Question E5C07:
Where is the impedance of a pure resistance plotted on rectangular coordinates?  

Choices:  
A: On the vertical axis  
B: On a line through the origin, slanted at 45 degrees  
C: On a horizontal line, offset vertically above the horizontal axis  
D: On the horizontal axis    

Correct Answer is  D: On the horizontal axis  

To plot impedance on rectangular (Cartesian) coordinates, we use the impedance plane with:
- Horizontal axis = resistance, $R$
- Vertical axis = reactance, $X$

1) Why the correct answer is correct (D):
- A pure resistance has no reactance: $Z = R + j0$.
- Since $X = 0$, points lie on the horizontal axis (the $R$-axis).

2) Why the other choices are incorrect:
- A: Vertical axis is $X$ (reactance). That’s for pure reactance ($R=0$), not pure resistance.
- B: A 45-degree line through the origin corresponds to $X = R$ (constant phase angle $+45^\circ$), not $X=0$.
- C: A horizontal line above the axis implies $X$ is a positive constant and $R$ varies; that’s inductive impedance with $X>0$, not pure resistance.

3) Useful formulas/rules of thumb:
- Rectangular form: $Z = R + jX$
- Polar form: $Z = |Z|\angle\theta$
- Magnitude: $|Z| = \sqrt{R^2 + X^2}$
- Angle: $\theta = \tan^{-1}\!\left(\frac{X}{R}\right)$
- Pure resistance: $X = 0 \Rightarrow \theta = 0^\circ$ (on the horizontal axis)
- Pure reactance: $R = 0 \Rightarrow$ on the vertical axis (up for $+jX$ inductive, down for $-jX$ capacitive)