Question

Two cells having the same emf are connected in series through an external resistance R. Cells have internal resistances r₁& r₂ (r₁> r₂) respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of R is –

• A. r₁ + r₂
• B. r₁ – r₂
• C. $\frac{r_{1} + r_{2}}{2}$
• D. $\frac{r_{1} - r_{2}}{2}$

Answer 1

Answer: (B)

r₁ – r₂

Answer 2

i = $\frac{E_{1} + E_{2}}{R + r_{1} + r_{2}} = \frac{2E}{R + r_{1} + r_{2}}$ (E₁ = E ₂ = E)

P.D. across 1^st cell = E₁ – ir₁ = 0

E = $\frac{2E}{R + r_{1} + r_{2}}$. r₁ ⇒ R + r₁ + r₂ = 2r₁

⇒ R = r₁ – r₂