KCET 2018 Physics Solved Paper

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=‌

2E

R+r1+r2

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−‌

2E

R+r1+r2

×r1=0
⇒E=‌

2Er1

R+r1+r2

⇒R+r1+r2=2r
⇒R=2r1−r1−r2
⇒R=r1−r2