The permissible current rating of a power cable can be derived from the expression for the temperature rise above ambient temperature.

The equation is different for cables in air and buried cables.

The current rating for a four-core low-voltage cable may be taken to be equal to the current rating of a three-core cable for the same voltage and conductor size having the same construction, provided that the cable is to be used in a three-phase system where the fourth conductor is either a neutral conductor or a protective conductor. When it is a neutral conductor, the current rating applies to a balanced load.

Where it is desired that moisture migration be avoided by limiting the temperature rise of the cable surface to not more than $Δθ_x$, the corresponding rating shall be obtained from the equation below.However, depending on the value of $Δθ_x$ this may result in a conductor temperature which exceeds the maximum permissible value. The current rating used shall be the lower of the two values obtained.

For transient calculations, $I_c$ is the constant steady-state current applied to cable prior to application of a step function, cyclic rating or to emergency loading.

Symbol
$I_{\mathrm{c}}$
Unit
A
Formulae
$\sqrt{\frac{- \Delta \theta_{\mathrm{d}} - \Delta \theta_{\mathrm{sun}} - \theta_{\mathrm{a}} + \theta_{\mathrm{c}}}{R \left(T_{\mathrm{1}} + T_{\mathrm{2}} n_{\mathrm{c}} \left(\lambda_{\mathrm{1}} + 1\right) + \left(T_{\mathrm{3}} n_{\mathrm{c}} + n_{\mathrm{cc}} \left(T_{\mathrm{4i}} + T_{\mathrm{4ii}} + T_{\mathrm{4iii}}\right)\right) \left(\lambda_{\mathrm{1}} + \lambda_{\mathrm{2}} + 1\right)\right)}}$cables in air
$\sqrt{\frac{- \Delta \theta_{\mathrm{d}} - \Delta \theta_{\mathrm{p}} + \Delta \theta_{\mathrm{x}} \left(v_{\mathrm{4}} - 1\right) - \theta_{\mathrm{a}} + \theta_{\mathrm{c}}}{R \left(T_{\mathrm{1}} + T_{\mathrm{2}} n_{\mathrm{c}} \left(\lambda_{\mathrm{1}} + 1\right) + \left(T_{\mathrm{3}} n_{\mathrm{c}} + n_{\mathrm{cc}} \left(T_{\mathrm{4i}} + T_{\mathrm{4ii}} + T_{\mathrm{4\mu}} v_{\mathrm{4}}\right)\right) \left(\lambda_{\mathrm{1}} + \lambda_{\mathrm{2}} + 1\right)\right)}}$cables buried
$\sqrt{\frac{\Delta \theta_{\mathrm{x}} - W_{\mathrm{d}} n_{\mathrm{cc}} \left(T_{\mathrm{4i}} + T_{\mathrm{4ii}} + T_{\mathrm{4iii}}\right)}{R n_{\mathrm{cc}} \left(T_{\mathrm{4i}} + T_{\mathrm{4ii}} + T_{\mathrm{4iii}}\right)}}$cables buried where drying-out of soil is avoided
$\sqrt{\frac{- \Delta \theta_{\mathrm{d}} + \theta_{\mathrm{c}} - \theta_{\mathrm{de}}}{R \left(T_{\mathrm{1}} + T_{\mathrm{2}} n_{\mathrm{c}} \left(\lambda_{\mathrm{1}} + 1\right) + \left(T_{\mathrm{3}} n_{\mathrm{c}} + n_{\mathrm{cc}} \left(T_{\mathrm{4i}} + T_{\mathrm{4ii}}\right)\right) \left(\lambda_{\mathrm{1}} + \lambda_{\mathrm{2}} + \lambda_{\mathrm{3}} + 1\right)\right)}}$cables in tunnel
$\sqrt{\frac{- \Delta \theta_{\mathrm{0t}} - \Delta \theta_{\mathrm{d}} - \theta_{\mathrm{a}} + \theta_{\mathrm{cmax}}}{R \left(T_{\mathrm{1}} + T_{\mathrm{2}} n_{\mathrm{c}} \left(\lambda_{\mathrm{1}} + 1\right) + n_{\mathrm{c}} \left(T_{\mathrm{3}} + T_{\mathrm{4t}}\right) \left(\lambda_{\mathrm{1}} + \lambda_{\mathrm{2}} + \lambda_{\mathrm{3}} + 1\right)\right)}}$cables in tunnel (IEC 60287-2-3)
$\sqrt{\frac{- \Delta \theta_{\mathrm{d}} - \theta_{\mathrm{at}} + \theta_{\mathrm{c}}}{R \left(T_{\mathrm{1}} + T_{\mathrm{2}} n_{\mathrm{c}} \left(\lambda_{\mathrm{1}} + 1\right) + \left(T_{\mathrm{3}} n_{\mathrm{c}} + n_{\mathrm{cc}} \left(T_{\mathrm{4i}} + T_{\mathrm{4ii}} + T_{\mathrm{4iii}}\right)\right) \left(\lambda_{\mathrm{1}} + \lambda_{\mathrm{2}} + 1\right)\right)}}$cables in trough
$\sqrt{\frac{- \Delta \theta_{\mathrm{d}} - \theta_{\mathrm{air}} + \theta_{\mathrm{c}}}{R \left(T_{\mathrm{1}} + T_{\mathrm{2}} n_{\mathrm{c}} \left(\lambda_{\mathrm{1}} + 1\right) + \left(T_{\mathrm{3}} n_{\mathrm{c}} + n_{\mathrm{cc}} \left(T_{\mathrm{4i}} + T_{\mathrm{4ii}} + T_{\mathrm{4iii}}\right)\right) \left(\lambda_{\mathrm{1}} + \lambda_{\mathrm{2}} + 1\right)\right)}}$cables in trough (Anders et al 2010)
$DF_{\mathrm{X}} I_{\mathrm{c}}$cables crossing external heat sources
Related
$\Delta \theta_{\mathrm{0t}}$
$\Delta \theta_{\mathrm{d}}$
$\Delta \theta_{\mathrm{p}}$
$\Delta \theta_{\mathrm{sun}}$
$\Delta \theta_{\mathrm{x}}$
$\lambda_{\mathrm{1}}$
$\lambda_{\mathrm{2}}$
$\lambda_{\mathrm{3}}$
$n_{\mathrm{c}}$
$n_{\mathrm{cc}}$
$T_{\mathrm{3}}$
$T_{\mathrm{4ii}}$
$T_{\mathrm{4\mu}}$
$\theta_{\mathrm{a}}$
$\theta_{\mathrm{air}}$
$\theta_{\mathrm{at}}$
$\theta_{\mathrm{c}}$
$\theta_{\mathrm{cmax}}$
$\theta_{\mathrm{de}}$
$W_{\mathrm{d}}$
Used in
$\Delta W_{\mathrm{0}}$
$I_{\mathrm{c_{\mathrm{peak}}}}$
$I_{\mathrm{EMF}}$
$L_{\mathrm{crit}}$
$W_{\mathrm{c}}$
$W_{\mathrm{encl}}$
$W_{\mathrm{sA_{\mathrm{1}}}}$
$W_{\mathrm{sA_{\mathrm{2}}}}$