A cell, shunted by a 8 Ω resistance, is balanced across a potentiometer wire of length 3 m . The balancing length is 2 m when the cell is shunted by 4 Ω resistance. The value of internal resistance of the cell will be _____ Ω .

Step-by-step solution

Potential difference across test battery is, ∵   V = E R R + r ∝ l ;   R R + r ∝ l Therefore, we can write, 8 8 + r 4 4 + r = 3 2 ⇒ 4 4 + r = 3 8 + r ⇒ 16 + 4 r = 24 + 3 r ⇒ r = 8   Ω