PHYS345 Electricity and Electronics

Answer for P4.8

Mesh Analysis
Solve the following two equations for I2:
(2+j2)I1 - 2I2 = 8
-2 I1 + (4-j2)I2 = 6

Life is short! I put this into MathCAD and found
I2 = 3.4+j0.2 A = 3.41 A \/ -3.4 deg

Nodal Analysis
Solve the following two equations for V1 and V2:
Eq. 1:   jV1 + V2 = 8
Eq. 2:   V1 + (-1+j)V2 = -j6

Multiplying Eq. 1 times j and then adding to Eq. 2 yields:
(-1+j2)V2 = j2,
thus
V2 = 0.8-j0.4
(after conversion of the two complex numbers to polar form, division, then conversion back).

Back substitution into Eq. 1 yields:
V1 = 0.4-j7.2
so that
V1-V2 = -0.4-j6.8

Finally,
I2 = (V1-V2)/(-j2) = (-0.4-j6.8)/(-j2) = 3.4-j0.2

Life is too short for that too!


"http://www.physics.udel.edu/~watson/phys345/protected/exercises/answers/P4-8.html"
Last updated Oct. 1, 1998.
Copyright George Watson, Univ. of Delaware, 1998.