Question

18. Two cells x and y of identical emf but different internal resistance r, and r, (r, >r,) are connected in
series to an external resistance R. If the terminal voltage across x is zero, then
1) R = r1 +2
2) R = r1 - r2
3) R = √r1r2
4) R=(r1+r2)/2
​

Answer 1

Given info : Two cells x and y of identical emf but different internal resistance r₁ and r₂, (r₁ >r₂) are connected in series to an external resistance R.

if the terminal voltage across the first cell is found to be zero then...

solution : let emf of each cell is E.

so, in series total emf = E + E = 2E

and total current in the circuit, i = 2E/(r₁ + r₂ + R)

now potential drops across the 1st cell, V = E - ir₁

as V = 0 [ from question ]

⇒E = ir₁

⇒E = 2E/(r₁ + r₂ + R) × r₁

⇒ r₁ + r₂ + R = 2r₁

⇒R = r₁ - r₂

Therefore the correct option is (2)

Answer 2

$\huge \tt 2) \: R\: = { \: }^{ \huge r} {1}^{ \: } - { \: }^{ \huge r} {2}^{ \: }$