Since the two cells are connected in series, therefore, total emf is
E=E1+E2 Since the emf is same, therefore,
E=2E[∵E1=E2=E(say)] Total resistance
=R+r1+r2 Thus, current in circuit,
I=
Now, terminal potential difference across cell of internal resistance
r1 is
E−Ir1 Given, this terminal potential difference is zero, therefore,
E−Ir1=0 E−×r1=0 ⇒E= ⇒R+r1+r2=2r ⇒R=2r1−r1−r2 ⇒R=r1−r2