The length of a potentiometer wire is 'L'. A cell of e.m.f. 'E' is balanced at a length L 4 from the positive end of the wire. If the length of the original wire is increased by L 3 , then using the same cell null point is obtained at

Step-by-step solution

The potentiometer principle establishes that cell e.m.f. is proportional to balancing length under uniform potential gradient. For a wire of original length L with applied potential V_p , the initial gradient is k₁ = V_p L . With cell e.m.f. E balanced at x₁ = L 4 , we have E = k₁ x₁ = ( V_p L ) L 4 = V_p 4 . After increasing the wire length by L 3 , the new length becomes L' = 4L 3 . The potential gradient becomes k₂ = V_p L' = 3V_p 4L . Equating the e.m.f. expressions V_p 4 = ( 3V_p 4L ) x₂ yields x₂ = L 3 . The