*Question E5B03:
How is impedance in polar form converted to an equivalent admittance?*  

*Correct Answer is  B: Take the reciprocal of the magnitude and change the sign of the angle*  

### AI Response: (may contain errors)  

To convert impedance in polar form to an equivalent admittance, you need to understand the relationship between impedance ($Z$) and admittance ($Y$). Admittance is the reciprocal of impedance.

1. **Correct Answer Explanation (B):**  
   - **Reciprocal of the Magnitude:** If the impedance is given as $Z = |Z| \angle \theta$, the magnitude of the admittance $|Y|$ is the reciprocal of the magnitude of the impedance:  
     $$|Y| = \frac{1}{|Z|}$$
   - **Change the Sign of the Angle:** The angle of the admittance is the negative of the angle of the impedance:  
     $$\angle Y = -\theta$$
   - Therefore, the admittance in polar form is $Y = \frac{1}{|Z|} \angle -\theta$.

2. **Why the Other Choices are Incorrect:**
   - **Choice A:** "Take the reciprocal of the angle and change the sign of the magnitude" is incorrect because angles are not reciprocated in polar form conversions. The magnitude should be reciprocated, not the angle.
   - **Choice C:** "Take the square root of the magnitude and add 180 degrees to the angle" is incorrect because the square root operation and adding 180 degrees do not apply to converting impedance to admittance.
   - **Choice D:** "Square the magnitude and subtract 90 degrees from the angle" is incorrect because squaring the magnitude and subtracting 90 degrees are not part of the conversion process from impedance to admittance.

3. **Useful Formula:**
   - The relationship between impedance and admittance in polar form is given by:  
     $$Y = \frac{1}{Z} = \frac{1}{|Z|} \angle -\theta$$

Understanding these concepts will help you correctly convert impedance to admittance in polar form.