Op Amp Practice with Voltage Division

Question

Find the value of Vout.

Answer

The first step would be to solve for i using Ohm's Law.
$ i = \frac{12}{4} $
$ i = 3A $

We know that $ V_+ = V_- $.
In order to find $ V_+ $ we need to use voltage division at the node connecting the 2 and 4 ohm resistor.
$ V_+ = \frac{4}{4 + 2} * 9 $
$ V_+ = 6 = V_- $

Now that we know the voltage at the $ V_- $ node we can find Vout by using the following equation. $ \begin{align} i = \frac{V_- - Vout}{8}\\ 3 = \frac{6 - Vout}{8}\\ 24 = 6 - Vout\\ Vout = -18 V\\ \end{align} $

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