Electrical Voltage Drop Calculation

Voltage drop is the decrease in electrical potential along the path of a current flowing in an electrical circuit. It is a critical factor in electrical design, as excessive voltage drop can cause equipment to malfunction or operate inefficiently. Standards (such as the NEC) typically recommend that the maximum voltage drop for both feeders and branch circuits not exceed 5% overall.

1. Core Concepts

All electrical conductors have some inherent resistance (and reactance in AC circuits). When current ($I$) flows through a conductor with impedance ($Z$), a voltage is developed across it according to Ohm's Law ($V = IZ$). This voltage is "lost" to the load.

Single-Phase AC or DC Circuits

For a simple single-phase AC or a DC circuit, the approximate voltage drop $V_d$ can be calculated using the resistance of the wire. A common practical formula is:

$V_d = \frac{2 \times K \times I \times L}{A}$

Where:

• $V_d$ = Voltage drop in volts.
• $K$ = Specific resistivity of the conductor material (often given in ohms-cmil/ft).
• $I$ = Current in amperes.
• $L$ = One-way length of the circuit (ft).
• $A$ = Cross-sectional area of the conductor in circular mils (cmil).
• The factor of 2 accounts for the current traveling out and back.

2. AC Circuits with Power Factor

In AC circuits, especially for larger conductors where inductive reactance becomes significant, both resistance ($R$) and reactance ($X$) must be considered, along with the load power factor ($\cos \theta$).

The approximate voltage drop formula for an AC circuit is:

$V_d = I(R \cos \theta + X \sin \theta)$

Where:

• $R$ is the effective AC resistance of the conductor.
• $X$ is the inductive reactance of the conductor.
• $\theta$ is the phase angle of the load.

3. Engineering Checks

• Code Compliance: Ensure the calculated voltage drop meets local electrical code requirements (e.g., max 3% for branch circuits, 5% total).
• Motor Starting: Consider the high inrush current of motors, which can cause severe temporary voltage drops (voltage sag).