Temperature and I-V characteristics

An I-V graph shows how a component's current responds to different potential differences. Its shape tells you whether the resistance stays constant.

At any nonzero-current operating point, R = V/I. Read both values from that same point. The graphs here put current I in amperes on the vertical axis and p.d. V in volts on the horizontal axis.

Why a hotter metal has greater resistance

When a metallic conductor's temperature rises, the ions in its structure vibrate more vigorously. Their increased vibration hinders the drift of mobile electrons, so the resistance increases in the normal operating range considered here.

At the same p.d., the hotter conductor therefore carries a smaller current. This explanation concerns metals; it is not a rule that every material or component has increasing resistance with temperature.

Read and sketch three characteristic shapes

Start with labelled axes and an origin. Positive and negative values represent opposite voltage polarities and current directions under a fixed reference convention.

Metallic conductor at constant temperature

Sketch a straight line through the origin, extending into both positive and negative quadrants. Current is proportional to p.d., so V/I is constant. This is an ohmic conductor under those conditions. A wire that heats significantly is no longer being compared at constant temperature.

Filament lamp

Sketch a curve through the origin that becomes less steep as the voltage magnitude increases, with a corresponding branch for reversed polarity. Greater current heats the metal filament, increasing its resistance. Doubling the p.d. therefore need not double the current.

Semiconductor diode

Identify the forward and reverse polarities. In the forward direction, current rises strongly over the illustrated higher-voltage part of the curve. In reverse, it is negligible over the range shown. Sketch this asymmetric behaviour; there is no single exact turn-on voltage for every diode.

The diode's forward and reverse directions describe its orientation in the circuit. They are not a claim that all positive voltages in every drawing are forward: check the stated reference and component orientation. The displayed small reverse-current range does not establish zero current at every possible reverse voltage.

Calculate resistance at a point

For the straight I-V line through the origin, the gradient is I/V = 1/R. Here 0.30/6.0 = 0.050 A/V, whose reciprocal is 20 Ω. A steeper straight line on the same scales means smaller resistance.

For a curved graph, use the point's V/I. A tangent gradient describes how current changes close to that point; its reciprocal is not the resistance V/I there. Likewise, a ratio of changes between two separated points does not generally give either point's resistance. If the axes are exchanged to V vertically and I horizontally, the constant-resistance line instead has gradient R.

Collect readings that can distinguish the behaviours

Measure current through and p.d. across the component while varying a suitable low-voltage supply. Record paired readings, then plot I against V. For the constant-temperature wire comparison, limit heating and allow the wire to return to the same conditions between readings where needed.

For a lamp characteristic, let each reading settle at its operating condition; the changing filament temperature is part of the behaviour being observed. Use suitable component ratings and current limits. To investigate the opposite polarity, switch off before reversing the source connections and record the resulting signs consistently.

State the graph's axes and conditions. A straight line through the origin supports constant resistance over the range shown. A changing gradient on a lamp curve must be interpreted with the filament's changing temperature.