vault backup: 2025-11-03 17:15:51

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+---
+id:
+aliases: []
+tags:
+  - authorship/original
+  - destiny/permanent
+  - status/incomplete
+  - topic/construction/electrical
+title: Voltage Drop
+---
+# Voltage Drop
+
+> [!info] Ohm's Law
+>
+> $$
+> V = I \times R, \quad R = \frac{V}{I}, \quad I = \frac{V}{R}
+> $$
+
+## Step 1: Effective Impedance $Z$
+
+$$
+Z = R \cos(\theta) + X \sin(\theta)
+$$
+
+where
+* $Z$ = Effective impedance
+* $R$ = AC resistance
+* $X$ = Reactance
+* $\theta$ = Power factor angle = $\arccos(PF)$
+
+### 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
+
+$$
+\Delta V_{3\phi} = \sqrt{3} \times \left( I \times Z \times L )
+$$
+
+where
+* $\Delta V$ = Voltage drop in volts ($V$)
+* $I$ = Current in amperes ($A$)
+* $L$ = Length of wire one way in feet ($\text{ft}$)
+
+> [!important]
+> "Current" is not the OCPD rating,
+> but the actual load.
+
+***
+
+It is often more useful to know the maximum length
+a certain wiring configuration is suitable for.
+
+$$
+L = \frac{ \Delta V }{ I \times M } \times \frac{1}{Z}
+$$