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Annex 1 (BE01) Consolidated Reference • Quick-lookup tables, mathematical formulas, circuit laws, and fault diagnostic matrices covering BE.01.02 through BE.01.09.

Annex 1 Formula & Reference Sheet

1. Engineering Notation, `LARS` & Rounding Rules (`BE.01.03`)

Scientific Notation: $1 \le \text{Coefficient} < 10$ with any integer power $10^n$ .
Engineering Notation: $1 \le \text{Coefficient} < 1{,}000$ with powers of ten in multiples of $3$ ( $10^{\pm 3n}$ ).
LARS Rule: Moving decimal Left $\rightarrow$ Add to exponent; moving decimal Right $\rightarrow$ Subtract from exponent.
Rounding Rule: Round only the final answer to two decimal places ( $0.01$ ). Never round intermediate steps.

Prefix	Tera ( $\text{T}$ )	Giga ( $\text{G}$ )	Mega ( $\text{M}$ )	Kilo ( $\text{k}$ )	Base Unit	Milli ( $\text{m}$ )	Micro ( $\mu$ )	Nano ( $\text{n}$ )	Pico ( $\text{p}$ )
Power of $10$	$10^{12}$	$10^{9}$	$10^{6}$	$10^{3}$	$10^{0}$	$10^{-3}$	$10^{-6}$	$10^{-9}$	$10^{-12}$

2. EIA 4-Band Resistor Color Code (`BE.01.03`)

Color	Band 1 (1st Digit)	Band 2 (2nd Digit)	Band 3 (Multiplier)	Band 4 (Tolerance)
Black	—	$0$	$\times 1$ ( $10^0$ )	—
Brown	$1$	$1$	$\times 10$ ( $10^1$ )	—
Red	$2$	$2$	$\times 100$ ( $10^2$ )	—
Orange	$3$	$3$	$\times 1{,}000$ ( $10^3$ )	—
Yellow	$4$	$4$	$\times 10{,}000$ ( $10^4$ )	—
Green	$5$	$5$	$\times 100{,}000$ ( $10^5$ )	—
Blue	$6$	$6$	$\times 1{,}000{,}000$ ( $10^6$ )	—
Violet	$7$	$7$	$\times 10{,}000{,}000$ ( $10^7$ )	—
Gray	$8$	$8$	$\times 100{,}000{,}000$ ( $10^8$ )	—
White	$9$	$9$	$\times 1{,}000{,}000{,}000$ ( $10^9$ )	—
Gold	—	—	$\times 0.1$ ( $10^{-1}$ )	$\pm 5%$
Silver	—	—	$\times 0.01$ ( $10^{-2}$ )	$\pm 10%$
None	—	—	—	$\pm 20%$

\text{Tolerance Value} = R_{\text{nominal}} \times \text{Tolerance \%} \qquad\implies\qquad \text{Range} = R_{\text{nominal}} \pm \text{Tolerance Value}

3. Core DC Formulas: Ohm’s Law & Watt’s Law (`BE.01.03` – `BE.01.08`)

Solve For	Primary Ohm’s Law Formula	Primary Power (Watt’s Law) Formula	Substituted Formula
Voltage ( $E$ or $V$ , Volts)	$E = I \times R$	$E = \frac{P}{I}$	$E = \sqrt{P \times R}$
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"/>
Current ( $I$ , Amperes)	$I = \frac{E}{R}$	$I = \frac{P}{E}$	$I = \sqrt{\frac{P}{R}}$
c-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514
c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20
s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121
s209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081
l0 -0c4,-6.7,10,-10,18,-10 H400000
v40H1014.6
s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185
c-2,6,-10,9,-24,9
c-8,0,-12,-0.7,-12,-2z M1001 80
h400000v40h-400000z"/>
Resistance ( $R$ , Ohms $\Omega$ )	$R = \frac{E}{I}$	—	$R = \frac{E^2}{P} = \frac{P}{I^2}$
Power ( $P$ , Watts $\text{W}$ )	—	$P = I \times E$	$P = \frac{E^2}{R} \quad\text{or}\quad P = I^2 \times R$

Charge & Current Benchmark: $1,\text{Coulomb ©} = 6.25 \times 10^{18},\text{electrons}$ ; $1,\text{Ampere (A)} = 1,\text{C/s}$ ; $1,\text{Volt (V)} = 1,\text{J/C}$ .
Valence Shell Classification: Conductors $\le 3$ valence electrons • Semiconductors $= 4$ • Insulators $\ge 5$ .

4. Series vs. Parallel vs. Series-Parallel Circuit Laws (`BE.01.06` – `BE.01.08`)

Parameter	Series Circuit (`BE.01.06`) (Single Path)	Parallel Circuit (`BE.01.07`) (Multiple Branches)	Series-Parallel Circuit (`BE.01.08`) (6-Step Combination)
Current ( $I$ )	Common: $I_T = I_{R1} = I_{R2} = \dots = I_{RN}$	Additive (KCL): $I_T = I_{R1} + I_{R2} + \dots + I_{RN}$	Series sections carry $I_T$ ; parallel branches split $I_T$ via $I_x = \frac{V_{REQ}}{R_x}$
Voltage ( $E / V$ )	Additive (KVL): $V_A = V_{R1} + V_{R2} + \dots + V_{RN}$	Common: $V_A = V_{R1} = V_{R2} = \dots = V_{RN}$	$V_A = V_{R\text{-series}} + V_{REQ}$ ; parallel branches share common $V_{REQ}$
Resistance ( $R_T / R_{EQ}$ )	Additive ( $R_T > R_{\text{largest}}$ ): $R_T = R_1 + R_2 + \dots + R_N$	Always $< R_{\text{smallest}}$ : 1. Reciprocal: $R_{EQ} = \frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\dots}$ 2. Two-Branch: $R_{EQ} = \frac{R_1 \times R_2}{R_1 + R_2}$ 3. Equal-Value: $R_{EQ} = \frac{R}{#}$	Step 1: Reduce parallel banks to $R_{EQ}$ Step 2: Redraw & sum $R_T = R_{\text{series}} + R_{EQ}$
Power ( $P_T$ )	Always Additive: $P_T = P_{R1} + P_{R2} + \dots + P_{RN}$	Always Additive: $P_T = P_{R1} + P_{R2} + \dots + P_{RN}$	Always Additive: $P_T = P_{R1} + P_{R2} + \dots + P_{RN} = I_T \times V_A$
Divider Rule	Voltage Divider: $V_x \propto R_x$ ( $V_x = V_A \frac{R_x}{R_T}$ )	Current Divider: $I_x \propto \frac{1}{R_x}$ (smaller $R \rightarrow$ larger $I$ )	Loaded Voltage Divider: $R_L \ge 10 \times R_2$ prevents excessive $V_L$ droop

5. Safety, Power Sources, Switches & Variable Resistors Quick Reference

60 Hz Electrical Shock & ESD Benchmarks (`BE.01.02`)

Shock Thresholds: $1.1,\text{mA}$ (Perception) • $10.0,\text{mA}$ (Can’t Let Go, $120,\text{lb}$ ) • $16.0,\text{mA}$ (Can’t Let Go, $175,\text{lb}$ ) • $18.0,\text{mA}$ (Can’t Breathe / Chest Paralysis) • $65.0,\text{mA}$ (Heart Fibrillation).
Static Voltages: Carpet ( $1{,}500\text{–}35{,}000,\text{V}$ ) • Poly Bags ( $1{,}200\text{–}20{,}000,\text{V}$ ) • Vinyl Floor ( $250\text{–}12{,}000,\text{V}$ ) • Bench Worker ( $100\text{–}6{,}000,\text{V}$ ).
ESD Causes: Friction, Separation, Induction • ESD Controls: Grounding (conductors/body), Shielding (metalized bags), Ionization (insulators).

Battery Cells & Multi-Source Hookups (`BE.01.04`)

Primary (Non-Rechargeable Dry, any position): Carbon-Zinc ( $1.5,\text{V}$ ), Zinc Chloride ( $1.5,\text{V}$ ), Lithium ( $3.0,\text{V}$ ).
Secondary (Rechargeable Wet): NiCad ( $1.25,\text{V}$ , sealed/any position), Lead-Acid ( $2.0\text{–}2.2,\text{V}$ , vented/must stay upright).
Series-Aiding ( $+$ to $-$ ): $V_T = V_1 + V_2$ , $I_T$ common (lowest cell) • Series-Opposing ( $+$ to $+$ or $-$ to $-$ ): $V_T = |V_1 - V_2|$ • Parallel ( $+$ to $+$ and $-$ to $-$ ): $V_T$ common, $I_T = I_1 + I_2$ .

Switches & Variable Resistors (`BE.01.05` & `BE.01.09`)

Open Switch / Open Component: $R = \text{MAX}\ (\infty/\text{OL})$ , $I = \text{MIN}\ (0,\text{A})$ , $V_{\text{across open}} = \text{MAX}\ (V_A)$ .
Closed Switch / Shorted Component: $R = \text{MIN}\ (0,\Omega)$ , $I = \text{MAX}$ , $V_{\text{across short}} = \text{MIN}\ (0,\text{V})$ .
Tapers: Linear (S) $= 50%\ R$ at $50%$ rotation • Logarithmic (Z) $= 10%\ R$ at $50%$ rotation.
Rheostat ( $2$ leads, in series with $R_L$ , controls $I_L$ ): At $100%$ CW ( $R_{\text{max}}$ ) $\rightarrow R_T = \text{MAX}, I_L = \text{MIN}, V_L = \text{MIN}$ . At $0%$ CCW ( $R_{\text{min}}$ ) $\rightarrow R_T = \text{MIN}, I_L = \text{MAX}, V_L = \text{MAX}$ .
Potentiometer ( $3$ leads, across $R_L$ , controls $V_L$ ): At $100%$ CW $\rightarrow R_T = \text{MIN}, I_T = \text{MAX}, V_L = \text{MAX}$ . At $0%$ CCW (shorts $R_L$ ) $\rightarrow R_T = \text{MAX}, I_T = \text{MIN}, V_L = 0,\text{V (MIN)}$ .

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Annex 1 Formula & Reference Sheet

1. Engineering Notation, LARS & Rounding Rules (BE.01.03)

2. EIA 4-Band Resistor Color Code (BE.01.03)

3. Core DC Formulas: Ohm’s Law & Watt’s Law (BE.01.03 – BE.01.08)

4. Series vs. Parallel vs. Series-Parallel Circuit Laws (BE.01.06 – BE.01.08)

5. Safety, Power Sources, Switches & Variable Resistors Quick Reference

60 Hz Electrical Shock & ESD Benchmarks (BE.01.02)

Battery Cells & Multi-Source Hookups (BE.01.04)

Switches & Variable Resistors (BE.01.05 & BE.01.09)

1. Engineering Notation, `LARS` & Rounding Rules (`BE.01.03`)

2. EIA 4-Band Resistor Color Code (`BE.01.03`)

3. Core DC Formulas: Ohm’s Law & Watt’s Law (`BE.01.03` – `BE.01.08`)

4. Series vs. Parallel vs. Series-Parallel Circuit Laws (`BE.01.06` – `BE.01.08`)

60 Hz Electrical Shock & ESD Benchmarks (`BE.01.02`)

Battery Cells & Multi-Source Hookups (`BE.01.04`)

Switches & Variable Resistors (`BE.01.05` & `BE.01.09`)