Two cells having same emf E are connected in series through an external resistance R. Cells have internal resistances r₁ and r₂ (r₁ > r₂). When circuit is closed, potential difference across first cell is zero. Value of R is:
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Question

Two cells having same emf E are connected in series through an external resistance R. Cells have internal resistances r₁ and r₂ (r₁ > r₂). When circuit is closed, potential difference across first cell is zero. Value of R is:

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G1 Physics · Accepted Answer

Step 1: Series current I = 2E/(R+r₁+r₂). Step 2: First cell terminal voltage is zero, E−Ir₁ = 0 ⇒ I = E/r₁. Step 3: E/r₁ = 2E/(R+r₁+r₂) ⇒ R+r₁+r₂ = 2r₁ ⇒ R = r₁−r₂.