Resistance is a quantity that represents how strongly the flow of electric current is opposed, and its value varies depending on the material, shape, and temperature of the conductor.
This section examines electrical resistance in greater detail.

1.5.1 Factors Determining Resistance

The resistance R [Ω] of a conductor with a length l [m] and cross-sectional area A [m²] can be expressed by the following equation.

Here, ρ is called the resistivity and represents the inherent opposition of a material to the flow of electricity.
Its unit is the ohm-metre (unit symbol: Ω·m).

Equation 1.5-1 shows that the resistance R [Ω] of a conductor is proportional to its length l [m] and inversely proportional to its cross-sectional area A [m²].

1.5.2 Resistivity

The resistance of a conductor varies according to its material, shape—including its length and cross-sectional area—and ambient temperature.
Therefore, the conditions must be standardized when comparing conductors made of different materials.

Accordingly, the resistance measured between the ends of a conductor with a length of 1 [m] and a cross-sectional area of 1 [m²] is defined as the resistivity of that conductor.
This makes it possible to distinguish resistivity as an intrinsic property of the material.

【Note】
※Although temperature is treated as an external factor that changes resistivity, the electrical industry generally uses the value at 20°C as the standard resistivity in accordance with standards such as JIS C 3001 for electrical copper wires.

1.5.3 Temperature Coefficient of Resistance

In general, the electrical resistance of a metal increases as its temperature rises.
The rate of change in resistance per ohm of conductor resistance for each 1°C increase in temperature is called the temperature coefficient of resistance and is represented by the symbol α.

If a conductor has a resistance of R_t [Ω] at t [°C] and a resistance of R_T [Ω] at T [°C], the temperature coefficient of resistance α_t can be calculated using the following equation.

Rearranging Equation (1.5-2) gives the following equation.

Resistance values at 20°C are commonly used as a reference. In this case, the temperature coefficient of resistance at 20°C, α₂₀, is used, giving the following equation.

About This Article

Reference
・Fundamentals of Electricity, Volume I, Corona Publishing Co., Ltd., by Toshio Utsunomiya, Hiroshi Takahashi, and Isao Izumi
※This article was prepared with reference to the source listed above and organized based on the author’s understanding.