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Grand Valley State University Prof. Bogdan Adamczyk Exam 2
Name:
This is a closed book, closed notes exam. Calculators are allowed. Read and follow the
instructions. Use the specified methods. No credit will be given for using alternate
approaches.
Provide complete solutions (not just the answers) to all problems. The final answers will
constitute only a part of your grade, substantial part of it will be based on the process
(explanation) of how the answers have been obtained.
This means: Explain in words what you are doing and why while showing the
calculations. The numerical results (with 4 digits after the decimal point) should include
proper units.
Consider the circuit shown. Determine its Thevenin resistance between the nodes A - B
using the formula :
sc
oc
N
T T i
v
I
V
R = =
Determine voc using node voltage analysis. Determine isc using mesh current analysis.
2.4 A
Vx
A^4^ Ω
2Vx
B
Grand Valley State University Prof. Bogdan Adamczyk Exam 2
Name:
Solution:
2.4 A
20 Ω^10^ Ω
C
Vx
A^4^ Ω^ D
2Vx voc
B
We will calculate the open-circuit voltage using the node analysis.
Note that
voc = VC = V x (1.1)
At node C:
VC VC − VD
At node D:
VC VD VD VD − V x = + +
Grand Valley State University Prof. Bogdan Adamczyk Exam 2
Name:
Note that:
i (^) sc = − i 1 (1.8)
In mesh 1:
4 i 1 (^) + 20 ( i 1 − i 2 ) = 0 (1.9)
In mesh 2:
− 20 ( i 1 (^) − i 2 ) + 12 ( i 2 − i 4 ) + 10 ( i 2 − i 3 ) = 0 (1.10)
In mesh 3:
− 10 ( i (^) 2 − i 3 ) + 2 i 3 + 2 Vx = 0 (1.11)
In mesh 4:
i 4 (^) =− 2. 4 (1.12)
Now,
V (^) x = 20 ( i 1 − i 2 ) (1.13)
Utilizing Eqs. (1.13) and (1.14), Eqs. (1.10) and (1.11) can be re-written as:
− 20 ( i 1 (^) − i 2 ) + 12 ( i 2 + 2. 4 ) + 10 ( i 2 − i 3 ) = 0 (1.14)
and
− 10 ( i 2 (^) − i 3 ) + 2 i 3 + 40 ( i 1 − i 2 ) = (^0) (1.15)
Solving Eqs. (1.9), (1.14) and (1.15) for the mesh currents produces:
3
2
1
i
i
i
Thus,
Grand Valley State University Prof. Bogdan Adamczyk Exam 2
Name:
i sc = − i 1 = 2. 0971 [ A ] (1.17)
Finally,
= = = 823. 995 [ Ω]
sc
oc T i
v R (^) (1.18)
The equivalent Thevenin circuit is
A
1728 V
B
