Coulomb's Law

F=14⋅π⋅ϵ0⋅ϵr⋅Q1⋅Q2r2F = \frac 1{4\cdot\pi\cdot\epsilon_0\cdot\epsilon_r}\cdot\frac{Q_1\cdot Q_2}{r^2}

Electrical Field

E→=F→Q\overrightarrow{E} = \frac{\overrightarrow{F}}Q
E=UdE = \frac Ud

Point Charge

E=14⋅π⋅ϵ0⋅ϵr⋅Qr2E = \frac 1{4\cdot\pi\cdot\epsilon_0\cdot\epsilon_r}\cdot\frac{Q}{r^2}

Gauss Law For Electric Fields

ΦE=∮E→⋅dA→=Qnetϵ0ϵr\Phi_E = \oint\overrightarrow{E}\cdot d\overrightarrow{A} = \frac{Q_\textup{net}}{\epsilon_0\epsilon_r}

Electrical Potential

U=wq,W=q⋅UU = \frac wq, \quad W = q\cdot U

Electrical Voltage

UPQ=UP−UQU_{PQ} = U_P - U_Q
WPQ=q⋅UPQW_{PQ} = q\cdot U_{PQ}

Capacitor

Q=C⋅UQ = C\cdot U
C=ϵr⋅ϵ0⋅Ad(plate capacitor)C = \frac{\epsilon_r\cdot\epsilon_0\cdot A}{d} \quad \textup{(plate capacitor)}
W=12⋅C⋅U2(energy storage)W = \frac 12\cdot C\cdot U^2 \quad \textup{(energy storage)}

Current

I=Qt,i(t)=dqdtI = \frac Qt, \quad i(t) = \frac{dq}{dt}

Ohm's Law

U=R⋅IU = R\cdot I

Resistors in serie and parallell

Serie:Rers=R1+R2+R3+...\text{Serie:} R_{ers} = R_1+R_2+R_3+...
Parallell:1Rers=1R1+1R2+1R3+...\text{Parallell:} \frac{1}{R_{ers}} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...

Capacitors in serie and parallell

Serie:1Cers=1C1+1C2+1C3+...\text{Serie:} \frac{1}{C_{ers}} = \frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+...
Parallell:Cers=C1+C2+C3+...\text{Parallell:} C_{ers} = C_1+C_2+C_3+...

Inner resistance

Upol=ϵ−Ri⋅IU_{pol} = \epsilon - R_i \cdot I

Resistance in material

R=ρ⋅LAR = \rho\cdot\frac LA
RT=R0(1+α(T−T0))R_T = R_0 ( 1 + \alpha ( T - T_0))

Voltage Sharing and Current Sharing

U2=R2R1+R2⋅EU_2 = \frac{R_2}{R_1 + R_2}\cdot E
I1=R2R1+R2⋅I0I_1 = \frac{R_2}{R_1 + R_2}\cdot I_0

Faraday's Induction Law

Uind=−dΦmdtU_\textup{ind} = -\frac{d\Phi_m}{dt}

Coil

U=L⋅didtU = L\cdot\frac{di}{dt}
L=μ0⋅μr⋅N2⋅AlL = \frac{\mu_0\cdot\mu_r\cdot N^2\cdot A}l
W=12⋅L⋅I2W = \frac 12\cdot L \cdot I^2

Effect

P=U⋅I=R⋅I2=U2RP = U\cdot I = R\cdot I^2 = \frac{U^2}R
P=WtP = \frac W t

Magnetic Flux

Φ=B⋅A⋅cos⁡θ\Phi = B\cdot A\cdot \cos\theta

Where

θ\theta

is the angle between the normal of

A→\overrightarrow{\bm A}

and

B→\overrightarrow{\bm B}

.

Charge in Magnetic Fields

F=q(v→×B→)F = q (\overrightarrow{v} \times \overrightarrow{B})

For a straight conductor:

F=I(l→×B→)F = I (\overrightarrow{l} \times \overrightarrow{B})

Magnetic Fields Created by Live Conductors

Long straight conductor:

B=μr⋅μ0⋅I2⋅π⋅rB = \frac{\mu_r\cdot\mu_0\cdot I}{2\cdot\pi\cdot r}

Coil:

B=μr⋅μ0⋅N⋅IlB = \frac{\mu_r\cdot\mu_0\cdot N\cdot I}l

Toroid:

B=μ0⋅μr⋅N⋅I2⋅π⋅RB = \frac{\mu_0\cdot\mu_r\cdot N\cdot I}{2\cdot \pi\cdot R}

Alternating Voltage, Alternating Current

u(t)=u^⋅sin⁡(ω⋅t)u(t) = \hat{u}\cdot\sin(\omega\cdot t)
i(t)=i^⋅sin⁡(ω⋅t+φ)i(t) = \hat{i}\cdot\sin(\omega\cdot t + \varphi)
ω=2⋅π⋅ff=1T\omega = 2\cdot\pi\cdot f \qquad f = \frac 1T
U=ueff=u^2I=ieff=i^2U = u_\textup{eff} = \frac{\hat u}{\sqrt 2} \qquad I = i_\textup{eff} = \frac{\hat i}{\sqrt 2}
P=U⋅I⋅cos⁡(φ)P = U\cdot I\cdot\cos(\varphi)

Where

φ\varphi

is the angle phase angle between voltage and current.

Addition of Sinus Waves

∑i=1NAi⋅sin⁡(ω⋅t+αi)=A⋅sin⁡(ω⋅t+α)\sum_{i = 1}^NA_i\cdot\sin(\omega\cdot t + \alpha_i) = A\cdot\sin(\omega\cdot t + \alpha)

Where

A=X2+Y2A = \sqrt{X^2 + Y^2}

and

tan⁡α=YX\tan\alpha = \frac YX

, where

XX

and

YY

is given by:

X=∑i=1NAi⋅cos⁡αi,Y=∑i=1NAi⋅sin⁡αiX = \sum_{i = 1}^N A_i\cdot\cos\alpha_i, \quad Y = \sum_{i = 1}^N A_i\cdot\sin\alpha_i

RC-Circuit

Capacitor Discharge:

u(t)=U0⋅e−tτu(t) = U_0\cdot e^{-\frac t \tau}

Capacitor charging

u(t)=U0⋅(1−e−tτ)u(t) = U_0\cdot\left(1 - e^{-\frac t \tau}\right)

Time Constant:

τ=R⋅C\tau = R\cdot C

\textbf{Impedance} Kapacitive:

ZC=XC=1ω⋅CZ_C = X_C = \frac 1{\omega\cdot C}

Inductive:

ZL=XL=ω⋅LZ_L = X_L = \omega\cdot L
Z=UIZ = \frac UI
Ztotseries=R2+(ωL−1/ωC)2Z_\textup{totseries} = \sqrt{R^2 + (\omega L - 1/ { \omega C})^2}
tan⁡φ=ωL−1/ωCR\tan\varphi = \frac{\omega L - 1 / \omega C}R

Average Effect:

Peff=Ueff⋅Ieff⋅cos⁡φP_\textup{eff} = U_\textup{eff}\cdot I_\textup{eff}\cdot\cos\varphi

Resonance:

ω0=1L⋅C\omega_0 = \frac 1{\sqrt{L\cdot C}}
f0=12⋅π⋅L⋅Cf_0 = \frac 1{2\cdot \pi\cdot\sqrt{L\cdot C}}

Transformer

U1U2=N1N2I2I1=N1N2\frac{U_1}{U_2} = \frac{N_1}{N_2} \quad \frac{I_2}{I_1} = \frac{N_1}{N_2}

Impedance Transform:

Z2=Z1(N2N1)2Z_2 = Z_1\left(\frac{N_2}{N_1}\right)^2