edynamik_Aufgabe6.m 1.61 KB
 Niklas Wahl committed Nov 14, 2019 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 %% Aufgabe 6 %% Gegeben: %% clear all; U0a = 5 %V U0b = 8 %V U0c = 7 %V R1 = 1 %Ohm R2 = 5 %Ohm R3 = 3.5 %Ohm R4 = 2 %Ohm R5 = 0.3 %Ohm R6 = 4.8 %Ohm %% Stromstrke Kirchoff % Knoten: $I_1 = I_2 + I_3$ % % Masche $abef$: $-U_{0a} - R_1 I_1 - R_2 I_3 + U_{0b} - R_6 I_1 = 0 \Leftrightarrow % I_1 = \frac{U_{0b} - U_{0a} - R_2 I_3}{R_1 + R_6}$ % % Masche $bcde$: $-R_3 \underbrace{I_2}_{I_1 - I_3} - U_{0c} - R_{ers45} % \underbrace{I_2}_{I_1 - I_3} - U_{0b} + R_2 I_3 = 0 \Leftrightarrow I_1 = \frac{R_3 % I_3 - U_{0c} + R_{ers45} I_3 - U_{0b} + R_2 I_3}{R_3 + R_{ers45}}$ % % Gleichsetzen: % % $$\frac{U_{0b} - U_{0a} - R_2 I_3}{R_1 + R_6} = \frac{I_3 (R_3 + R_{ers45} % + R_2) - U_{0c} - U_{0b}}{R_3 + R_{ers45}}$$ % % $$\frac{U_{0b} - U_{0a}}{R_1 + R_6} - \frac{R_2 I_3}{R_1 + R_6} = \frac{I_3 % (R_3 + R_{ers45} + R_2)}{R_3 + R_{ers45}} -\frac{ U_{0c} + U_{0b}}{R_3 + R_{ers45}}$$ % % $$I_3 \left[\frac{(R_3 + R_{ers45} + R_2)(R_1 + R_6) + R_2(R_3 + R_{ers45})}{(R_1 % + R_6)(R_3 + R_{ers45})}\right] = \frac{(U_{0b} - U_{0a})(R_3 + R_{ers45}) + % (U_{0c} + U_{0b})(R_1 + R_6)}{(R_3 + R_{ers45})(R_1 + R_6)}$$ % % $$I_3 = \frac{(U_{0b} - U_{0a})(R_3 + R_{ers45}) + (U_{0c} + U_{0b})(R_1 % + R_6)}{(R_3 + R_{ers45} + R_2)(R_1 + R_6) + R_2(R_3 + R_{ers45})}$$ Rers45 = 1/sum(1./[R4 R5]) I3 = ((U0b - U0a)*(R3 + Rers45) + (U0c + U0b)*(R1 + R6))/((R3 + Rers45 + R2)*(R1 + R6) + R2*(R3+Rers45)) %Buch: %I3 = ((-U0a)*(R3 + Rers45) + (U0c + U0b)*(R1 + R6))/((R3 + Rers45 + R2)*(R1 + R6) + R2*(R3+Rers45)) I1 = (I3*(R3 + Rers45 + R2) - U0c - U0b) / (R3 + Rers45) I1_check = (U0b - U0a - R2*I3)/(R1 + R6) I2 = I1 - I3 %% %