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

Choices:  
A: The X axis represents the resistive component, and the Y axis represents the reactive component  
B: The X axis represents the reactive component, and the Y axis represents the resistive component  
C: The X axis represents the phase angle, and the Y axis represents the magnitude  
D: The X axis represents the magnitude, and the Y axis represents the phase angle    

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

Correct answer: A

1) Why A is correct
- In rectangular (Cartesian) form, impedance is written as:
  $$Z = R + jX$$
  where:
  - $R$ is the resistive (real) component
  - $X$ is the reactive (imaginary) component
- On a rectangular plot:
  - X-axis = real axis = resistance $R$
  - Y-axis = imaginary axis = reactance $X$
- Inductive reactance is positive (plotted above the axis), capacitive reactance is negative (plotted below the axis).

2) Why the other choices are incorrect
- B: Swaps the axes; in standard complex-plane convention, real (resistive) is horizontal, imaginary (reactive) is vertical.
- C and D: These describe polar coordinates (magnitude and phase), not rectangular coordinates.

3) Useful formulas and tips
- Impedance components:
  $$Z = R + jX$$
  $$X_L = +2\pi f L$$
  $$X_C = -\frac{1}{2\pi f C}$$
- From rectangular to polar:
  $$|Z| = \sqrt{R^2 + X^2}$$
  $$\phi = \tan^{-1}\!\left(\frac{X}{R}\right)$$
- Quadrants:
  - Inductive: $X > 0$ (above the axis)
  - Capacitive: $X < 0$ (below the axis)