Two cells E₁ and E₂ having equal e.m.f ' E ' and internal resistances r₁ and r₂ (r₁>r₂ ) respectively are connected in series. This combination is connected to an external resistance ' R '. It is observed that the potential difference across the cell E ₁ becomes zero. The value of R will be

Step-by-step solution

Given two cells of equal emf E connected in series with internal resistances r₁ and r₂ , and an external resistance R . The total emf is E_ total = E + E = 2E , and the total internal resistance is r₁ + r₂ . The circuit resistance is R + r₁ + r₂ , so the current is I = 2E R + r₁ + r₂ . The potential difference across the first cell becomes zero when E - I r₁ = 0 , or E = I r₁ . Substituting for I : E = 2E r₁ R + r₁ + r₂ Dividing both sides by E (since E 0 ): 1 = 2r₁ R + r₁ + r₂ R + r₁ + r₂ = 2r₁ R = r₁ - r₂ The ext