In an experiment to measure the internal resistance of a cell by potentiometer it is found that the balance point is at the length 2m when the cell is shunted by a 5ohm resistance, and is at a length of 3m when the cell is shunted by a 10ohm resistance. The internal resistance of the cell is?

Dear Aayushi

 

Let internal resistance be r.
                    when r || 5Ω then ℓ = 2m
                    when r || 10Ω, then ℓ = 3m
                    We know R ∝ ℓ
                    hence {(r || 5) / (r || 10)} = (2/3)
                              ∴ [{(5r) / (r + 5)} / {(10r) / (r + 10)}] = (2/3)
                              ∴ {(5r) / (r + 5)} × {(r + 10) / (10r)} = (2/3)
                              ∴ {(r + 10) / (r + 5)} = (4/3)
                              ∴ r = 10Ω     

 

 

Regards
Arun (askIITians forum expert)