Is the source V_s in the network absorbing or supplying power, and how much?

Image from: Irwin, J. David., and R. M. Nelms. Basic Engineering Circuit Analysis, Tenth Edition. N.p.: John Wiley & Sons, 2010. Print.

#### Solution:

### P_{10v}=(10)(3)=30W

### P_{6v}=(6)(3)=18W

### P_{9A}=(16)(-9)=-144W

### P_{V_s}=(V_s)(6)=6V_sW

### P_{8v}=(8)(6)=48W

##### In the circuit, all power absorbedĀ must equal the power supplied. In our case, one sourceĀ supplies power (the element with the negative power value), and the power absorbed by the other elements must equal each other. In other words, if we add all of the power together, the ones that supply power and absorb power, it must all equal to 0. Thus, we can write the following equation:

### -144+30+18+6V_s+48=0

##### (Isolate for V_s)

### 6V_s=48

### V_s=8v

### Now, let us calculate the power absorbed or supplied by the V_s element.

### P_{V_s}=(8)(6)=48W

### The value we got for the element is positive, meaning it absorbs power.

###### This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 1, question 1.42.