Question E5C05:
What kind of diagram is used to show the phase relationship between impedances at a given frequency?  

Choices:  
A: Venn diagram  
B: Near field diagram  
C: Phasor diagram  
D: Far field diagram    

Correct Answer is  C: Phasor diagram  

Correct answer: C — Phasor diagram

Why it’s correct:
- A phasor diagram represents AC quantities (voltages, currents, impedances) as rotating vectors in the complex plane at a specific frequency.
- It shows phase angles clearly: the angle between vectors represents the phase relationship.
- Impedance is plotted as a vector with real part $R$ and imaginary part $X$; the angle gives the phase.

Key relationships shown on a phasor diagram:
- Impedance: $Z = R + jX$ with magnitude and angle
  $$|Z| = \sqrt{R^2 + X^2}, \quad \phi = \tan^{-1}\!\left(\frac{X}{R}\right)$$
- Reactances:
  $$X_L = 2\pi f L \quad(\text{inductive, } +j) \qquad X_C = \frac{1}{2\pi f C} \quad(\text{capacitive, } -j)$$
- Rule of thumb: If $X>0$ (inductive), current lags voltage by $\phi$; if $X<0$ (capacitive), current leads by $\phi$.

Why the other choices are incorrect:
- A: Venn diagram — used for set relationships in math/logic, not electrical phase.
- B: Near field diagram — depicts fields close to an antenna; not circuit phase or impedance relationships.
- D: Far field diagram — radiation pattern in the far field; again not used for impedance phase relationships.

Tip:
- On a phasor diagram, place $R$ on the horizontal axis and $X$ on the vertical axis; the impedance vector’s angle $\phi$ immediately shows the phase relationship at that frequency.