on November 19th 17,597

Temperature Coefficient of Resistance (TCR): Formula, Types, Material Values, and Applications

The temperature coefficient of resistance (TCR) helps you understand how a material’s resistance changes when its temperature shifts. In this article, you’ll learn the basic formula, see the TCR values of different materials, and understand what positive, negative, and near-zero TCR mean. You’ll also look at a simple circuit example to see how temperature can affect current and voltage. These ideas will help you see why TCR matters in sensing, protection, and stable circuit design.

Catalog

Figure 1. Temperature Coefficient of Resistance Graph

What is Temperature Coefficient of Resistance?

The temperature coefficient of resistance (TCR) defines how a material’s electrical resistance changes when its temperature varies. It indicates how much resistance will rise or fall for every 1°C change in temperature. TCR is represented by the Greek letter α (alpha) and is important for predicting the thermal behavior of electronic components.

The figure above shows how resistance increases as temperature rises, which is exactly what the temperature coefficient of resistance (TCR) describes. At 0°C, the resistance is R₀, and at a higher temperature t°C, it becomes Rₜ. The dashed line points back to a temperature where resistance would reach zero, called the inferred zero-resistance temperature.

Temperature Coefficient of Resistance Formula

TCR is calculated using the standard equation:

$$R_T=R_0(1+\alpha \Delta T)$$

Where:

• R₀ = resistance at the reference temperature (commonly 20°C or 25°C)

• RT = resistance at the elevated temperature

• α = temperature coefficient of resistance

• ΔT = temperature change (T − T₀)

This formula makes it possible to anticipate how a resistor’s value changes with temperature. In precision electronics.

Temperature Coefficient of Resistance at 20°C

The temperature coefficient of resistance (TCR) of various materials and substances at 20°C is listed below:

Material / Substance	Chemical Symbol / Composition	TCR (per °C at 20°C)
Silver	Ag	0.0038
Copper	Cu	0.00386
Gold	Au	0.0034
Aluminum	Al	0.00429
Tungsten	W	0.0045
Iron	Fe	0.00651
Platinum	Pt	0.003927
Nickel	Ni	0.00641
Tin	Sn	0.0042
Zinc	Zn	0.0037
Tantalum	Ta	0.0033
Manganese	Mn	0.00001
Brass	Cu (50–65%) + Zn (35–50%)	0.0015
Manganin	Cu (84%) + Mn (12%) + Ni (4%)	0.000002
Constantan	Cu (55%) + Ni (45%)	0.00003
Mercury	Hg	0.0009
Nichrome	Ni (60%) + Cr (15%) + Fe (25%)	0.0004
Nichrome 70/30	Ni (70%) + Cr (30%)	0.0002
Nichrome 80/20	Ni (80%) + Cr (20%)	0.00013
Nichrome V	Ni (80%) + Cr (20%) + Fe (trace)	0.00018
Kanthal A1	Fe (72%) + Cr (22%) + Al (6%)	0.00014
Carbon	C	–0.0005
Graphite	C	–0.0008
Pyrolytic Carbon	C	–0.0010
Silicon	Si	–0.07
Germanium	Ge	–0.05
Silicon Carbide	SiC	–0.0006
Silicon Nitride	Si₃N₄	–0.0015
Gallium Arsenide	GaAs	–0.02
Lead	Pb	0.004
Titanium	Ti	0.0038
Titanium Alloy (Ti-6Al-4V)	Ti + Al6% + V4%	0.0032
Stainless Steel 304	Fe + Cr18% + Ni8%	0.001
Stainless Steel 316	Fe + Cr17% + Ni12% + Mo2.5%	0.00094
Phosphor Bronze	Cu + Sn (3–10%) + P (0.03%)	0.001
Invar	Fe (64%) + Ni (36%)	9E-07
Kovar	Fe (54%) + Ni (29%) + Co (17%)	0.000005
Polystyrene	(C₈H₈)n	0.00002
Rubber (general)	—	0.0001–0.0003
Glass	SiO₂	0.00001
Polymers (general)	—	≈0.00001

Types of Temperature Coefficient

Materials change resistance differently when heated, and the temperature coefficient of resistance (TCR) describes how this happens. Below are the main types of TCR, each showing a specific resistance-to-temperature behavior used in electronic and sensing applications.

Positive Temperature Coefficient (PTC)

Figure 2. PTC Graph

A material with a positive temperature coefficient (PTC) shows a steady rise in electrical resistance as temperature increases, as illustrated in the figure above. This behavior is typical in metals such as copper conductors, platinum RTDs, and PTC thermistors used in protection circuits. As the material heats up, stronger atomic vibrations interfere with electron movement, causing resistance to climb. Because of this predictable response, PTC components are ideal for self-regulating heaters, overcurrent protection, and systems that rely on accurate temperature coefficient of resistance characteristics.

Negative Temperature Coefficient (NTC)

Figure 3. NTC Graph

Materials with a negative temperature coefficient (NTC) show the opposite effect, where resistance decreases as temperature rises, as shown in the figure above. NTC thermistors, silicon semiconductors, and manganese-oxide sensing elements commonly exhibit this behavior. As heat injects energy into the material, more charge carriers become available, allowing current to flow more easily. This makes NTC thermistors suitable for temperature sensing, inrush-current limiting, and circuits requiring precise thermal compensation.

Zero or Near-Zero Temperature Coefficient

Figure 4. Zero TCR Graph

Certain engineered alloys exhibit zero or near-zero TCR, meaning their resistance stays nearly constant even as temperature changes, as demonstrated in the figure above. Constantan, Manganin, and specialized Nichrome alloys are known for this highly stable thermal behavior. Their long-term stability ensures consistent resistance values across wide temperature ranges. Because of this reliability, zero-TCR materials are widely used in precision measurement, shunt resistors, and industrial systems requiring high electrical accuracy.

Circuit Example of How TCR Changes Resistance

Figure 5. Circuit Example Showing TCR Effect

The figure above shows a basic series circuit with a 14 V supply, a 250 Ω load, and two wires that each have 15 Ω of resistance at 20°C. This simple setup helps explain how the Temperature Coefficient of Resistance (TCR) affects circuits. Although the wires are labeled as 15 Ω, their resistance does not stay the same when the temperature changes. Most metal wires have a positive TCR, which means their resistance increases as the temperature rises.

So if the temperature goes above 20°C, each wire’s resistance becomes slightly higher. When this happens, the total resistance of the circuit increases, the current decreases, and the load receives less voltage and power. This example shows that even small temperature changes can affect how a circuit performs, making TCR an important factor in wiring, power distribution, and temperature-sensitive electronics.

Advantages and Disadvantages

Advantages

• Predictable resistance behavior

• Accurate temperature sensing capability

• Supports thermal compensation in circuits

• Enables self-regulating and protection functions

• Allows selection of materials optimized for stability or sensitivity

Disadvantages

• Nonlinear behavior at high temperatures

• Resistance drift in inexpensive materials

• Requires compensation in precision designs

• Potential long-term instability in low-cost components

• Temperature variations can affect measurement accuracy

Applications of Temperature Coefficient of Resistance

Temperature Sensing

The temperature coefficient of resistance plays a role in temperature-sensing devices such as RTDs and thermistors. These sensors rely on predictable resistance changes to deliver accurate measurements across industrial, automotive, and environmental applications. Because TCR directly links resistance to temperature variations, it enables stable and precise monitoring in both low- and high-temperature conditions.

Overcurrent Protection

In overcurrent protection systems, the TCR property of PTC thermistors helps safeguard circuits by increasing resistance when excessive heat is detected. As the component’s temperature rises, its resistance sharply climbs, effectively limiting current flow. This behavior protects power supplies, chargers, and battery management systems from damage caused by overloads or short circuits.

Circuit Stabilization

Low-TCR materials are important for circuit stabilization, especially in precision analog and measurement systems. These components maintain nearly constant resistance even as temperature changes, helping achieve consistent voltage and current levels. By minimizing drift, low-TCR resistors improve long-term accuracy and enhance overall system reliability.

Industrial Instrumentation

Industrial instrumentation frequently uses low-TCR resistors to ensure accurate readings in demanding environments. Equipment exposed to heat, vibration, or mechanical stress benefits from the stability that a controlled temperature coefficient of resistance provides. This consistent performance supports reliable data acquisition and long-term equipment operation.

Power Electronics

In power electronics, components with defined TCR characteristics help manage thermal behavior in converters, inverters, and high-current motor drives. A predictable temperature coefficient of resistance allows you to control heat buildup and maintain safe operating conditions. These thermal-aware designs enhance efficiency and extend the lifespan of power systems and battery-powered devices.

Conclusion

The temperature coefficient of resistance helps you predict how resistance changes with temperature in different materials. By understanding the formula and the behavior of PTC, NTC, and zero-TCR types, you can choose components that stay accurate and stable in conditions. The circuit example shows how even small temperature changes can affect performance, and the advantages, disadvantages, and applications help you see where TCR matters most. With this knowledge, you can design circuits that handle temperature changes more effectively.