*Question E5C09:
When using rectangular coordinates to graph the impedance of a circuit, what do the axes represent?*  

*Correct Answer is  A: The X axis represents the resistive component, and the Y axis represents the reactive component*  

### AI Response: (may contain errors)  

When graphing the impedance of a circuit using rectangular coordinates, the axes represent different components of impedance:

1. **Correct Answer: A**  
   - **X Axis (Horizontal):** Represents the resistive component of impedance, denoted as $R$. This is the real part of the impedance and is measured in ohms ($\Omega$).
   - **Y Axis (Vertical):** Represents the reactive component of impedance, denoted as $X$. This is the imaginary part of the impedance and is also measured in ohms ($\Omega$).

   Impedance ($Z$) in rectangular form is expressed as:
   $$ Z = R + jX $$
   where $j$ is the imaginary unit.

2. **Why the Other Choices are Incorrect:**
   - **Choice B:** Incorrect because it reverses the roles of the axes. The X axis should represent the resistive component, not the reactive component.
   - **Choice C:** Incorrect because it confuses impedance with polar coordinates. In polar form, the phase angle and magnitude are used, but not in rectangular coordinates.
   - **Choice D:** Incorrect for the same reason as Choice C. Magnitude and phase angle are not represented on the X and Y axes in rectangular coordinates.

3. **Useful Formulas:**
   - Impedance in polar form can be converted to rectangular form using:
     $$ Z = |Z| \cos(\theta) + j|Z| \sin(\theta) $$
   - Here, $|Z|$ is the magnitude of the impedance, and $\theta$ is the phase angle.

Understanding these concepts is crucial for analyzing and designing circuits, as impedance affects how circuits respond to AC signals.