Electricity/Electricity generator

Source of DC Electricity		Electricity types	Mathematical formula
Electrolysis		DC	${\displaystyle v(t)=V}$
Electrovoltaic		DC	${\displaystyle v(t)=V}$
Photonvoltaic		DC	${\displaystyle v(t)=V}$
Electromagnetic inducton		AC	${\displaystyle v(t)=VSin\omega t}$

Electricity falls into the 2 types AC (Alternating Current) and DC (Direct Current)

Electricity provides a sinusoidal time varying voltage over time

${\displaystyle v(t)=VSin\omega t}$

When connect AC source to ground, current starts to flow from the source to ground

${\displaystyle i(t)={\frac {d}{dt}}Q(t)}$

From above,

${\displaystyle Q(t)=\int i(t)dt}$

${\displaystyle v(t)={\frac {d}{dt}}{\frac {dW(t)}{dQ(t)}}}$

${\displaystyle W(t)=\int v(t)dQ(t)=\int v(t)i(t)dt}$

${\displaystyle E(t)={\frac {d}{dt}}W(t)={\frac {d}{dt}}\int v(t)i(t)dt}$

Electricity provides constant voltage over time

${\displaystyle v(t)=V}$

When connect AC source to ground, current starts to flow from the source to ground

${\displaystyle I={\frac {Q}{t}}}$

${\displaystyle Q=It}$

${\displaystyle V={\frac {W}{Q}}}$

${\displaystyle W=QV}$

${\displaystyle E={\frac {W}{t}}={\frac {QV}{t}}=IV}$

${\displaystyle v(t)=V}$