Two cells of internal resistance ( r₁ ) and ( r₂ ) and of same emf are connected in series across a resistor of resistance ( R ). If the terminal potential difference across the cells of internal resistance ( r₁ ) is zero, then the value of ( R ) is

Step-by-step solution

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