Resistors and IV characteristics
Different components have different IV graphs. You must recognise four standard shapes and explain them in physics terms.
The four standard IV shapes
1. Fixed (ohmic) resistor. Straight line through origin, both quadrants. Constant resistance. Reversing the polarity reverses the current with the same magnitude.
2. Filament lamp. S-shaped curve: gradient is steepest near the origin, then flattens off. Resistance increases as current grows. Why? The current heats the filament; hotter ions vibrate more, scattering electrons more, so resistance rises. Non-ohmic.
3. Diode. Asymmetric. In the forward direction (current flowing in the direction of the triangle): negligible current until ~0.6 V "turn-on", then a steep rise. In reverse: virtually zero current at any p.d. (until breakdown). The diode is a one-way valve for current.
4. Thermistor. Resistance decreases with rising temperature (the opposite of a metal wire). At higher temperatures more electrons are freed in the semiconductor, so current grows faster than V. The IV graph curves upwards.
Why the lamp's resistance changes
A filament is a thin tungsten wire. When cold (low current), atoms vibrate gently — electrons drift through with few collisions. As current rises, the filament heats and vibrations grow → more collisions → fewer charges per second → resistance rises. This is not a failure of Ohm's law — Ohm's law only ever applied at constant temperature.
How to identify a component from its IV graph
- Straight line both ways → fixed resistor.
- Curve that flattens at high current (in both directions) → filament lamp.
- One-way conduction → diode.
- Steepening curve (resistance falls) → thermistor (or LDR if light-controlled).
How to read resistance from an IV graph
- Pick a point on the curve and compute $V/I$. The gradient is not $R$ unless the line is straight; the gradient is $\frac{dI}{dV} = 1/R$ at that point only.
✦Worked example— Worked example — filament lamp
At 1.0 V the lamp draws 0.10 A. At 6.0 V it draws 0.30 A. Show that the resistance has increased.
- At 1.0 V: $R_1 = 1.0/0.10 = 10$ Ω.
- At 6.0 V: $R_2 = 6.0/0.30 = 20$ Ω.
- Resistance has doubled — consistent with the filament heating up.
⚠Common mistakes
- Saying the lamp "fails Ohm's law" — Ohm's law was always conditional on constant temperature.
- Reading the gradient as $R$ instead of $V/I$ for a non-linear curve.
- Forgetting the diode blocks reverse current — drawing it as a straight line.
- Confusing thermistor and LDR (both have falling resistance, but with different stimuli — temperature vs light).
AI-generated · claude-opus-4-7 · v3-deep-physics