The topic of this problem is Ohm's Law and also using the well-known equation for Power, as well. The problem is determine the resistance R and the voltage source V sub s. So we have a current source, on the left-hand side of the circuit that also has a voltage associated with it. And that's the V sub S that we're looking for. To solve this problem, you have to use the passive sign convention in order to be able to assign the polarities across a voltage drop of the elements. So in this case, we have a voltage drop across the resistor that is unknown as far as the polarity goes. So we first assign a direction for the current. And then, knowing the direction for the current that we've assigned, we can then assign the polarity across the resistor. In the passive sign convention, the current is assumed to enter the positive side of the voltage polarity across the element. So if we assign the current to go clockwise around this single loop circuit, then the voltage drop across the resistor, P sub R is going to be, as shown in the circuit now, and ultimately we're going to decide what the resistance is and what the voltage source of this V sub S is? So we know that using the equation for power, that power = I squared R. And we're given the power in this problem. The power in the resistor is equal to 80 milliwatts. We're also given the current, the current is equal to 4 milliamps. And the problem is on the left-hand side as a current source. So we have everything we need in order to solve for the resistance. So the resistance is going to be equal to P/I squared, and P=80mW, it's positive, I=4mA I'm going to square that and ultimately we end up with a resistance, That's equal to 5 kiloohms. So that solves for our resistance. The next thing we need to find, is we need to find the voltage associated with the current source. So it's the source voltage across the current source. We can do this because we know that all that voltage that's across the voltage source is also the voltage across the resistor. It's the only other element in the circuit. So if we could solve for the voltage across the resistor, then we know that that is going to be equal to the voltage across the current source. So the voltage across the resistor, which is equal to V sub S, is going to be equal to the current times the resistance, and so the current is 4 mA. We calculated the resistance from a previous part of the problem, and so we end up with a voltage which is equal to 20 volts. So the voltage associated with the source is going to be 20 volts.
