# Fundamental Physics/Electricity/Electric Formulas

## Electric Charged Particles

All matter's Atom's are made from smallest indivisible electric charged particles of three types liste in the table below

 Charged Particle Symbol Mass Electric Charge Carry Electron ${\displaystyle e^{-}}$ ${\displaystyle m_{e}}$ - Proton ${\displaystyle p^{+}}$ ${\displaystyle m_{p}}$ + Neutron ${\displaystyle n^{o}}$ ${\displaystyle m_{n}}$ 0

## Electric Charge

### Electric Charge Properties

 Charge Process Electric Charge Symbol Electric Field Magnetic Field Neutral Matter + e- Negative Charge - Q -->E<-- B ↑ Neutral Matter - e- Positive Charge + Q <--E--> B ↓

### Electric Charge Interaction

 Electric Force Definition Symbol Mathematical Formula Electrostatic Force Force of attraction of 2 opposite charges follows Coulomb's Law ${\displaystyle F_{Q}}$ ${\displaystyle K{\frac {Q_{+}Q_{-}}{r}}}$ Eletromotive Force Force interacts with electric charge to creates Electric Field ${\displaystyle F_{E}}$ ${\displaystyle QE}$ Eletromagnetomotive Force Force interacts with electric charge to creates Magnetic Field ${\displaystyle F_{B}}$ ${\displaystyle \pm QvB}$ Eletromagnetic Force Sum of Eletromotive Force and Eletromagnetomotive Force ${\displaystyle F_{EB}}$ ${\displaystyle F_{E}+F_{B}=Q(E\pm vB)}$

## Electricity

### Electricity types

 Electricity types Definition Mathematical Formula Source DC Electricity Electricity that provides constant voltage over time ${\displaystyle v(t)=V}$ Electrolysis, Electrochemcial Cell, PhotonVoltaic AC Electricity Electricity that provides sinusoidal changing voltage over changing time ${\displaystyle v(t)=VSin\omega t}$ Electromagnetic induction

### DC & AC Response

#### Resistive circuit

 Characteristics DC AC Voltage ${\displaystyle V=IR}$ ${\displaystyle v=iR}$ Current ${\displaystyle I={\frac {V}{R}}}$ ${\displaystyle i={\frac {v}{R}}}$ Resistance ${\displaystyle R={\frac {V}{I}}}$ ${\displaystyle R={\frac {v}{i}}}$ Power provided ${\displaystyle P_{V}=IV}$ ${\displaystyle P_{V}=iv}$ Power Loss ${\displaystyle P_{R}=I^{2}R(T)={\frac {V^{2}}{R(T)}}}$ ${\displaystyle P_{R}=i^{2}{\frac {v^{2}}{R(T)}}}$ Power delivered ${\displaystyle P=P_{V}-P_{R}}$ Reactance ${\displaystyle X_{R}=0}$ Impedance ${\displaystyle Z_{R}=X_{R}+R=R}$ Phase ${\displaystyle 0}$

#### Capacitor circuit

 Characteristics DC AC Voltage ${\displaystyle V=QC={\frac {W}{Q}}}$ ${\displaystyle v={\frac {1}{C}}\int idt}$ Charge ${\displaystyle Q={\frac {V}{C}}}$ Capacitance ${\displaystyle C={\frac {V}{Q}}}$ Current ${\displaystyle I={\frac {Q}{t}}}$ ${\displaystyle i=C{\frac {dv}{dt}}}$ Power provided ${\displaystyle P_{V}=IV=({\frac {Q}{t}})({\frac {W}{Q}})={\frac {W}{t}}}$ ${\displaystyle p={\frac {1}{2}}Cv^{2}}$ Reactance ${\displaystyle X_{C}(t)={\frac {v}{i}}}$ ${\displaystyle X_{C}(j\omega )={\frac {1}{j\omega C}}}$ ${\displaystyle X_{C}(\omega \theta )={\frac {1}{\omega C}}\angle -90}$ Impedance ${\displaystyle Z_{C}(t)=X_{C}+R_{C}}$ ${\displaystyle X_{C}(j\omega )={\frac {1}{j\omega C}}+R_{C}}$${\displaystyle X_{C}(\omega \theta )={\frac {1}{\omega C}}\angle -90+R\angle 0}$ Phase ${\displaystyle Tan\theta ={\frac {1}{\omega T}}}$ Time Constant ${\displaystyle T=CR_{C}}$

#### Inductor circuit

 Characteristics DC AC Magnetic Field Strength ${\displaystyle B=LI}$ Current ${\displaystyle I={\frac {B}{L}}}$ Inductance ${\displaystyle C={\frac {B}{I}}}$ Current ${\displaystyle I={\frac {Q}{t}}}$ Power provided ${\displaystyle P_{V}=IV=({\frac {B}{l}})({\frac {W}{Q}})={\frac {W}{t}}}$ Reactance ${\displaystyle X_{L}(t)={\frac {v}{i}}}$ ${\displaystyle X_{L}(j\omega )=j\omega L}$ ${\displaystyle X_{L}(\omega \theta )=\omega L\angle 90}$ Impedance ${\displaystyle Z_{C}(t)=X_{C}+R_{C}}$ ${\displaystyle X_{C}(j\omega )=j\omega L+R_{L}}$${\displaystyle X_{C}(\omega \theta )=\omega L\angle 90+R\angle 0}$ Phase ${\displaystyle Tan\theta =\omega T}$ Time Constant ${\displaystyle T={\frac {L}{R_{L}}}}$

### Electrical Oscillation

 Modes of Oscillation Oscillation equation Wave Function Angular Speed Time Constant Oscilation Constant ' Decay constant Electric decay current sinusoidal wave oscillation ${\displaystyle {\frac {d^{2}}{dt^{2}}}i=-2\alpha {\frac {d}{dt}}i-\beta i}$ ${\displaystyle i=A(\alpha )Sin\omega t}$ ${\displaystyle \omega ={\sqrt {\beta -\alpha }}}$ ${\displaystyle T=LC}$ ${\displaystyle \beta ={\frac {1}{T}}}$ ${\displaystyle \alpha =\beta \gamma }$ ${\displaystyle \gamma =RC}$ Electric peak current sinusoidal wave oscillation ${\displaystyle Z_{L}=-Z_{C}}$${\displaystyle Z_{t}=R}$ ${\displaystyle i(\omega =0)=0}$${\displaystyle i(\omega =\omega _{o})={\frac {v}{2}}}$${\displaystyle i(\omega =00)=0}$ ${\displaystyle \omega _{o}={\sqrt {\frac {1}{T}}}}$ ${\displaystyle T=LC}$ Electric current sinusoidal wave oscillation ${\displaystyle {\frac {d^{2}}{dt^{2}}}i=-{\frac {1}{T}}i}$ ${\displaystyle i=ASin\omega t}$ ${\displaystyle \omega ={\sqrt {\frac {1}{T}}}}$ ${\displaystyle T=LC}$ Electric current sinusoidal standing wave oscillation ${\displaystyle Z_{L}=-Z_{C}}$ ${\displaystyle V_{L}=-V_{C}}$ ${\displaystyle \omega _{o}={\sqrt {\frac {1}{T}}}}$ ${\displaystyle T=LC}$

## Electric Heat

Electric Heat . Electricity and resistance interact to creates Heat energy

${\displaystyle E_{R}=I^{2}R(T)}$
${\displaystyle R(T)=R_{o}+nT}$ for Conductor
${\displaystyle R(T)=R_{o}e^{nT}}$ for Non-Conductor

## Electromagnetism

### Electromagnetic Field

 Definition Symbol Mathematica; Formula Magnetic Field Strength Electric current flows through conductor to creates Magnetic field ${\displaystyle B}$ ${\displaystyle LI}$ Induced Magnetic Field Strength Induced magnetic field created from magnetic field ${\displaystyle \phi }$ ${\displaystyle -NB=-NLI}$ Magnetization Field Strength Magnetization magnetic field created from magnetic field ${\displaystyle H}$ ${\displaystyle {\frac {B}{\mu }}={\frac {\phi }{n\mu }}}$

### Electromagnetic Induction

 Definition Symbol Mathematica; Formula Magnetic Field Electricity and conductor interact to creates Magnetic field of strength ${\displaystyle B}$ ${\displaystyle B=IL}$ Electromagnetic Potential Electricity and conductor interact to creates Magnetic field of strength ${\displaystyle V}$ ${\displaystyle {\frac {dB}{dt}}=L{\frac {dI}{dt}}}$ Induced Magnetic Field Electricity and conductor interact to creates Magnetic field of strength ${\displaystyle \phi }$ ${\displaystyle -NB=-NLI}$ Induced Electromagnetic Postential Electricity and conductor interact to creates Magnetic field of strength ${\displaystyle \epsilon }$ ${\displaystyle -{\frac {d\phi }{dt}}=-N{\frac {d\phi }{dt}}=-NL{\frac {dI}{dt}}}$

### Electromagnetization

 Electromagnetization Definition Vector Equation Electromagnetization Permanent electromagnet ${\displaystyle \nabla \cdot D=\rho }$${\displaystyle \nabla \times E=-\nabla B}$${\displaystyle \nabla \cdot B=0}$${\displaystyle \nabla \times H=J+\nabla B}$

### Electromagnetic oscillation wave

 Electromagnetic Oscillation Definition Vector Equation Electromagnetic oscillation vector equation Oscillation of 2 fields E and B ${\displaystyle \nabla \cdot E=0}$${\displaystyle \nabla \times E={\frac {1}{T}}E}$${\displaystyle \nabla \cdot B=0}$${\displaystyle \nabla \times B={\frac {1}{T}}B}$ Electromagnetic wave equation ${\displaystyle \nabla ^{2}E=-\omega E}$${\displaystyle \nabla ^{2}B=-\omega B}$ Electromagnetic wave function ${\displaystyle E=ASin\omega t}$${\displaystyle B=ASin\omega t}$${\displaystyle \omega ={\sqrt {\frac {1}{T}}}=C=\lambda f}$${\displaystyle T=\mu \epsilon }$

### Electromagnetic Wave Propagation

 Electromagnetic Wave Propagation Symbol Mathematical Formulas Electromagnetic Wave Speed ${\displaystyle v}$ ${\displaystyle v=\omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f}$ Electromagnetic Wave Energy ${\displaystyle E}$ ${\displaystyle pv=pC=p\lambda f=hf}$ Electromagnetic Wave Quanta ${\displaystyle h}$ ${\displaystyle h=p\lambda }$ Electromagnetic Wave Length ${\displaystyle \lambda }$ ${\displaystyle \lambda ={\frac {h}{p}}}$ Electromagnetic Wave Momentum ${\displaystyle p}$ ${\displaystyle p={\frac {h}{\lambda }}}$

Electromagnetic wave proparates at speed of light carries quanta of energy called photon and radiates as visibile light at fo or electricity at f>fo . Visible light and electricity are called photon's state . Photon cannot exist in 2 state at the same time according to Heinsberg's Uncertainty principle which can be expressed mathematically ${\displaystyle \Delta p\Delta \lambda >{\frac {1}{2}}{\frac {h}{2\pi }}={\frac {h}{4\pi }}}$

 Electromagnetic Wave Radiation In Vaccum and Free air In Material Medium Photon energy level ${\displaystyle E=hf_{o}}$ ${\displaystyle E=hf}$ Quantization ${\displaystyle h=p\lambda _{o}}$ ${\displaystyle h=p\lambda }$ Quanta's Particle-wave duality Particle ${\displaystyle p=h\lambda _{o}}$ Wave ${\displaystyle \lambda _{o}={\frac {h}{p}}}$ Particle ${\displaystyle p=h\lambda }$ Wave${\displaystyle \lambda ={\frac {h}{p}}}$ Photon's State radiant photon of visible Light Electric photon of free electron Uncertainty photon's state visible light only free electron only

### Electromagnetic Light

${\displaystyle v=\omega _{o}={\sqrt {\frac {1}{\mu _{o}\epsilon _{o}}}}=C=\lambda _{o}f_{o}}$
${\displaystyle E=pv=pC=p\lambda _{o}f_{o}=hf_{o}}$
${\displaystyle h=p\lambda _{o}}$

### Electromagnetic Electricity

${\displaystyle v=\omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f}$
${\displaystyle E=pv=pC=p\lambda f=hf}$
${\displaystyle h=p\lambda }$