*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 polar coordinates are described by their **magnitude** and **phase angle**. This is because polar coordinates represent a complex number in terms of its distance from the origin (magnitude) and the angle it makes with the positive real axis (phase angle).

### Explanation:

1. **Correct Answer: C - By magnitude and phase angle**
   - In polar form, an impedance $Z$ is expressed as $Z = |Z| \angle \theta$, where:
     - $|Z|$ is the magnitude of the impedance.
     - $\theta$ is the phase angle in degrees or radians.
   - This form is useful for understanding the total effect of an impedance on both the amplitude and phase of an AC signal.

2. **Why the other choices are incorrect:**
   - **A: By X and R values**
     - This describes impedance in rectangular coordinates, where $R$ is the resistance (real part) and $X$ is the reactance (imaginary part).
   - **B: By real and imaginary parts**
     - This is another way to describe impedance in rectangular form, where the impedance $Z = R + jX$.
   - **D: By Y and G values**
     - These refer to admittance, not impedance. Admittance is the reciprocal of impedance and is described by conductance ($G$) and susceptance ($B$).

### Useful Formulas:

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

Understanding these concepts will help you analyze AC circuits and solve problems involving impedance in different forms.