Problem 4-59

Find the Thevenin equivalent.

NOTE: Blue items were added to solve the problem and are not part of the original diagram.


I will use mesh analysis to find voc.

Express current source in terms of mesh currents.

ia = 8 A

Now, erasing the current source leaves only one mesh (b) around which to write KVL.

12 (ib - ia) + 6 ib - 12 = 0

18 ib - 12 ib = 12

18 ib - 12 (8) = 12

18 ib = 108

ib = 6 A

Now, by KVL,

voc = v2 + v6

voc = 2 ia + 6 ib

voc = 16 + 36 = 52 V

thus

vTh = 52 V

Next, I will find RTh by "killing" the independent sources and using resistor combinations.

Hopefully by this point in the course, you can easily see that

Req = (12||6) + 2 = 6 W

Thus

RTh = 6 W

so the Thevenin equivalent circuit is:


Note that RTh could also be obtained by finding isc then RTh = voc / isc.


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