Two cells, having the same emf, are connected in series through an external resistance R. Cells have internal resistances r₁ and r₂ (r₁ > r₂), respectively. Which the circuit is closed, the potential difference across the first cell is zero. The value of R is

detailed solution

Correct option is A

Current in the circuit is given by Ohm's law.Net resistance of the circuit = r1 + r2 + RNet emf in series - E + E = 2ETherefore, from Ohm's law, current in the circuiti=Net emfNet  resistance⇒    i=2Er1+r2+R             …..(i)It is given that, as circuit is closed, potential difference across the first cell is zero. That isV=E−ir1=0⇒    i=Er1              ……(ii)Equating equations (i) and (ii), we get Er1=2Er1+r2+R2r1  =  r1  +  r2  +  RR=external resistance =r1−r2