*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 polar coordinates, impedance is represented as a magnitude and a phase angle. For a pure inductive reactance, the phase angle is $+90$ degrees. This is because inductors cause the current to lag the voltage by $90$ degrees.

### Explanation:

1. **Correct Answer: A positive 90 degree phase angle**
   - **Why it's correct:**  
     - Inductive reactance ($X_L$) is represented as $jX_L$ in complex form, where $j$ is the imaginary unit. In polar form, this is expressed as a magnitude with a $+90$ degree phase angle. This indicates that the voltage leads the current by $90$ degrees, which is characteristic of inductors.

2. **Why the other choices are incorrect:**
   - **A positive 45 degree phase angle:**  
     - This would represent a combination of resistance and inductive reactance, not a pure inductive reactance.
   - **A negative 45 degree phase angle:**  
     - This would represent a combination of resistance and capacitive reactance, not a pure inductive reactance.
   - **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 inductive behavior.

### Useful Formula:

- **Impedance in polar form:**  
  $$ Z = |Z| \angle \theta $$  
  - For a pure inductor, $|Z| = X_L$ and $\theta = +90^\circ$.

Understanding these concepts will help you identify the characteristics of inductive and capacitive reactances in polar coordinates.