# Voltage Drop

Voltage drop is calculated in accordance with CENELEC technical report CLC/TR 50480 "Determination of cross-sectional area of conductors and selection of protective devices", dated February 2011.

The voltage drop (as a percentage) is given by:

$ΔU= b( Rcosφ+Xsinφ ) I b U o ⋅100$

where
ΔU         = cable voltage drop, %
Uo             = nominal  line to neutral voltage, V
R           = cable resistance, Ω
X           = cable reactance, Ω
Ib           = cable design current, A
b            = circuit factor (=2 for d.c. and single phase, =1 for three phase)

Note: within myCableEngineering, we use complex arithmetic and the above is evaluated as:

$ΔU= b( R+jX ) I b U o ⋅100$

Note: R and X are per line conductor.  For example, the resistance of a single phase two core circuit (live and neutral) would be 2R (assuming the live and neutral circuits are of equal resistance).  For parallel cables, R and X are the per line resultant values. For example, nph cables in parallel, with the resistance of one line conductor is Rc0ph then the R = Rc0ph/nph.

myCableEngineering - for a.c. systems, the absolute voltage drop is related to the line-neutral voltage for single phase and line-line voltage for three-phase (by multiplying the above by √3).

### BS 7671  Voltage Drop Tables

BS7671 "Requirements for Electrical Installations", the IET Wiring Regulations, appendix 4 voltage drop tables, values are given in mV/A/m (or effectively mΩ).  However, these tables are related to the line to neutral voltage for single phase circuits and line to line voltage for three phase circuits.

To convert the three-phase table values so that they relate to the input resistance (or reactance) required by CENELEC 50480 it is necessary to divide the BS 7671 three phase values by √3 (the square root of three).  No adjustment is required for single phase values.  Given values of voltage drop for three-phase balanced systems are related to the line voltage.

Note: the values in the tables are given at the maximum conductor operating temperature.  myCableEngineering uses circuit theory (see Impedance) to calculate impedance and voltage drops are calculated using CENELEC 50480.  Our testing shows that the difference in resistance calculation by circuit theory and that given in BS 7671 is small.