understand that the resistance of a thermistor decreases as the temperature increases (it will be assumed that thermistors have a negative temperature coefficient)

Resistance and Resistivity

🔌 Resistance (R) is the opposition to the flow of electric current in a conductor.

📐 Resistivity (ρ) is an intrinsic property of a material that tells us how strongly it resists current.

The basic relationship is: \$R = \rho \frac{L}{A}\$

where L is the length of the conductor and A its cross‑sectional area.

How Temperature Affects Resistance

Most metals have a positive temperature coefficient (PTC): their resistance increases as temperature rises.

This happens because the atoms vibrate more, scattering electrons more.

The change can be approximated by: \$R(T) = R0 \bigl[1 + \alpha (T - T0)\bigr]\$

where α is the temperature coefficient (positive for metals).

Thermistors – Negative Temperature Coefficient (NTC)

🔥 A thermistor is a special resistor made from semiconductor material.

It has a negative temperature coefficient (NTC): its resistance decreases as temperature increases.

Think of it like a cooling fan that speeds up when it gets hot – the more heat, the less resistance, so more current flows.

The relationship is often exponential: \$R(T) = R0 \, e^{-\beta (T - T0)}\$

where β is a material constant.

Practical Example: Thermistor in a Heater

Imagine a small heater with a thermistor inside.

1️⃣ At room temperature, the thermistor has high resistance, limiting current.

2️⃣ As the heater warms the air, the thermistor’s temperature rises.

3️⃣ Its resistance drops, allowing more current to flow, which in turn heats the heater faster – a self‑regulating cycle.

This is why thermistors are used in temperature sensors and over‑current protection.

Exam Tips for A‑Level Physics

  1. Remember the key difference: PTC materials (metals) increase R with T, while NTC thermistors decrease R with T.
  2. When given a graph of R vs. T, identify the slope sign to determine the type of material.
  3. Use the formula \$R = \rho L/A\$ to calculate resistance if resistivity, length, and area are provided.
  4. For thermistors, you may be asked to estimate R at a new temperature using the exponential relation or a given table of values.
  5. Always check units: resistivity in Ω·m, resistance in Ω, temperature in °C or K.
  6. In multiple‑choice questions, look for clues like “decreases with temperature” → NTC.

Quick Reference Table

MaterialTemperature CoefficientEffect on R
Copper (metal)+0.0039 / °CR ↑ with T
NTC Thermistor–0.02 / °C (approx.)R ↓ with T