B.5 · IB Physics
Resistivity and I–V characteristics
Vary the potential difference across a component and read the current. A metal wire at constant temperature is ohmic with R = ρL/A, a filament lamp heats up so its resistance rises, and a diode barely conducts one way. Compare R = V/I with the gradient of the graph.
Predict first
Start from the default settings (nichrome wire, L = 1.00 m, V = 3.00 V). Increase Wire length L to 2.00 m. What happens to the current?
R = ρL ÷ A, so doubling L doubles R. At constant V the current I = V ÷ R halves, from about 545 mA to about 273 mA.
Check it in the model: Move the Wire length L slider from 1.00 m to 2.00 m and compare the Current I readout.
line from origin: gradient I/V = 1/R tangent: gradient ΔI/ΔV operating point
Material, length and area apply to the wire only.
wire: R = ρL ÷ A
lamp: R rises with filament temperature
diode: I = I₀(e^(Vd ÷ nVT) − 1)
P = VI
Try this
- Choose the filament lamp and raise the potential difference from 1.00 V to 6.00 V. Compare R = V/I at each, and explain why the I–V graph bends towards the V axis.
- Choose the wire with L = 0.50 m and A = 0.20 mm², then set L = 1.00 m and A = 0.80 mm² (four times the area, as when the diameter doubles). Predict R from ρL/A and check the readout.
- Choose the diode and sweep V from −6 V to +2 V. Where does the current become noticeable, and why are R = V/I and ΔV/ΔI so different at V = 1.50 V?
Common error: Resistance is V/I at a point, the gradient of the line from the origin to that point; for a lamp or diode the tangent gives ΔV/ΔI, which is not the resistance, and the lamp breaks Ohm's law only because its temperature changes.