# How to read catalog data - DC resistance

DC(direct current) resistance of electrical cable is determined by conductor structure and used temperature, therefore it is indicated at 20 degree C normally. (Note 1)

Electrical resistance of metal at around normal temperaturecan be roughly calculated by following equation.

```  Rt = R0 * (1 + α * (t - t0))
hereby,
Rt = resistance at temperature t (Ω)
R0 = resistance at reference temperature t0 (Ω)
t0 = reference temperature (C)
t = around normal temperature (C)
α = constant
```
Typical value of α are the followings.

α value for common metals
CopperTinGoldsilverAluminumIron
4.3e-34.5e-34.0e-34.1e-34.2e-36.6e-3

In case of alloy, a very small amount of additional element afffects it largely. For example, in case of 0.3% of tin included copper tin alloy is about 3.65e-3.

When temperature becomes low, electron scattering generated by atomic thermal motion is reduced which is called phonon scattering, resistance decreases proportionally to the fifth power of the absolute temperature, and at further lower temperature, electrical resistance generated by collision between electrons decreases proportionally to the square of the absolute temperature, following relation is know at wider temperature range which is called Matthiessen's Law.

```  Rt = Rmin + a * t^2 + b * t^5 + c * t
hereby,
Rt = electrical resistance at temperature t(K) (Ω)
Rmin = lowest electrical resistance determined by impurities (Ω)
t = temperature (K)
a, b, c = constant fixed by characteristic of respective metal
```
However, at further lower temperature, there are some substances that becomes superconductive, which is out of this application range.

By the way, since we call it DC(direct current) resistance, resistance value changes with flown frequency.

AC(alternate) resistance is determined by frequency and conductor structure involving its periphery (surroundings), it is always larger than DC resistance. Majority of its cause is conductor skin effect, and affection of eddy current generated in other conductors is added to it.

Since AC resistance is proportional to the square root of frequency when frequency becomes high, there is a distinctive feature that cannot be found in other parts that attenuation at high frequency also increases proportionally to the square root of frequency. This becomes the cause that makes it hard to compensate it by general circuit component. However, because of recent development of LSI that can be stuffed with plenty of parts, it became possible to compensate pretty well so that it has become possible to manage up to very high frequency and or long distance that had been regarded impossible to transmit signal by cable in the past.

Then, up to how much of frequency DC resistance value can be used, there is an expedient indicator called skin depth, if thickness of conductor (in case of column it becomes radius of it) is sufficiently small compared to 1.5 times as large as skin depth, DC resistance and AC resistance do not differ almost at all.

```  δ = sqrt(2 / (ω * μ * σ)
hereby,
δ = skin depth (m)
= 2 * π * f
f  = frequency (Hz)
π = 3.141592..
μ = magnetic permeability (H/m) .. in case of non-magnetic material 4e7*¦Đ
σ = conductivity (S/m) .. in case of annealed copper 5.80e7
σ = conductivity (S/m) .. in case of annealed copper 5.80e7
in case of hard drawn copper 5.65e7
```

For example, in case of JIS C 3005, the following value is used, considering electron collisions.

```  R20 / Rt = 1 - (0.003945 - 1.55e-5 * (t - 20)) * (t - 20)
hereby,
R20 = electric resistance at 20 C (Ω)
Rt  = electric resistance at t C (Ω)
t   = temperature (ˇî)
```
However, it does not mean that JIS C 3005 used this formula, but it was worked out (calculated) by myself out of the table listed there.