Question E5C06:
What does the impedance 50 - j25 ohms represent?  

Choices:  
A: 50 ohms resistance in series with 25 ohms inductive reactance  
B: 50 ohms resistance in series with 25 ohms capacitive reactance  
C: 25 ohms resistance in series with 50 ohms inductive reactance  
D: 25 ohms resistance in series with 50 ohms capacitive reactance    

Correct Answer is  B: 50 ohms resistance in series with 25 ohms capacitive reactance  

To interpret complex impedance, use:
- General form: $$Z = R + jX$$
  - $R$ is resistance (ohms), the real part.
  - $X$ is reactance (ohms), the imaginary part.
- Sign convention:
  - Inductive reactance: $$X_L = +\omega L = +2\pi f L \quad (\text{positive, } +jX)$$
  - Capacitive reactance: $$X_C = -\frac{1}{\omega C} = -\frac{1}{2\pi f C} \quad (\text{negative, } -j|X|)$$

Why the correct answer (B) is correct:
- Given $$Z = 50 - j25\ \Omega,$$ the real part is $R = 50\ \Omega$ and the reactive part is $X = -25\ \Omega$.
- A negative reactance indicates capacitance.
- Therefore, it represents 50 ohms resistance in series with 25 ohms capacitive reactance.

Why the other choices are incorrect:
- A: “50 ohms resistance in series with 25 ohms inductive reactance” would be $$Z = 50 + j25\ \Omega.$$ The sign is wrong.
- C: “25 ohms resistance in series with 50 ohms inductive reactance” would be $$Z = 25 + j50\ \Omega.$$ Both the values and the sign/type are wrong.
- D: “25 ohms resistance in series with 50 ohms capacitive reactance” would be $$Z = 25 - j50\ \Omega.$$ The resistance and reactance magnitudes don’t match the given impedance.

Rules of thumb:
- If the imaginary part is negative ($-jX$), the reactance is capacitive.
- If the imaginary part is positive ($+jX$), the reactance is inductive.
- A single $R + jX$ implies series combination of resistance and reactance.