The topic of this problem is Electric Power. In this problem, we want to determine the power for each one of these elements in the circuit. We want to determine the power itself and whether it's absorbed power or supplied power. So we'll start this problem with looking at the 36-volt source on the left-hand side of the circuit. If we look at the power in the 36-volt source, We're going to use our well-known equation that power is equal to voltage times current. And so in this case, we see that our voltage is 36 volts, but the current is flowing up through this leg of the circuit, this branch of the circuit. So that the positive 4 amps of current, I sub x, first encounters the negative polarity of that voltage source, the 36-volt source. So the voltage in this case is -36 volts, since we hit the negative polarity of the voltage source first, and the current is 4 amps. And so in this case, we end up with -144 watts of power associated with the 36-volt source. This is a negative power, so that tells us that we have 144 watts supplied by this element, that is the 36-volt source. If we look next at element 1, which is on the upper left-hand side of the circuit, and try to determine what the power is in element 1, P sub 1 using the same approach, is going to be the 4 amps. And the 4 amps, a positive 4 amps, is flowing into the element 1 which has 12 volts plus to minus, left to right, across that element. So that 4 amps encounters the positive polarity of the 12-volt source, or the 12 volts dropped across element 1. So it's (12v)(4A) and that gives us 48 watts of power. And since that is a positive 48 watts, we have 48 watts absorbed, By element 1. If we do the same thing for element 2, looking in the center of the circuit, we see that there's 24 volts plus to minus, top to bottom, across element 2. We also see that we have 2 amps positive flowing down through element 2. The 2 amps would encounter the positive of the polarity. The 24 volts has dropped across element 2. So power for element 2 is going to be (24v)(2A), and that gives us 48 watts of power once again. And again that's a positive power, so we end up with 48 watts of absorbed power associated with element 2. Next we can look at the current control voltage source. So it's a dependent source at the top right-hand side of the circuit. And so the power in that source, which is 1 times I sub x, where I sub x is the current in the left-hand side of the circuit, And the 1 is the amplification factor for this current control voltage source. Then if we look at the power in that case, we see that the voltage across it is 1I sub x, minus to plus, so it's going to be a -1I sub x for the voltage, and the current is 2 amps. And again, that 2-amp current is encountering the negative polarity of the dependent source first. So it's (-1I sub x)(2A), and so that gives us a -2 I sub x watts. And we know what I sub x is, I sub x is equal to 4 amps. So we can then plug that into this and we get a -8 watts of power associated with that current control voltage source. And as before, if we end up with a negative power, then we know that that is supplied power. So we have 8 watts of supplied power. From that dependent source. The mixed element and the last element is element 3. Element 3 has 28 volts dropped across it with a polarity shown, and 2 amps of current flowing down through it. So, using the same approach as we did for the other elements, we see that we had 28 volts and we have 2 amps which encounters the positive polarity of the voltage source first. And so that again gives us 56 watts of power. And since it has a positive power, we know that we have 56 watts absorbed by element 3.
