Installation design
Voltage drop with resistance and reactance
- where
- voltage drop (V)
- current (A)
- one-way length (m)
- resistance per conductor (Ω/km)
- power factor
- reactance per conductor (Ω/km)
Explain this equation
Gives the voltage drop on a single-phase circuit from the cable's resistance and reactance, rather than a tabulated mV/A/m value. Use it for larger cables, where reactance matters, or with manufacturer data.
I is the current in amperes and L the one-way length in metres. r and x are the resistance and reactance of one conductor in ohms per kilometre. cos φ is the load power factor and sin φ the matching reactive fraction. The 2 accounts for the outgoing and return conductors.
The load current is partly in step with the voltage and partly lagging. The in-step part drops voltage mainly across r and the lagging part across x, hence the cos φ and sin φ weighting. The 1000 converts L in metres to kilometres to match the Ω/km values.
10 A over 100 m with r = 1 and x = 0.1 Ω/km at PF 0.8 gives about 1.72 V. At PF 0.8, sin φ is 0.6. At unity power factor the reactance term drops out.
Watch out: r must be the value at conductor operating temperature. For a balanced three-phase circuit, replace the 2 with √3 to get the line-to-line drop. This is an approximation for lagging loads.
For a single-phase two-wire circuit, both conductors contribute impedance. Resolve resistance and reactance using the load power factor, then multiply by twice the one-way length and current.
With cos φ = 0.8, sin φ = 0.6 for a lagging load. A balanced three-phase circuit uses √3 instead of 2 and gives line-to-line drop.
Enter your values to see the result.
Common mistake
Adding r and x directly without the power-factor terms.
Limits
Steady sinusoidal lagging-load approximation; r must match conductor temperature. Do not combine per-metre data with kilometres.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.