*Question E5B09:
What is the relationship between the AC current through a capacitor and the voltage across a capacitor?*  

*Correct Answer is  D: Current leads voltage by 90 degrees*  

### AI Response: (may contain errors)  

In an AC circuit, the relationship between the current through a capacitor and the voltage across it is characterized by a phase difference. Here's how it works:

1. **Correct Answer: D - Current leads voltage by 90 degrees**

   - In a capacitive circuit, the current ($I$) leads the voltage ($V$) by 90 degrees. This means that the current reaches its maximum value a quarter cycle before the voltage does.
   - This phase relationship is due to the nature of capacitors, which store energy in an electric field. When an AC voltage is applied, the capacitor charges and discharges, causing the current to change direction before the voltage does.

2. **Why the other choices are incorrect:**

   - **A: Voltage and current are in phase**  
     This is incorrect because, in a capacitive circuit, the current and voltage are not in phase. They are separated by a phase angle of 90 degrees.

   - **B: Voltage and current are 180 degrees out of phase**  
     This is incorrect because a 180-degree phase difference would mean that when the voltage is at its maximum, the current is at its minimum (and vice versa), which is not the case for capacitors.

   - **C: Voltage leads current by 90 degrees**  
     This is incorrect because, in a capacitive circuit, it is the current that leads the voltage, not the other way around.

3. **Useful Formula:**

   - The phase relationship in a capacitive circuit can be expressed using the impedance of a capacitor, $Z_C$, which is given by:  
     $$Z_C = \frac{1}{j\omega C}$$  
     where:
     - $j$ is the imaginary unit, representing a 90-degree phase shift.
     - $\omega$ is the angular frequency in radians per second.
     - $C$ is the capacitance in farads.

   - The presence of $j$ in the impedance formula indicates that the current leads the voltage by 90 degrees in a purely capacitive circuit.

Understanding this phase relationship is crucial for analyzing AC circuits involving capacitors.