---
title: Voltage Drop
tags:
  - topic/construction/electrical
  - type/encyclopedia-entry
---
# Voltage Drop

> [!info] Ohm's Law
>
> $$
> V = I \times R, \quad R = \frac{V}{I}, \quad I = \frac{V}{R}
> $$

## Step 1: Effective Impedance $Z$

The formula for effective impedance $Z$ is given by

$$
Z = R \cos(\theta) + X \sin(\theta)
$$

where
* $R$ = AC resistance
* $X$ = Reactance
* $\theta$ = Power factor angle = $\arccos(\text{PF})$

### Parallel Runs

The equivalent resistance of parallel resistances is given by

$$
\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_n}
$$

For $n$ parallel resistances of value $R$

$$
\begin{align*}
\frac{1}{R_{\text{eq}}} &= n \times \left(\frac{1}{R}\right) \\
&= \frac{n}{R} \\
R_{\text{eq}} &= \frac{R}{n}
\end{align*}
$$

## Step 2: Voltage Drop

> [!important]
> This section assumes a 3-phase
> 208Y/120V or 480Y/277V voltage system

> [!info] 3-Phase Voltage
>
> $$
> V_{L} = \sqrt{3} \times V_{P}, \quad V_{P} = \frac{V_{L}}{\sqrt{3}}
> $$

3% allowable voltage drop for a 120V line-to-neutral load:

$$
\text{Max}\ \Delta V = 0.03 \times 120 \text{V}_{P} = 3.60 \text{V}_{P}
$$

3% allowable voltage drop for a 208V line-to-line load:

$$
\text{Max}\ \Delta V = 0.03 \times 208 \text{V}_{L} = 6.24 \text{V}_{L}
$$

### Line to Neutral Loads

$$
\Delta V_{P} = I \times Z \times 2L
$$

### Line to Line Loads

$$
\Delta V_{L} = I \times Z \times 2L
$$

### 3-Phase Loads

$$
\Delta V_{3\phi} = \sqrt{3} ( I \times Z \times L )
$$

where
* $\Delta V$ = Voltage drop in volts (V)
* $I$ = Current in amperes (A)
* $Z$ = Effective impedance in ohms
* $L$ = Length of wire one way in feet ($\text{ft}$)

> [!important]
> "Current" is not the OCPD rating,
> but the actual load.

***

When exact length is unknown,
it is often most useful to calculate the maximum length
a certain wiring configuration is suitable for.

$$
L = \frac{ \Delta V }{ I \times M } \times \frac{1}{Z}
$$

where
* $M$ is the "phase multiplier" (2 for single phase, $\sqrt{3}$ for 3-phase)
* $Z$ is the linear resistance of the wiring configuration

***

When exact length is known,
it is often most useful to calculate the linear resistance
that will result in a specified voltage drop,
the maximum linear resistance for a specific feeder.

$$
Z = \frac{ \Delta V }{ I \times M \times L }
$$
