Question:

Please convert the below content to rendered equations without any errors.This is a **NEC box-fill calculation** problem. We’ll solve it clearly step-by-step using **NEC 314.16** rules. --- ## ? Step 1: Determine Box Volume Box size: * **4 11/16 in × 4 11/16 in** * Depth = **2 1/8 in** From NEC box tables: A **4-11/16" square box, 2-1/8" deep** has a volume of: [ \boxed{42.0 \text{ cubic inches}} ] --- ## ? Step 2: Conductor Volume Allowance All conductors are **12 AWG THHN copper**. From NEC Table 314.16(B): [ \boxed{12 \text{ AWG = 2.25 cubic inches per conductor}} ] --- ## ? Step 3: Count Existing Conductor Equivalents Now we count everything inside the box according to NEC rules. ### (A) Current-Carrying Conductors Given: * 2 black * 2 white * 2 grounding conductors ⚠ Important: * Equipment grounding conductors together count as **only ONE conductor** * So 2 grounds = 1 conductor equivalent So: [ 2 + 2 + 1 = 5 \text{ conductor equivalents} ] --- ### (B) Internal Cable Clamps There are **two internal cable clamps** Internal clamps count as **one conductor equivalent total** So add: [ +1 ] Now total = **6** --- ### (C) Devices (Receptacles) There are **two receptacles** Each yoke-mounted device counts as **two conductor equivalents** So: [ 2 \text{ receptacles} \times 2 = 4 ] Add: [ 6 + 4 = 10 ] --- ### (D) Equipment Bonding Jumper The bonding jumper does **NOT** count separately (It is considered part of grounding conductors) So no additional count. --- ## ? Step 4: Total Volume Used Total conductor equivalents = **10** Each is 2.25 cubic inches: [ 10 \times 2.25 = 22.5 \text{ cubic inches used} ] --- ## ? Step 5: Remaining Volume [ 42.0 - 22.5 = 19.5 \text{ cubic inches remaining} ] --- ## ? Step 6: How Many More 12 AWG Conductors? Each new conductor needs: [ 2.25 \text{ cubic inches} ] [ \frac{19.5}{2.25} = 8.66 ] We must round **down** (cannot exceed box volume). [ \boxed{8 \text{ additional 12 AWG conductors}} ] --- # ✅ Final Answer: [ \boxed{8 \text{ more 12 AWG THHN copper conductors can be added}} ] --- If you'd like, I can also show you a shortcut method to solve these box-fill problems in under 2 minutes for exams.