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Potentiometer: principle and applications (EMF comparison, internal resistance)

Electric current and circuits · Physics

DC circuit

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Study notes

Worked example: A standard cell E0 = 1.0186 V balances at l0 = 508 cm. (a) Find the potential gradient k. (b) An unknown cell balances at l = 620 cm — find its EMF. (c) With R = 10 Ω across the unknown cell, balance shifts to l2 = 600 cm — find its internal resistance. Step 1: k = E0/l0 = 1.0186/508 = 2.005 × 10⁻³ V/cm ≈ 2 mV/cm. Step 2: E = k·l = (2.005 × 10⁻³)(620) = 1.243 V. (Equivalently E = E0·l/l0.) Step 3: r = R·(l1 − l2)/l2 = 10 × (620 − 600)/600 = 10 × 20/600 = 0.333 Ω. Step 4: Sanity check — the loaded balance length is shorter (terminal V < EMF), exactly as theory demands; a longer l2 than l1 would signal a wiring error.

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