To measure the internal resistance of a battery, potentiometer is used. For R = 10 Ω, the balance point is observed at ℓ = 500 cm and for R = 1 Ω the balance point is observed at ℓ = 400 cm. The internal resistance of the battery is approximately:
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Question

To measure the internal resistance of a battery, potentiometer is used. For R = 10 Ω, the balance point is observed at ℓ = 500 cm and for R = 1 Ω the balance point is observed at ℓ = 400 cm. The internal resistance of the battery is approximately:

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G1 Physics · Accepted Answer

Let the potential gradient be k. For R = 10 Ω: 10i = 500k Therefore: i = 50k Also: 500k = ε - i rₛ = ε - 50k rₛ For R = 1 Ω: i' = 400k and: 400k = ε - 400k rₛ Subtracting the two equations: 100k = 350k rₛ rₛ = 100/350 ≈ 0.286 Ω ≈ 0.3 Ω