Lab: Resistivity and Ohm's Law

A wire resists current because its atoms get in the way of moving electrons. A thin wire packs the same collisions into a smaller cross section, so each electron has less room to slip through, and the wire fights back harder. Length matters too: a longer wire means more collisions along the way. Resistivity, rho, captures the material itself, separate from shape, so copper always has lower resistivity than nichrome no matter how the wire is cut.

To measure resistance directly, you wire a battery, a variable resistor or rheostat, the test wire, an ammeter in series with the wire, and a voltmeter across the wire. The ammeter reads current through the wire, the voltmeter reads the voltage drop across it, and you adjust the rheostat to collect several current and voltage pairs rather than trusting one reading. Plotting voltage on the vertical axis against current on the horizontal axis gives a straight line through the origin for an ohmic resistor, and the slope of that line is the resistance, since V = IR.

The same logic extends to resistivity. If you measure the resistance of wires with different lengths but the same cross-sectional area, R = rho L / A says that plotting R against L gives a line whose slope is rho divided by A. Multiply that slope by the known cross-sectional area and you recover rho. This connects back to the rest of the unit because it is the same pattern used everywhere in lab: force a linear relationship, read the physical quantity off the slope, and treat scatter in the points as a signal to collect more data rather than trust a single trial.