Question

Two cells, having the same e.m.f. are connected in series through an external resistance R. Cells have internal resistances r₁ and 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. $\frac{r_{1} + r_{2}}{2}$
• C. $\frac{r_{1} - r_{2}}{2}$
• D. r₁ + r₂

Answer 1

Answer: (A)

r₁ – r₂

Answer 2

Given, V₁ = 0

E – i r₁ = 0 ⇒  E = i r₁

E = $\frac{2E \times r_{1}}{R + r_{1} + r_{2}}$

∴ R + r₁ + r₂ = 2r₁∴ R = r₁ – r₂