Electricity/Electricity generator

Electricity generators

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

Electricity types

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

AC (Alternating Current)

Electricity provides a sinusoidal time varying voltage over time

$v(t)=VSin\omega t$

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

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

From above,

$Q(t)=\int i(t)dt$

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

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

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

DC (Direct Current)

Electricity provides constant voltage over time

$v(t)=V$

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

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

$Q=It$

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

$W=QV$

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

$v(t)=V$