*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 AC circuit, the relationship between the voltage across an inductor and the current through it is characterized by a phase difference. This is due to the inductive reactance, which causes the voltage to lead the current.

### Explanation:

1. **Correct Answer: Voltage leads current by 90 degrees (Choice A)**
   - In an inductor, the voltage ($V$) across it leads the current ($I$) by 90 degrees. This is because the inductor resists changes in current, causing the current to lag behind the voltage. This phase relationship is a fundamental property of inductors in AC circuits.

2. **Why the Other Choices are Incorrect:**
   - **Choice B: Current leads voltage by 90 degrees**  
     This is incorrect because, in an inductor, the current lags the voltage, not the other way around. This behavior is opposite to that of a capacitor, where the current leads the voltage.
   
   - **Choice C: Voltage and current are 180 degrees out of phase**  
     This is incorrect because a 180-degree phase difference would imply that the voltage and current are completely out of phase, which is not the case for an inductor. This scenario is more typical of a purely resistive circuit with a negative power factor.
   
   - **Choice D: Voltage and current are in phase**  
     This is incorrect because, in an inductor, the voltage and current are not in phase. In-phase behavior is characteristic of purely resistive components, where the voltage and current rise and fall together.

### Useful Formula:

The relationship between voltage and current in an inductor can be expressed using the formula for inductive reactance ($X_L$):

$$
V = I \cdot X_L
$$

Where:
- $V$ is the voltage across the inductor.
- $I$ is the current through the inductor.
- $X_L = 2\pi f L$ is the inductive reactance, with $f$ being the frequency and $L$ the inductance.

This formula shows that the voltage is proportional to the rate of change of current, reinforcing the concept that voltage leads current by 90 degrees in an inductor.