Potentiometer Calibration with an Oxidised Wire Section
During a practical exam, a student sets up a 10.0 m long potentiometer wire with a uniform clean section and a 2.0 V accumulator as driver cell. The first 1.0 m of the wire is oxidized, but all balance points are obtained beyond 5 m. A standard cell of emf 1.018 V balances at 5.09 m from the common end. An unknown cell balances at 7.64 m. The student then replaces the unknown cell with a 1.50 V cell and predicts a balance length of 7.50 m. The examiner asks the student to justify whether the oxidized section affects the result, and to check the prediction from the calibration. The accumulator is not changed during the measurements, and its internal resistance is negligible.
1. Calculate the potential gradient in the clean section and the emf of the unknown cell. Show how the standard-cell balance is used.
Read the worked answer
The standard cell gives the calibration:k = E_s / l_s = 1.018 / 5.09 = 0.2000 V/m.
The unknown balance is also in the clean section, soE_x = k l_x = 0.2000 × 7.64 = 1.528 V ≈ 1.53 V.
The oxidized first metre changes the total resistance and hence the current, but it does not make the clean section non-uniform. Since both the standard and unknown balances occur beyond 5 m, the calibration measured in that same clean section cancels the changed current. If the unknown had balanced inside the oxidized part, the simple proportional result would not be valid.
2. Check the student's prediction for a 1.50 V cell. Does the oxidized section alter this prediction? State any necessary condition.
Read the worked answer
For the same setting,l = E / k = 1.50 / 0.2000 = 7.50 m.
This agrees with the prediction. The result is valid only while the driver current, and hence k, remains unchanged and both cells balance in the clean, uniform part of the wire. Replacing the cell does not alter the driver circuit, so k is unchanged. The oxidized section still affects the total current, but not the calibration ratio, as long as calibration and measurement are made in the same clean region.