Conductor Resistance: DC, AC, Temperature and IEC 60228 Values

Conductor resistance is one of the main inputs to cable voltage drop, power loss, short-circuit and thermal calculations. It depends on conductor material, cross-sectional area, conductor construction, frequency and operating temperature.

This article consolidates the general conductor resistance calculation note with the IEC 60228 d.c. resistance table. It links directly to Cable Impedance, Cable Power Loss and Voltage Drop.

D.C. resistance

The d.c. resistance of a conductor can be estimated using the CENELEC CLC/TR 50480 relationship:

$$R=\frac{{\rho }_{20}}{S}$$

R	D.C. resistance of the conductor, ohm/m
ρ20	Electrical resistivity of the conductor material at 20 °C, ohm.m
S	Conductor cross-sectional area, m2

IEC 60228 provides an alternative by specifying maximum conductor resistance values at 20 °C for standard conductor classes. myCableEngineering uses IEC 60228 values where they apply, and falls back to calculated resistance where the cable is outside the IEC 60228 tabulated range.

IEC 60228 conductor classes

• Class 1: solid conductors.
• Class 2: stranded conductors.
• Class 5: flexible conductors.
• Class 6: flexible conductors with greater flexibility than class 5.

IEC 60228 maximum d.c. resistance at 20 °C

CSA, mm2	Copper plain, class 1 & 2, mΩ/m	Copper plain, class 5 & 6, mΩ/m	Copper tinned, class 5 & 6, mΩ/m	Aluminium, class 1 & 2, mΩ/m
0.5	36.0	39.0	40.1	–
0.75	24.5	26.0	26.7	–
1	18.1	19.5	20.0	–
1.5	12.1	13.3	13.7	–
2.5	7.41	7.98	8.21	–
4	4.61	4.95	5.09	–
6	3.08	3.30	3.39	–
10	1.83	1.91	1.95	3.08
16	1.15	1.21	1.24	1.91
25	0.727	0.78	0.795	1.20
35	0.524	0.554	0.565	0.868
50	0.387	0.386	0.393	0.641
70	0.268	0.272	0.277	0.443
95	0.193	0.206	0.210	0.320
120	0.153	0.161	0.164	0.253
150	0.124	0.129	0.132	0.206
185	0.0991	0.106	0.108	0.164
240	0.0754	0.0801	0.0817	0.125
300	0.0601	0.0641	0.0654	0.100
400	0.0470	0.0486	0.0495	0.0778
500	0.0366	0.0384	0.0391	0.0605
630	0.0283	0.0287	0.0292	0.0469
800	–	–	–	0.0367
1000	–	–	–	0.0291
1200	–	–	–	0.0247

For screened cables, or other cables with magnetic metallic screens or shields earthed at both ends, effective resistance may increase. IEC 60909-2 gives correction methods for short-circuit calculations involving these arrangements.

A.C. resistance

A.C. resistance is always higher than d.c. resistance. The main causes are skin effect and proximity effect. IEC 60287 expresses a.c. resistance using:

$$R_{\mathrm{ac}}=R\left[1+{\gamma }_s+{\gamma }_p\right]$$

Rac	A.C. resistance of the conductor
R	D.C. resistance of the conductor
γs	Skin effect factor
γp	Proximity effect factor

Skin effect

As frequency increases, current tends to concentrate nearer the surface of the conductor. At power frequencies, the effect is modest but still relevant for larger conductors.

$${\gamma }_s=\frac{X_s^4}{192+0.8X_s^4}$$ $$X_s^2=\frac{8\pi f}{R}{10}^{–7}{k}_s$$

Proximity effect

The proximity effect occurs because nearby conductors distort the magnetic field and current distribution. The proximity factor depends on conductor spacing and cable construction.

For two-core cables or two single-core cables:

$${\gamma }_p=\frac{X_p^4}{192+0.8X_p^4}{\left(\frac{d_c}{s}\right)}^2\times 2.9$$

For three-core cables or three single-core cables:

$${\gamma }_p=\frac{X_p^4}{192+0.8X_p^4}{\left(\frac{d_c}{s}\right)}^2\left[0.312{\left(\frac{d_c}{s}\right)}^2+\frac{1.18}{\frac{X_p^4}{192+0.8X_p^4}+0.27}\right]$$

For both cases:

$$X_p^2=\frac{8\pi f}{R}{10}^{–7}{k}_p$$

• For three single-core cables with uneven spacing, use an appropriate geometric mean spacing.
• For shaped conductors, γ_p is two-thirds of the value calculated above.
• For shaped conductors, d_c is the diameter of the equivalent circular conductor with the same cross-sectional area, and s may be taken as d_x + t, where t is the insulation thickness between conductors.

For spacing concepts, see Geometric Mean Distance.

Skin and proximity coefficients

Material	Conductor form	ks	kp
Copper	Round stranded or solid	1	1
Copper	Round segmental	0.435	0.37
Copper	Sector-shaped	1	1
Aluminium	Round stranded or solid	1	1
Aluminium	Round 4 segment	0.28	0.37
Aluminium	Round 5 segment	0.19	0.37
Aluminium	Round 6 segment	0.12	0.37

Temperature adjustment

Conductor resistance increases with temperature. The resistance at temperature t can be estimated from:

$$R_t=R_{20}\left[1+{\alpha }_{20}\left(t–20\right)\right]$$

Rt	Resistance of conductor at temperature t
R20	Resistance of conductor at 20 °C
t	Conductor temperature, °C
α20	Temperature coefficient of resistance at 20 °C

Cable operating temperature

At zero current, the conductor temperature is approximately the ambient temperature. At the maximum sustained current rating, the conductor reaches the insulation limiting temperature. Between these points, the operating temperature can be estimated as:

$$t={\left(\frac{I_b}{I_z}\right)}^2\times \left(T_c–T_a\right)+T_a$$

Ib	Cable design current, A
Iz	Sustained current rating of cable, A
Ta	Ambient temperature, °C
Tc	Conductor or insulation limiting temperature, °C

For related calculations, see Cable Thermal Analysis and Estimating Cable Life.

For the material property behind conductor resistance, see Electrical Resistivity.

For background on the basic resistance formula and temperature coefficient, see Electrical Resistance.