The topic of this problem is circuits with dependent sources. The problem is to determine the output or load voltage, V0. We have the circuit, which is drawn below, as a 10 milliamp source on the left-hand side of the circuit. And it has a current source on the right-hand side of the circuit, which is a dependent source, it's a current controlled current source. With a current controlling that current source, is the current I sub 0 through the 3 kiloohm resistor, downward through the 3 kiloohm resistor. The output voltage is the voltage across the load resistance, which is four kiloohms. So in this case the output voltage is found in the center of the circuit across the lower element in the lower left part of the circuit. So in order to solve this problem we have to use Kirchhoff's laws. And we notice that this is, essentially, a three node circuit. We have a node at the top of the circuit, we have a node at the bottom of the circuit, the ground node, and we also have this node kind of in the center of the circuit between the 2 and the 4 kiloohm resistances. So we're going to solve the circuit first of all using Kirchhoff's Current Law. And we're going to sum the currents into the top node, which we're going to designate as node 1. And so if we do that, then we'll end up with. A falling equation, it's Kirchhoff's Current Law. And instead of summing the currents into the node one, we're going to sum the currents out of node one just to show that it doesn't matter whether you sum the current into or out of the node just so your consistent throughout the problem. So it's KCL out of node 1 at the top of the circuit. So first of all we know that we have 10 milliamps flowing out on the left hand side of the circuit. We also have the voltage, which is across the 2 kiloohm and the 4 kiloohm resistances. That results in a current, which is going to be V1, the nodal voltage associated with node 1, divided by the 2 kiloohm plus the 4 kiloohm resistance for that particular part of the circuit. We also have the voltage, which is flowing through the 3 kiloohm resistance, which is I not or I sub 0, it's going to be V1 divided by 3 kiloohm. And on the right hand side of the circuit we have a current flowing into the top node, which is going to be 4 I sub zero. And so that's all the currents flowing into node one. And so the sum of those current in any instance of time is going to be equal to zero. That's our first equation. We notice in that equation we have two unknowns. We have V sub one, and we have I sub zero. So we need another equation that relates V sub one and I sub zero, and that's fairly easy to come up with using Ohm's law. We know that the voltage, V sub 1, which is a voltage from the top node to the ground node, is a voltage across the 3 kiloohm resistor. So V sub 1 is equal to I sub 0 times 3 kiloohms. So that gives us our second equation, which is independent of the first equation. So we have two equations, and we have two unknowns. So if we go through, and we solve for the nodal voltage, then we'll have a nodal voltage V1, which is equal to 12 volts. If we know that we can step back and we can use our voltage division that we've learned early in the course to find the voltage across the 4 kilo ohms resistor. Namely Vout, V sub 0 the output voltage is equal to the 12 volts, which is dropped across both the 2k and the 4 k resistances, and using voltage division we know that the amount of that voltage drop across the 4k is simply 4K divided by 2K plus 4K. And so that it gives us 8 volts for the voltage drop across the 4 kiloohm resistor. So V sub 0 is equal to 8 volts, and we could've just as easily I've written that as V sub 4K. The output across the load resistance 4K.
