APPENDIX	B
Formulas for electrical principles

Advanced Principles Formulas

  1.  Trigonometry

c² = a² + b²

•  $\text{Transpose}\text{for}\text{c}=\sqrt{a^2+b^2}$

•  $\text{Transpose}\text{for}\text{a}=\sqrt{c^2-b^2}$

•  $\text{Transpose}\text{for}\text{b}=\sqrt{c^2-a^2}$

  2.  Ohms Law

V = I × R,

•  $\text{Transpose}\text{for}\text{I\hspace{0.17em}}=\frac{\text{V}}{\text{R}}$

•  $\text{Transpose}\text{for}\text{R\hspace{0.17em}}=\frac{\text{V}}{\text{I}}$

  3.  Power = Voltage (V) × I (current)

•  $\text{Transpose}\text{for}\text{I\hspace{0.17em}}=\frac{\text{P}}{\text{V}}$

•  $\text{Transpose}\text{for}\text{V}=\frac{\text{P}}{\text{I}}$

  4.  Power = I² × R

•  $\text{Transpose}{\text{for I}}^2=\frac{\text{Power}}{{\text{R}}^2}$

•  $\text{Transpose}\text{for R}=\frac{\text{Power}}{{\text{I}}^2}$

  5.  $Power=\frac{{\text{V}}^2}{\text{R}}$

•  Transpose for V² = P × R

•  $\text{Transpose}\text{for}\text{R\hspace{0.17em}}=\frac{{\text{V}}^2}{\text{R}}$

  6.  $Resistorinseries\text{Rt}=\text{R}1+\text{R}2+\text{R}3$

•  $\text{Transpose}\text{for}\text{R1}=\text{Rt}-\text{R}2-\text{R}3$

  7.  $Resistorsinparallel\frac{\text{1}}{\text{Rt}}=\frac{1}{\text{R1}}+\frac{1}{\text{R2}}+\frac{1}{\text{R3}}$

•  $\text{Transpose}\text{for}\frac{\text{I}}{\text{R3}}=\frac{1}{\text{Rt}}-\frac{1}{\text{R}2}-\frac{1}{\text{R3}}$

  8.  Left Hand Rule for motors

Force = β (Flux Density) x I (Current) x L (length of conductor)

F = β I L

•  $\text{Transpose}\text{for}\text{I\hspace{0.17em}}=\frac{\text{F}}{\text{β}\text{L}}$

•  $\text{Transpose}\text{for}\text{L}=\frac{\text{F}}{\text{β}\text{I}}$

•  $\text{Transpose}\text{for}\text{β}=\frac{\text{F}}{\text{I L}}$

  9.  Right Hand Rule for Generators

e (electro motive force) = β (Flux Density) x L (length of conductor) x V(Velocity)

e = β L V

•  $\text{Transpose}\text{for}\text{L}=\frac{\text{e}}{\text{β}\text{V}}$

•  $\text{Transpose}\text{for}\text{V}=\frac{\text{e}}{\text{β}\text{L}}$

•  $\text{Transpose}\text{for}\text{β}=\frac{\text{e}}{\text{L}\text{V}}$

10.  Phase Systems

Star: VL = $\surd$3 VP

•  $\text{Transpose}\text{for}VP=\frac{VL}{\surd 3}$

Star IL = IP

Delta: IL = $\surd$3 IP

•  $\text{Transpose}\text{for}\text{I}P=\frac{IL}{\surd 3}$

11.  Single Phase Power Factor:

$\text{Power}(\text{P})=\text{V}\times \text{I}\times \text{Cos}(\text{PF})$

•  $\text{Transpose}\text{for}\text{V}=\frac{\text{P}}{\text{I}\times \text{Cos}(\text{pf})}$

•  $\text{Transpose}\text{for}\text{I\hspace{0.17em}}=\frac{\text{P}}{\text{V}\times \text{Cos}(\text{pf})}$

12.  Three Phase Power Factor (V=400V):

•  $\text{Power}(\text{P})=\surd 3\times \text{V}\times \text{I}\times \text{Cos}(\text{PF})$

•  $\text{Transpose}\text{for}\text{I\hspace{0.17em}}=\frac{\text{P}}{\surd 3\times \text{V}\times \text{Cos}(\text{PF})}$

•  $\text{Transpose}\text{for}\text{V}=\frac{\text{P}}{\surd 3\times \text{I}\times \text{Cos}(\text{PF})}$

13.  XL Inductive Reactance= 2 π F (frequency) L (inductance in Henrys) XL = 2 π F L

•  $\text{Transpose}\text{for}\text{F}=\frac{\text{XL}}{2\text{π}\text{L}}$

•  $\text{Transpose}\text{for}\text{L}=\frac{\text{XL}}{2\text{π}\text{F}}$

14.  $\text{XC}\text{Capacitive}\text{Reactance}=\frac{1}{2\text{π}\text{F}\text{C}}$

•  $\text{Transpose}\text{for}\text{C}=\frac{1}{2\text{π}\text{F}\text{XC}}$

•  $\text{Transpose}\text{for}\text{F}=\frac{1}{2\text{π}\text{C}\text{XC}}$

15.  $\begin{array}{cc}\text{Impedance}\text{Z}=\sqrt{{\text{R}}^2+{\text{XI}}^2}& (\text{Resistance}\text{\&}\text{XL}\text{only})\end{array}$

16.  $\begin{array}{cc}\text{Impedance}\text{Z}=\sqrt{{\text{R}}^2+{\text{XC}}^2}& (\text{Resistance}\text{\&}\text{XC}\text{only})\end{array}$

17.  $\begin{array}{cc}\text{Impedance}\text{Z}=\sqrt{{\text{R}}^2+{(\text{XC}-\text{XL})}^2}& (\text{Resistance,}\text{XC}\&\text{XL})\end{array}$

18.  Extracting power factor (pf) from Impedance Triangle $\text{Pf}=\frac{\text{R}}{\text{Z}}$

•  $\text{Transpose}\text{for}\text{R\hspace{0.17em}}=\text{pf}\text{XZ}$

•  $\text{Transpose}\text{for}\text{Z}=\frac{\text{R}}{\text{pf}}$

19.  Extracting power factor (pf) from power Triangle: $\text{pf}=\frac{\text{Real}\text{Power}}{\text{Apparent}\text{power}}$

•  $\text{Transpose}\text{for}\text{Real}\text{Power}=\text{pf}\times \text{Apparent}\text{power}$

•  $\text{Transpose}\text{for}\text{Apparent}\text{power}=\frac{\text{Real}\text{Power}}{\text{Pf}}$

20.  $\text{Inverse}\text{square}\text{law}=\frac{\text{Light}\text{Intensity}}{{\text{d}}^{\text{2}}}$

21.  $\text{Cosine}\text{law}=\frac{\text{Light}\text{Intensity}\text{×}\text{cos}}{{\text{d}}^{\text{2}}}$

3 rules of Transposition

+ (positive) - (negative)

X (multiply-Top) and (Divide-bottom)/

X² (Raise to a power) and $\surd$ (Square root)