Question E9G10:
What do the arcs on a Smith chart represent?  

Choices:  
A: Frequency  
B: SWR  
C: Points with constant resistance  
D: Points with constant reactance    

Correct Answer is  D: Points with constant reactance  

Correct answer: D — Points with constant reactance

Why D is correct:
- On an impedance Smith chart, the curved lines that arc above and below the horizontal (real) axis are lines of constant reactance, often called “reactance arcs.”
- Above the axis: inductive reactance ($+jX$). Below the axis: capacitive reactance ($-jX$).
- These are loci where the normalized impedance has $z = r + jx$ with $x$ fixed and $r$ varying.

Why the other choices are incorrect:
- A: Frequency
  - Frequency is not a family of printed arcs. Changing frequency makes an impedance trace move along some path on the chart, but the chart’s printed arcs are not “frequency arcs.”
- B: SWR
  - Constant SWR corresponds to circles of constant reflection coefficient magnitude $|\Gamma|$ centered on the chart’s center, not the reactance arcs.
- C: Points with constant resistance
  - Constant resistance appears as circles (often called “resistance circles”) that cross the horizontal axis; they are different from the reactance arcs.

Useful formulas and tips:
- Normalize impedance: $$z = \frac{Z}{Z_0} = r + jx$$
  - Constant reactance arcs: $x = \text{constant}$
  - Constant resistance circles: $r = \text{constant}$
- Reflection coefficient mapping: $$\Gamma = \frac{z - 1}{z + 1}$$
- SWR from reflection coefficient magnitude: $$\text{SWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|}$$
- On the horizontal axis ($x=0$) the impedance is purely resistive. Inductive (positive $x$) is above; capacitive (negative $x$) is below.