JEE Main 17 March 2021 Shift 2 Solved Paper

The given circuit can be drawn as
Since in series combination, the current through each resistance remains same. So, equivalent resistance of the circuit is given as
R‌equivalent ‌=R+r1+r2
and equivalent emf, E‌equivalent ‌=2E+E=3E
From Ohm's law, I =

E‌equivalent

R‌equivalent‌

⇒I=

3E

R+r1+r2

When potential difference is zero across the first cell, then potential positive terminal is equal to the potential at negative terminal.
VP=VN
2E=Ir1
Substituting the values in the above equation, we get
2E=‌

3E

R+r1+r2

r1
2R+2r1+2r2=3r1⇒R=‌

r1−2r2

2

⇒‌‌R=‌

r1

2

−r2