$$U_{sr} = \ \frac{1}{T}\int_{0}^{T}{U\left( t \right)\text{dt}}$$
$$U_{\text{sk}} = \ \sqrt{\frac{1}{T}\int_{0}^{T}{U^{2}\left( t \right)\text{dt}}}$$
Rezystor: Z=R, $Y = \ \frac{1}{R}$ = G
Kondensator: $Z_{c} = \ \frac{1}{j\text{ωC}} = \ - j\frac{1}{\text{ωC}} = \ - jX_{c}$ , Y= jωC
Cewka: ZL = jωL = jXL , $Y = \ \frac{1}{j\text{ωL}} = j\frac{1}{X_{L}}$
Wartość czasowa do liczby zespolonej:
$$Uz = \ \frac{U}{\sqrt{2}}\ e^{jkata} = \frac{U}{\sqrt{2}}(\cos\left( kata \right) + jsin\left( kata \right))\ $$
Wartość zespolona do wartości czasowej:
U = -5(a) – j8(b)
$U\left( t \right) = \ \sqrt{a^{2} + b^{2}}\text{\ \ }e^{\text{jarctg}\frac{b}{a}}$ = $\sqrt{a^{2} + b^{2}}\text{\ sin}$($\omega t + (arctg\frac{b}{a})$)
I = 1A = 1ej0 = 1*$\sqrt{2}$ sin ωt
U=220 V = 220ej0 =220*$\sqrt{2}$ sin ωt
Moce:
S = P + jQ
S= U*Ix (sprzężenie, zmiana znaku przy I)