Battery Internal-Resistance Misestimation in Student-Built Engineering Education Cell-Test Benches: A Four-Wire Kelvin Probe Evaluation Linking Contact Resistance to State-of-Health Classification Reliability

Student-built cell-test benches in engineering education frequently report internal resistance from two-wire measurements, yet the contact resistance at the probe-electrode interface is rarely separated from the cell's own ohmic resistance. The model treats the measured resistance as the sum of the cell's true internal resistance and a contact term whose magnitude depends on probe geometry, electrode surface condition and applied force. A sensitivity analysis over plausible bench parameters shows that a contact resistance of 5 mΩ, well within the range reported for student-assembled fixtures, can shift a 50 mΩ cell across a 20% state-of-health threshold when the reference resistance is drawn from a single baseline measurement. The derived reliability bound is expressed as a function of the ratio of contact resistance to cell resistance and the width of the classification band. The contribution is a design rule: a four-wire Kelvin probe with a contact-resistance ceiling of 1 mΩ or less, verified against a calibration shunt before each session, keeps classification error below 5% for cells above 40 mΩ. The analysis is methodological and does not report primary measurements; it specifies the probe geometry, calibration procedure and acceptance criterion that a student bench must satisfy to produce state-of-health labels that are stable under repeated measurement.