*Question E5C03:
Which of the following represents a pure inductive reactance in polar coordinates?*  

*Correct Answer is  C: A positive 90 degree phase angle*  

### AI Response: (may contain errors)  

In AC circuit analysis, reactance is the opposition to the flow of alternating current caused by inductors and capacitors. Inductive reactance is represented in polar coordinates by a phase angle.

### Correct Answer: C - A positive 90 degree phase angle

1. **Why the correct answer is correct:**
   - A pure inductor has a reactance that causes the current to lag the voltage by 90 degrees. In polar coordinates, this is represented as a positive 90-degree phase angle. This means that if you were to plot the voltage and current on a complex plane, the current vector would be rotated 90 degrees counterclockwise from the voltage vector.

2. **Why the other choices are incorrect:**
   - **A: A positive 45 degree phase angle**  
     - This represents a combination of resistive and reactive components, not purely inductive.
   - **B: A negative 45 degree phase angle**  
     - Similar to A, this indicates a combination of resistive and reactive components, but with the current leading the voltage, which is not characteristic of a pure inductor.
   - **D: A negative 90 degree phase angle**  
     - This represents a pure capacitive reactance, where the current leads the voltage by 90 degrees, which is the opposite of what occurs in a pure inductor.

### Useful Rules of Thumb:
- **Inductive Reactance ($X_L$)**: The formula for inductive reactance is given by:
  $$X_L = 2 \pi f L$$
  where:
  - $f$ = frequency in hertz
  - $L$ = inductance in henries

- **Phase Relationships**:
  - For a pure inductor: Current lags voltage by 90 degrees (positive 90 degrees in polar).
  - For a pure capacitor: Current leads voltage by 90 degrees (negative 90 degrees in polar).

Understanding these relationships will help you identify the characteristics of inductive and capacitive reactance in AC circuits.