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

The total emf of the two cells connected in series is E_ total = E + E = 2E . The total resistance of the circuit is R_ total = R + r₁ + r₂ . The current I flowing through the circuit is given by I = 2E R + r₁ + r₂ . The potential difference V₁ across the first cell is given by V₁ = E - I r₁ . Given that the potential difference across the first cell is zero, we set V₁ = 0 , which implies E = I r₁ . Substituting the expression for I into this equation, we get E = ( 2E R + r₁ + r₂ ) r₁ . Dividing both sides by E , w