Assignment # 8

ECE 2004

Use Mesh Analysis to solve for all of the branch currents and node voltages in the circuits below. Show all work.

1.

and , thus

or

Which simplifies to (since I2=0):

Solving the 2 equations and 2 unknowns gives (along with the other mesh currents):

,

Where “m” denotes that the current is a mesh current.With the mesh currents found, we can now solve for the node voltages and branch currents:

We can now relate the different branch currents and node voltages to the mesh currents found previously (denoted with an “m” in the figure above).

1.

2.

3.

4.

5. ,

6. , , and

7.

In summary (same as from HW7):

Voltage / Current
Va / 12 V / I1 / 2 mA
Vb / 2 V / I2 / 0 A
Vc / 0 V / I3 / 0A
Vd / 2 V / I4 / -1 mA
Ve / -8 V / I5 / 10 mA
I6 / 1 mA
Ibat / 11 mA

2.

@:

@ 1k

@ 4k

This constitutes 4 equations and 4 unknowns (since I1m has already been determined). Solving gives:

Now, we have:

And:

Voltage (V) / Current(mA)
Va / -8 V / I1 / 1.67
Vb / -6.59 / I2 / -2.12
Vc / -4.56 / I3 / -0.456
I4 / 0.44
I5 / 1.02
I6 / -0.397
I7 / -1.41

3.

,

Since is known, we are left with 4 equations and 4 unknowns. Solving yields:

, , and

From the mesh currents, we can solve for the remaining currents and voltages:

,

Voltage / Current
/ -1.16 V / I1 / -4 A
/ -9.16 V / I2 / -116 mA
/ -18.96 V / I3 / -231 mA
/ 1.04 V / I4 / 347 mA
/ 1.36 V / I5 / 840 mA
I6 / -160 mA
I7 / 1.19 A