Question

Problem 1. (50 points) a) Using mesh analysis find the matrix R and E of the equation RxI-E b) Find the unknown currents ll, 12, 13, IRI, İR5of the network in mA using mesh analysis. c) Indicate on the circuit IRI, IRs current directions. R, IR E1-3 E2-15; R1-25 R2-8; R3-40 R4-26i R5-22 RS

Answer 1

Given data are: E_1 = 3V, R_1 = 25 omega E_2 = 15 V, R_2 = 8 omega R_3 = 40 omega, R_4 = 26 omega R_5 = 22 omega rightarrow The circuit is: rightarrow let us apply mesh analysis for the three meshes from 1^st mesh, by applying mesh analysis we get: rightdoublearrow R_3 I_1 + R_1 (I_1 - I_2) - E_1 = 0 40 I_1 + 25I_1 - 25 I_2 - 3 = 0 rightdoublearrow 65 I_1 - 25 I_2 - 3 = 0 rightarrow (1) rightarrow Now, from mesh (2), we have + R_4 I_2 + R_5 (I_2 - I_3) + R_1 (I_2 - I_1) + 3 = 0 26 I_2 + 22(I_2 - I_3) + 25(I_2 - I_1) + 3 = 0 73 I_2 - 22 I_3 - 25 I_1 + 3 = 0 -25 I_1 + 73 I_2 - 22 I_3 = 3 rightarrow (2) \r\n rightarrow similarly from mesh (3) we have: rightdoublearrow R_2 I_3 + R_5 (I_3 - I_2)