Why does resistance depend on temperature?

Resistance depends on temperature because heating changes how charge carriers move through a material. In a metal, higher temperature produces stronger lattice vibrations, causing more frequent scattering of conduction electrons, so resistivity and resistance usually increase. In a semiconductor, heating creates many more mobile charge carriers, so resistance usually decreases despite increased lattice scattering.

For IB Physics, you should connect this microscopic explanation to R = V/I, R = ρL/A, current-voltage characteristics, and the condition that temperature must remain constant when applying Ohm's law to an ohmic conductor. This article focuses specifically on the temperature effect; the broader circuit context is covered in IB Physics current and circuits explained (exam-focused).

Resistance, resistivity, and temperature

Resistance measures how strongly a particular component opposes electric current. It is defined by:

R = V/I

where R is resistance in ohms, V is potential difference in volts, and I is current in amperes. Resistance describes a specific object, so it depends on the object's material and dimensions.

For a uniform wire:

R = ρL/A

where:

• ρ is the material's resistivity in Ω m
• L is the conductor's length
• A is its cross-sectional area

Resistivity is an intrinsic material property at a specified temperature. Temperature primarily changes R by changing ρ, although thermal expansion can also alter L and A slightly.

This distinction matters in exam explanations. Saying only that “resistance is a property of the material” is incomplete because resistance also depends on geometry. It is resistivity that characterizes the material itself under stated physical conditions.

Why does resistance increase with temperature in metals?

A metal contains a lattice of positive ions and a large concentration of mobile conduction electrons. Without an electric field, the electrons move randomly, so there is no net current. When a potential difference creates an electric field, the electrons acquire a small average drift velocity opposite to the field direction.

The electrons do not accelerate freely across the entire wire. Their motion is repeatedly interrupted by scattering from lattice vibrations, impurities, defects, and boundaries within the material. These interactions limit drift velocity and therefore limit the current produced by a given potential difference.

Heating increases lattice vibrations

As a metal becomes hotter, its ions vibrate more strongly about their equilibrium positions. In a quantum description, these lattice vibrations are represented by phonons. The greater phonon population and stronger lattice disturbance increase the probability that conduction electrons will be scattered.

More scattering means that the electrons have a shorter average time between scattering events. Their drift response to the electric field is reduced, so a smaller current flows for the same potential difference. Since R = V/I, the measured resistance is larger.

The essential causal chain is:

higher temperature → stronger lattice vibrations → more electron-lattice scattering → lower electron mobility → smaller current for the same voltage → greater resistance

A strong IB answer should describe scattering or collisions as the reason for reduced charge-carrier mobility. Avoid implying that electrons are simply “blocked” or that heating removes the free electrons from a metal.

The number of carriers is approximately constant

In an ordinary metal, the concentration of conduction electrons changes relatively little over normal temperature ranges. Temperature therefore affects resistance mainly through mobility, not through a large change in the number of charge carriers.

A simplified conductivity relationship makes this clear:

σ = nqμ

Here, σ is conductivity, n is the charge-carrier number density, q is the charge of each carrier, and μ is mobility. Because resistivity is ρ = 1/σ, a reduction in mobility increases resistivity when n remains approximately constant.

The temperature coefficient of resistance

Over a limited range near a chosen reference temperature, the resistance of many metals can be approximated by:

R = R₀[1 + α(T − T₀)]

where:

• R₀ is the resistance at reference temperature T₀
• R is the resistance at temperature T
• α is the temperature coefficient of resistance in K⁻¹ or °C⁻¹
• T − T₀ is the temperature change

For common metals near room temperature, α is positive. This indicates that resistance increases as temperature increases. Temperature intervals have the same numerical size in kelvins and degrees Celsius, so either unit may be used for ΔT, provided the coefficient has the corresponding inverse-temperature unit.

The equation is a linear approximation, not a universal law. The temperature coefficient can itself vary with temperature, and resistance is not linear across every possible temperature range. At very low temperatures, the behavior of metals becomes more complex, and some materials undergo a transition to superconductivity.

Worked example

A copper wire has a resistance of 8.0 Ω at 20 °C. Taking α = 3.9 × 10⁻³ K⁻¹, estimate its resistance at 70 °C.

First calculate the temperature change:

ΔT = 70 − 20 = 50 K

Then apply the linear model:

R = 8.0[1 + (3.9 × 10⁻³)(50)]

R = 8.0(1.195) = 9.56 Ω

To an appropriate number of significant figures, the resistance is 9.6 Ω. A quick reasonableness check is useful: copper has a positive coefficient, so the calculated resistance should be greater than 8.0 Ω.

Why does semiconductor resistance decrease with temperature?

Semiconductors such as silicon behave differently because temperature strongly affects their charge-carrier concentration. At low temperature, relatively few electrons have enough energy to move from the valence band into the conduction band. Consequently, there are comparatively few mobile electrons and holes available to carry current.

Heating transfers energy to the semiconductor lattice and allows more electrons to cross the energy gap into the conduction band. Each promoted electron leaves behind a hole, which also behaves as a mobile positive charge carrier. The resulting increase in electron and hole concentrations can be very large.

Heating also increases lattice scattering and tends to reduce carrier mobility, just as it does in a metal. However, across the relevant operating range of an intrinsic semiconductor or an NTC thermistor, the increase in carrier concentration usually dominates the reduction in mobility. Conductivity therefore rises and resistance falls.

The corresponding chain is:

higher temperature → more electrons promoted into conducting states → more electrons and holes → much greater carrier concentration → greater conductivity → lower resistance

This comparison explains why “resistance always increases with temperature” is false. The direction of the change depends on the material's electronic structure and on which effect dominates.

Intrinsic and doped semiconductors

An intrinsic semiconductor is a pure semiconductor in which thermally generated electrons and holes occur in equal concentrations. A doped semiconductor contains deliberately introduced impurities that provide extra electrons or holes.

The temperature dependence of a doped semiconductor can involve several regimes. At low temperatures, dopant atoms may not all be ionized; over an intermediate range, the dopant carrier concentration may be relatively stable; at sufficiently high temperatures, thermally generated intrinsic carriers become dominant. IB questions will normally provide enough context or data for the trend being tested, so students should not assume that every semiconductor follows one simple linear relationship.

Thermistors and practical applications

A thermistor is a resistor designed to have a strong dependence on temperature. An NTC thermistor has a negative temperature coefficient, meaning its resistance decreases as temperature rises. NTC thermistors are commonly based on semiconducting materials.

Their resistance-temperature relationship is generally nonlinear. One simplified model is:

R = A e^(B/T)

where T must be measured in kelvins and A and B are constants for the device. Because T appears in the denominator of an exponential expression, the resistance falls as absolute temperature rises.

Thermistors are used in:

• digital thermometers and temperature probes
• fire alarms and thermal protection circuits
• battery and motor temperature monitoring
• inrush-current limiting
• temperature compensation in electronic systems

In an IB data-analysis question, you may be asked to interpret a curved resistance-temperature graph rather than use an explicit equation. Read values carefully, state whether the gradient is positive or negative, and do not describe an NTC thermistor's response as linear unless the supplied graph supports that approximation.

How temperature creates non-ohmic behavior

Ohm's law states that current is directly proportional to potential difference for a conductor when its temperature and other physical conditions remain constant. This qualification is essential.

Consider a metal filament lamp. At low current, the filament is relatively cool and has lower resistance. Increasing the potential difference increases the current and the rate of electrical energy transfer, given by:

P = IV = I²R = V²/R

The filament heats up significantly. Its resistance then increases, so each additional increase in voltage produces a progressively smaller increase in current. The current-voltage characteristic curves rather than remaining a straight line through the origin.

This does not mean that R = V/I has stopped being valid. That equation defines resistance at each operating point. The component is non-ohmic because R is not constant as V and I change, largely because its temperature is changing.

For a fixed resistor operated within its rated power, heating may be small enough that its resistance remains approximately constant. For further circuit interpretation, see how resistance affects current in a circuit and the focused IB notes on resistance and resistivity.

Does thermal expansion affect resistance?

Heating a wire can increase its length and cross-sectional area as well as changing its resistivity. From R = ρL/A, an increase in L tends to increase resistance, while an increase in A tends to decrease it.

For an isotropic solid with a small linear expansion, the cross-sectional area changes proportionally more than the length. Nevertheless, in ordinary metallic conductors near room temperature, the change in resistivity usually dominates the geometrical changes. IB calculations commonly treat L and A as constant unless thermal expansion data are provided or the question explicitly asks you to consider dimensional changes.

This is an example of an important exam habit: distinguish the dominant physical mechanism from smaller secondary effects. The resistance changes mainly because temperature changes the charge-transport properties of the material, not merely because the wire expands.

Experimental investigation of resistance and temperature

A typical investigation measures the resistance of a wire or thermistor at several controlled temperatures. Resistance may be obtained from simultaneous voltage and current measurements using R = V/I, or measured directly with an ohmmeter when the component is disconnected from an operating circuit.

Important controls and precautions include:

• keep the test current small to limit self-heating
• allow the component and temperature bath to reach thermal equilibrium
• measure temperature close to the component
• keep the immersed length and electrical contacts consistent
• use a stirred water bath to reduce temperature gradients
• repeat measurements while heating and cooling to check for thermal lag
• account for lead and contact resistance when measuring small resistances

A major source of systematic error is Joule heating by the measuring current. If the current warms the component above the recorded bath temperature, the measured resistance is not associated with the stated temperature. This can be reduced by using a smaller current, taking readings quickly, or switching the circuit on only during measurement.

For investigation design and evaluation, the RevisionDojo temperature and resistivity Physics IA exemplar provides a useful case study. It should be used to examine methodology and evaluation, not copied as a template.

What IB Physics students need to know

In the current IB Physics course, first assessed in 2025, electrical resistance appears within B.5 Current and circuits. The official subject brief identifies current and circuits as part of the particulate nature of matter theme, while detailed classroom treatment connects circuit quantities to microscopic charge behavior.

For exam purposes, be ready to:

• define resistance using R = V/I
• use R = ρL/A for a uniform conductor
• explain why metal resistance generally increases with temperature
• explain why semiconductor or NTC thermistor resistance generally decreases
• apply a supplied linear temperature-coefficient equation
• interpret resistance-temperature and current-voltage graphs
• recognize that Ohm's law requires constant temperature and physical conditions
• explain non-ohmic filament-lamp behavior through self-heating

The present IB assessment model includes multiple-choice, data-based, short-answer, and extended-response work. Temperature-dependent resistance can therefore appear as a qualitative explanation, calculation, graph interpretation, or experimental evaluation. The B.5 current and circuits Questionbank is useful for practising these different forms rather than memorizing one model answer.

Common mistakes and how to correct them

Saying electrons collide more because they move faster

This is an oversimplification for a metal. The central exam-level mechanism is that the lattice ions vibrate more strongly, increasing electron-lattice scattering. Focus on the lattice and the resulting reduction in mobility.

Claiming resistance is always proportional to temperature

The linear coefficient equation works only over a limited interval. Semiconductor and thermistor relationships are usually nonlinear, and metals also deviate from a simple line over sufficiently wide or very low temperature ranges.

Confusing resistance with resistivity

Resistance belongs to a particular component and depends on dimensions. Resistivity belongs to the material at specified conditions. Use R = ρL/A to make the relationship explicit.

Forgetting competing effects in semiconductors

Heating decreases carrier mobility but increases carrier concentration. Semiconductor resistance usually falls because the carrier-concentration increase dominates, not because scattering disappears.

Treating V = IR as proof of Ohm's law

The equation V = IR can be used to define resistance at an operating point. Ohm's law requires V to be proportional to I, which means constant resistance under constant physical conditions.

A concise exam-ready explanation

For a metal, an effective three-mark explanation is:

1. Increasing temperature increases the amplitude of lattice-ion vibrations.
2. Conduction electrons are scattered more frequently, reducing their mobility or mean time between scattering events.
3. Therefore, a smaller current flows for the same potential difference, so resistance increases.

For a semiconductor:

1. Heating gives more electrons enough energy to enter conducting states, producing electron-hole pairs.
2. The charge-carrier concentration increases substantially.
3. This effect usually outweighs reduced mobility, so conductivity increases and resistance decreases.

These answers identify the carriers, the microscopic change, and the macroscopic result. That causal structure is more reliable than memorizing isolated statements.

Conclusion

Temperature changes resistance because it changes the microscopic transport of charge. In metals, stronger lattice vibrations increase electron scattering, so resistivity and resistance generally rise. In semiconductors, heating greatly increases the number of mobile electrons and holes, so resistance generally falls even though scattering also becomes stronger.

For IB Physics, connect the particle model to R = V/I, R = ρL/A, temperature coefficients, thermistors, and non-ohmic current-voltage graphs. RevisionDojo's Study Notes can consolidate the definitions, while the Questionbank and Jojo AI can help identify whether mistakes come from the physical explanation, graph interpretation, or calculation method.

Sources and referenced URLs

• IB Diploma Programme Physics subject brief, first assessment 2025
• International Baccalaureate Physics curriculum updates
• American Physical Society explanation of electron-phonon scattering
• NIST survey of electrical resistivity measurements in pure metals
• RevisionDojo IB Physics B.5 Current and Circuits hub
• RevisionDojo B.5.3 Resistance and Resistivity notes
• RevisionDojo B.5 Current and Circuits Questionbank
• RevisionDojo guide to how resistance affects current
• RevisionDojo Physics IA exemplar on temperature and resistivity