Question

A potentiometer wire AB is of length 100 cm, with C as its middle point. The part AC is made of a uniform wire of a material of resistivity ρ₁. The diameter of this part is d₁. The part CB is made of another uniform wire of a material of resistivity ρ₂. The diameter of this part d₂. It is given that

ρ₁ : ρ₂ = 2 : 3 and d₁ : d₂ = 2 : 1

The balancing length, measured from A, for a cell for EMF E₁ is found to be 40 cm and that for a cell of EMF E₂, is found to be 65 cm. The ratio E₁ /E₂ is equal to

(1) 2/7

(2) 4/5

(3) 40/65

(4) 4/9

Answer 1

Correct option: (2/7)

Explanation: 

Now, let σ₁ and σ₂ be the resistance per unit length of each half.

Let I be the current through the wire, which must be the same for both the halves.

By using the principle of potentiometer, E = Iσ l