*Question E5C02:
How are impedances described in polar coordinates?*  

*Correct Answer is  C: By magnitude and phase angle*  

### AI Response: (may contain errors)  

Impedances in electrical circuits can be represented in different forms, and one of the most useful representations is in polar coordinates.

### Correct Answer: C - By magnitude and phase angle

- **Explanation**: 
  - In polar coordinates, an impedance $Z$ can be expressed as:
  
  $$
  Z = |Z| \angle \theta
  $$
  
  where:
  - $|Z|$ is the magnitude of the impedance (the absolute value).
  - $\theta$ is the phase angle (the angle in degrees or radians).
  
  This representation is particularly useful in AC circuit analysis, as it allows for easy calculations involving phase relationships and magnitudes.

### Why the Other Choices are Incorrect:

- **A: By X and R values**: 
  - This choice refers to the rectangular form of impedance, where $R$ is the real part (resistance) and $X$ is the imaginary part (reactance). While this is a valid way to describe impedance, it is not in polar coordinates.

- **B: By real and imaginary parts**: 
  - Similar to choice A, this describes the rectangular form of impedance, where the impedance is expressed as $Z = R + jX$. Again, this is not the polar representation.

- **D: By Y and G values**: 
  - This choice refers to admittance, which is the reciprocal of impedance. Admittance is expressed in terms of conductance ($G$) and susceptance ($B$), and is not relevant to the question about impedance.

### Useful Formulas or Rules of Thumb:

- To convert from rectangular to polar form:
  
  $$
  |Z| = \sqrt{R^2 + X^2}
  $$
  
  $$
  \theta = \tan^{-1}\left(\frac{X}{R}\right)
  $$

- To convert from polar to rectangular form:
  
  $$
  R = |Z| \cos(\theta)
  $$
  
  $$
  X = |Z| \sin(\theta)
  $$

Understanding these conversions and representations will help you analyze and solve problems related to impedance in both AC and DC circuits effectively.