syms Uab f Ia Rs
Ld=(2/3)*(1/(2*pi*f))*(((Uab*Uab)/(Ia*Ia))-((3/2)*Rs)^2)^(1/2) Ld =
(Uab^2/Ia^2 - (9*Rs^2)/4)^(1/2)/(3*pi*f) pretty(Ld)
/ 2 2 \1/2 | Uab 9 Rs | | ---- - --- | | 2 4 | \ Ia / --- 3 pi f
diff(Ld,Uab) ans =
Uab/(3*Ia^2*pi*f*(Uab^2/Ia^2 - (9*Rs^2)/4)^(1/2)) diff(Ld,Ia)
ans =
-Uab^2/(3*Ia^3*pi*f*(Uab^2/Ia^2 - (9*Rs^2)/4)^(1/2)) diff(Ld,Rs)
ans =
-(3*Rs)/(4*pi*f*(Uab^2/Ia^2 - (9*Rs^2)/4)^(1/2))
U=(((Uab/(3*Ia^2*pi*f*(Uab^2/Ia^2 -
(9*Rs^2)/4)^(1/2))*((((0.04/100)*Uab)+((0.06/100)*100))/(3)^1/2))^2+(- Uab^2/(3*Ia^3*pi*f*(Uab^2/Ia^2 -
(9*Rs^2)/4)^(1/2)))*((((0.04/100)*Ia)+(((0.06/100)*100)))/(3)^1/2))^2+((- (3*Rs)/(4*pi*f*(Uab^2/Ia^2 -
(9*Rs^2)/4)^(1/2))*((((0.04/100)*Rs)+(((0.06/100)*100)))/(3)^1/2))^2))^(1/2) U =
(((Uab^2*(Uab/15000 + 1/100)^2)/(9*Ia^4*pi^2*f^2*((9*Rs^2)/4 - Uab^2/Ia^2)) + (Uab^2*(Ia/15000 + 1/100))/(3*Ia^3*pi*f*(Uab^2/Ia^2 - (9*Rs^2)/4)^(1/2)))^2 - (9*Rs^2*(Rs/15000 + 1/100)^2)/(16*pi^2*f^2*((9*Rs^2)/4 - Uab^2/Ia^2)))^(1/2) Uab=1.4848315
Uab = 1.4848
Rs=2.7145468 Rs =
2.7145 Ia=0.15641069 Ia =
0.1564 f=50
f = 50 subs(U)*2 ans = 0.0019
