vault backup: 2025-10-08 18:16:15

conductor-sizing.md

@@ -116,28 +116,45 @@ either for spec requirements or conduit fill considerations.
 ## Voltage Drop
 
 $$
-V_d = I \times R \times L \times M
+Z = R \cos(\theta) + X \sin(\theta)
 $$
 
 where
-* $V_d$ = Voltage Drop in volts ($V$)
-* $I$ = Current in Amperes ($A$)
-* $R$ = Feeder linear resistance in ohms per foot ($VA^{-1}\text{ft}^{-1}$)
+* $Z$ = Effective impedance
+* $R$ = AC resistance
+* $X$ = Reactance
+* $\theta$ = Power factor angle = $\arccos(PF)$
+
+> [!info] 1-Phase, Line to Neutral Voltage Drop
+>
+> $$
+> \Delta V_{LN} = I \times Z \times 2L
+> $$
+
+> [!info] 1-Phase, Line to Line Voltage Drop
+>
+> $$
+> \Delta V_{LL} = \sqrt{3} \times I \times Z \times 2L
+> $$
+
+> [!info] 3-Phase Voltage Drop
+>
+> $$
+> \Delta V_{3\phi} = \sqrt{3} \times I \times Z \times L
+> $$
+
+where
+* $\Delta V$ = Voltage drop in volts ($V$)
+* $I$ = Current in amperes ($A$)
 * $L$ = Length of wire one way in feet ($\text{ft}$)
-* $M$ = Multiplier
-  * $2$ for 1-phase
-  * $\sqrt{3}$ for 3-phase
 
 It is often more useful to know the maximum length
 a certain wiring configuration is suitable for.
 
 $$
-L = \frac{ V_d }{ I \times M } \times \frac{1}{R}
+L = \frac{ \Delta V }{ I \times M } \times \frac{1}{Z}
 $$
 
-* $L$ = Max length of wire one way in feet ($\text{ft}$)
-* $\frac{ V_d }{ I \times M }$ = Max circuit resistance in ohms ($VA^{-1}$)
-
 > [!info] Ohm's Law
 >
 > $$
@@ -148,6 +165,24 @@ $$
 > "Current" is not the OCPD rating,
 > but the actual load.
 
+## Parallel Runs
+
+The equivalent resistance of parallel resistances is given by
+
+$$
+\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots
+$$
+
+For $P$ parallel resistances of value $R$
+
+$$
+\begin{align*}
+\frac{1}{R_{\text{eq}}} &= P \times \left(\frac{1}{R}\right) \\
+                        &= \frac{P}{R} \\
+          R_{\text{eq}} &= \frac{R}{P}
+\end{align*}
+$$
+
 ## Transformers
 
 $$
@@ -159,21 +194,14 @@ $$
 * $V$ = feeder voltage
 * $E$ = efficiency
 
-## Parallel Runs
+## Motors
+
+1 electric horsepower = 746 watts
+
+full-load current (FLC) / full-load amperes (FLA)
+
+minimum circuit ampacity (MCA)
 
 $$
-\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots
+\text{MCA} = 1.25 \times \text{FLC}
 $$
-
-where $R_1 = R_n$:
-
-$$
-\begin{align*}
-\frac{1}{R_{\text{eq}}} &= P \times \left(\frac{1}{R_1}\right) \\
-                        &= \frac{P}{R_1} \\
-          R_{\text{eq}} &= \frac{R_1}{P}
-\end{align*}
-$$
-
-where
-* $P$ = Number of parallel runs