*Question E5B10:
What is the relationship between the AC current through an inductor and the voltage across an inductor?*  

*Correct Answer is  A: Voltage leads current by 90 degrees*  

### AI Response: (may contain errors)  

In an inductor, the relationship between the AC current and the voltage is characterized by a phase difference. 

1. **Correct Answer Explanation**:  
   - The correct answer is **A: Voltage leads current by 90 degrees**.  
   - In an ideal inductor, when an alternating current (AC) flows through it, the voltage across the inductor reaches its maximum value a quarter cycle (90 degrees) before the current does. This is due to the property of inductance, where the inductor opposes changes in current, causing the voltage to rise before the current can follow.

2. **Incorrect Choices Explanation**:  
   - **B: Current leads voltage by 90 degrees**: This is incorrect because, in an inductor, the current lags behind the voltage, not the other way around.
   - **C: Voltage and current are 180 degrees out of phase**: This is incorrect as it suggests that when one is at a maximum, the other is at a minimum, which is not the case for inductors.
   - **D: Voltage and current are in phase**: This is incorrect because in an inductor, the voltage and current are not in phase; they have a phase difference of 90 degrees.

3. **Useful Formulas and Rules of Thumb**:  
   - The relationship can be represented in phasor notation, where:
     - If $V(t) = V_0 \sin(\omega t)$ (voltage), then the current can be expressed as:
     $$I(t) = I_0 \sin\left(\omega t - \frac{\pi}{2}\right)$$
   - This shows that the current lags the voltage by 90 degrees (or $\frac{\pi}{2}$ radians).

Understanding this phase relationship is crucial for analyzing AC circuits involving inductors, especially when calculating impedance and power factor.