × l   ∵   r   =   0 ,   R h   =   2   Ω ∴   1.08   =   2 1   m × R w R w + 2   ×   0.90   m 1.08 2 × 0.90 =   R w R w + 2 Hence : 0.6   = R w R w + 2 0.6   R w   +   1.2   =   R w ⇒ 1.2   =   0.4   R w   ⇒ 3   =   R w &#875