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 as the independent current source, an independent voltage source along with two resistors, a 10 kiloohm feedback resistor and a 20 kiloohm load resistance. I out is measured as a current through the 20 kiloohm 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. It has two inputs, has an output, has an 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. The properties of an ideal op-amp tell us that the current in both of these inputs are equal, and in fact, are equal to zero. So I minus is equal to I plus, and that's equal to zero. Also the ideal properties of an op amp tell us that the voltage at the inverting and the non-inverting inputs are equal to the same value V minus is equal to V plus. So I'm going to use these two properties of an ideal op amp in order to solve our original circuit. So let's go and back to the original circuit and solve it. So we know the voltage at this point, because it's crowned at the bottom of the circuit. And we go through a 5 volt source, so we're at 5 volts at the noninverting input. We know through our properties of the ideal op amp that the same voltage is at the noninverting 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, 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. Let's do that. Let's sum the currents into node one, so we're going to use Kirchhoff's current law at node one, and we're summing the currents into node one. First of all we have 0.1 milliamps flowing into node one from our current source. We also have current flowing through the 10 kiloohm resistor into node one. It's going to be the current at this point that's called V out minus the voltage at this point, which is 5 volts divided by 10k. So it's V out minus 5 volts divided by 10 kiloohms, and we also have the current flowing out of the inverting op amp or inverting input of the op amp, and we know that current is equal to 0. So want to have that in completeness, and the sum of those current using Kirchhoff's Current Law are equal to 0, so in this equation only has one unknown and that's this V sub 0 term. So if we solve for V sub 0, we end up with a V sub 0 is equal to 4 volts. Now that we have that value, it's easy for us to find a value for the output current through the 20 kilo ohm resistor. Because we know that current I out equals 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 kiloohms gives us one-fifth milliamps for I out.
