Linear Network Practice

Question

The box represents a linear network containing no independent sources. Given the data in the table below determine the voltage Vs' when Is = 4A and Vout = 20V.

Answer

In order to find Vs' we have the following equation:
$ 20 = Vs'a + 4b $

From the information present in the table two systems of equations can be created to solve for a and b.
First equation:
$ 10 = 4a + b $
Second equation:
$ 40 = 10a + 0b $
After solving the above system of equations you get:
$ a = 4 $ and $ b = -6 $

Since we have both a and b values you can plug that into the Vs' equation and solve for Vs'.
$ \begin{align} 20 = Vs'a + 4b\\ 20 = Vs'(4) + 4(-6)\\ 44 = 4Vs'\\ Vs' = 11 V \end{align} $

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