The topic of this problem is, Operational Amplifier Circuits, and the problem is to determine I out in the circuit shown below. It's a circuit that has two sources in it. It has an independent current source and an independent voltage source, along with two resistors, a 10 kilo-ohm feedback resistor and a 20 kilo-ohm load resistance. I out is measured as a current through the 20 kilo-ohm resistor. So to solve this problem, we start with the properties of an ideal op amp. So we'll draw the symbol for an ideal op amp first. Has two inputs, has an output, has a ground, internal ground. And each one of these inputs has a current associated with it. And each one of these inputs has a voltage associated with it, an inverting and non inverting input. Properties of an ideal op amp tell us that the current in both of these inputs are equal and in fact are equal to 0. So i- is equal to i+, and it's equal to 0. Also, the ideal properties of an op amp tell us that the voltage at the inverting and non-inverting inputs are equal to the same value. V- is equal to V+. So I want to use these two properties of an ideal op amp in order to solve our original circuit. So let's go back to the original circuit and solve it. So we know the voltage at this point because it's ground at the bottom of the circuit. And we go through a 5 volt source so we're at 5 volts at the not inverting input. We note through our properties of the ideal op amp that the same voltage is at the non inverting input as the inverting input, so that tells us that this node is also at 5 volts. So, if we know that, then we can then sum currents into this node, where perhaps we call this node one. And we'll sum currents into that node in order to find a value for this nodal voltage, so ultimately we can find the current in the circuit. So let's do that. Let's sum the currents into node one. So we're going to do Kirchhoff's Current Law at node one. There were so many currents into node one. First of all we have 0.1 mA flowing into node one from our current source. We also have current flowing through the 10 kilo-ohm resistor into node one. It's going to be the current at this point, let's call it V out, minus the voltage at this point, which is five volts divided by 10k. So it's V out minus five volts divided by 10 kilo-ohms. And we also have the current flowing out of the inverting op amp, our inverting input of the op amp, and we know that that current is equal to 0. So when we add that in completeness, and the sum of those currents used in Kirchhoff's Current Law are equal to 0. Total equation only has one unknown and that's this, V0 term. So if we solve for V0, we end up with a V0 that's equal to 4 volts. Now that we have that value, it's easy for us to find the value for the output current through the 20 kilo-ohm resistor. because we know that current I out is equal to V out, voltage at this node minus the voltage at the bottom node, which is 0 volts divided by 20 kilo-ohms. And V out is 4 volts. And 20 kilo-ohms gives us 1/5 mA for I out.
