Übungsaufgaben zum Transformator

Lösung zur Aufgabe 14.10.1 (Drosselspule)

Windungszahl
$N = √--U------ 2πfA Bˆ = √----------100V--------------= 450- (B.5.1) 2π ⋅ 50Hz ⋅ 10 ⋅ 10−4m2 ⋅ 1T$
Luftspaltlänge
$lL = RmL μ0A 5 −1 −7 V-s- − 4 2 = 1,5345 ⋅ 10 H ⋅ 4 π ⋅ 10 A m ⋅ 10 ⋅ 10 mm = 0,1928mm (B.5.2) -----------$

Lösung zur Aufgabe 14.10.2 (Drosselspule)

Windungszahl
$UL N = √--------- 2πfA Bˆ -----------221V-------------- = √2-π ⋅ 50Hz ⋅ 50 ⋅ 10−4m2 ⋅ 1T = 199 (B.5.3)$
Luftspaltlänge
$lL = Rm-μ0A 2 8,94-⋅ 105H-−-1 −7 V-s- −4 2 = 2 ⋅ 4π ⋅ 10 A m ⋅ 50 ⋅ 10 mm = 2,808mm (B.5.4) ----------$

Lösung zur Aufgabe 14.10.3 (Transformator)

Eisenverlustwiderstand
$U21N- (230V-)2 RF e = P10 = 85W = 622,35Ω-$ (B.5.5)

Induktiver Hauptwiderstand

$2 2 X = U-1N- = --(230V--)-- = 130,56Ω h Q10 405,18V ar --------$ (B.5.6)

Kupferwiderstände

$R R1 = R′2 = --K- = 0,273Ω- 2 -------$ (B.5.7)

Streublindwiderstände

$XK X σ1 = Xσ′2 = ---- = 0,342Ω- 2$ (B.5.8)
Wirkwiderstand und der Streublindwiderstand
$′ R2 = R-2 = 0,273-= 0,0683 Ω ¨u2 22 --------$ (B.5.9)

und

$X σ′ 0,342 X σ2 = --22 = ---2--= 0,0854-Ω- ¨u 2$ (B.5.10)
Sekundärspannung
$′ ⁄ ∘ U- = U-2 = (221V---−-2,7-) = (110,5V ⁄ − 2,7∘) (B.5.11) 2 ¨u 2 -----------------$