vault backup: 2025-10-07 16:32:57

conductor-sizing.md

@@ -9,14 +9,18 @@ tags:
 ---
 # Conductor Sizing
 
+Conductors are sized to be suitable for the load,
+overcurrent protection is sized to protect the conductors.
+
 ## "The 80% Rule"
 
 "The 80% Rule" is a rule of thumb
 referring to a common convention of several articles
 including:
 
-- [[nfpa-70_article-210_branch-circuits#210.19(A)(1) General.]]
-- [[nfpa-70_article-215_feeders#215.2(A)(1) General.]]
+* [[nfpa-70_210_branch-circuits#210.19(A)(1) General.]]
+* [[nfpa-70_215_feeders#215.2(A)(1) General.]]
+* [[nfpa-70_430_motors#430.22 Single Motor.]]
 
 which paraphrased states:
 
@@ -45,17 +49,26 @@ $$
 $$
 
 but the 180VA per yoke load specified in
-[[nfpa-70_article-220_load-calculations#220.14(I) Receptacle Outlets.|220.14(I)]]
+[[nfpa-70_220_load-calculations#220.14(I) Receptacle Outlets.|220.14(I)]]
 is specifically for calculating service and feeder sizing.
 
-Per [[nfpa-70_article-210_branch-circuits#210.19(A)(1) General.|210.19(A)(1)]]
+Per [[nfpa-70_210_branch-circuits#210.19(A)(1) General.|210.19(A)(1)]]
 a receptacle branch circuit's load
 is the load of the equipment intended to be served by it.
 
+Where general-use receptacles are provided
+without specific equipment in mind,
+circuits will be engineered at the minimum load.
+If a receptacle circuit's load is a whole multiple of 180VA
+there's a good chance that's the number of devices,
+or at least was at some point in the design.
+
 ## Feeders
 
-> [!cite] 250.122 Size of Equipment Grounding Conductors
-> **(A) General.** Copper, aluminum, or copper-clad aluminum
+> [!cite] NEC Article 250 (emphasis added)
+> ### 250.122 Size of Equipment Grounding Conductors
+> #### (A) General.
+> Copper, aluminum, or copper-clad aluminum
 > equipment grounding conductors of the wire type
 > shall not be smaller than shown in Table 250.122,
 > but in no case shall they be required to be larger
@@ -73,8 +86,10 @@ are in contradiction to this idea.
 
 Given a minimum ampacity, find all valid configurations.
 
-> [!cite] 310.10(H) Conductors in Parallel.
-> **(1) General.** Aluminum, copper-clad aluminum, or copper conductors,
+> [!cite] NEC Article 310 (emphasis added)
+> #### 310.10(H) Conductors in Parallel.
+> ##### (1) General.
+> Aluminum, copper-clad aluminum, or copper conductors,
 > for each phase, polarity, neutral, or grounded circuit
 > shall be permitted to be connected in parallel
 > (electrically joined at both ends)
@@ -101,31 +116,64 @@ either for spec requirements or conduit fill considerations.
 ## Voltage Drop
 
 $$
-V_d = \frac{ I \times R \times L \times M }{ P }
+V_d = I \times R \times L \times M
 $$
 
 where
-- $V_d$ = Voltage Drop in volts ($V$)
-- $I$ = Current in Amperes ($A$)
-- $R$ = Linear resistance in ohms per foot ($\Omega\text{ft}^{-1}$)
-- $L$ = Length of wire one way in feet ($\text{ft}$)
-- $M$ = Multiplier
-  - $2$ for 1-phase
-  - $\sqrt{3}$ for 3-phase
-- $P$ = Number of parallel runs
+* $V_d$ = Voltage Drop in volts ($V$)
+* $I$ = Current in Amperes ($A$)
+* $R$ = Feeder linear resistance in ohms per foot ($VA^{-1}\text{ft}^{-1}$)
+* $L$ = 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.
 
 $$
-L = \frac{ V_d }{ I \times M } \times \frac{ P }{ R }
+L = \frac{ V_d }{ I \times M } \times \frac{1}{R}
 $$
 
-- $L$ = Max length of wire one way in feet ($\text{ft}$)
-- $\frac{ V_d }{ I \times M }$ = Max circuit resistance in ohms ($\Omega$)
-- $\frac{ P }{ R }$ = ??? in feet per ohm ($\text{ft}\Omega^{-1}$)
+* $L$ = 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
+>
 > $$
 > V = I \times R, \quad R = \frac{ V }{ I }, \quad I = \frac{ V }{ R }
 > $$
+
+> [!important]
+> "Current" is not the OCPD rating,
+> but the actual load.
+
+## Transformers
+
+$$
+I = \frac{S}{ \sqrt{3} \times V \times E }
+$$
+
+* $I$ = nameplate current rating
+* $S$ = nameplate kVA rating
+* $V$ = feeder voltage
+* $E$ = efficiency
+
+## Parallel Runs
+
+$$
+\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots
+$$
+
+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