Two cells with the same emf E and different internal resistances r₁ and r₂ are connected in series to an external resistance R . If the potential difference across the first cell is zero then value of R .

Step-by-step solution

Here are two batteries with emf E each and the internal resistances r₁ and r₂ , respectively. We have I (R+r₁+r₂ )=2 E Now, the potential difference across the first cell would be equal to V=E-I r₁ . From the question, V=0 , there E=I r₁= 2 E r₁ R+r₁+r₂ [From Eq. (i)] where, R+r₁+r₂=2 r₁ Hence, R=r₁-r₂ .