Determine I_L in the circuit.

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

#### Solution:

### We can figure out I_L by writing Kirchhoff’s current law (KCL) for the whole circuit loop. (Forgot Kirchhoff’s current law?) When doing this question, it’s important to remember the following equation, V=IR, where V is voltage, I is current and R is resistance. Thus, isolating for current, I, lets us represent it as \frac{V}{R}.

### Now, let us write the KCL for the whole loop.

### 0.006A=\frac{V}{6000\Omega}+3I_x+0.003A+I_x+I_L

### (Here, for the 6k resistor, we wrote I in terms of \frac{V}{R})

### \frac{V}{6000\Omega}+4I_x+I_L=0.003A

### Now, we will write individual equations for I_x and I_L

### I_x=\frac{V}{2000\Omega}

### I_L=\frac{V}{3000\Omega}

### \frac{V}{6000\Omega}+4(\frac{V}{2000\Omega})+\frac{V}{3000\Omega}=0.003A

#### (Multiply both sides by 6000)

### V+12V+2V=18

### 15V=18

### V=\frac{18}{15}V

### I_L=\frac{18}{15(3000\Omega)}

### I_L=0.4mA

###### This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 2, question 2.15.