*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 involving a capacitor, the relationship between the current and voltage is defined by the phase difference between them.

1. **Correct Answer: Current leads voltage by 90 degrees**  
   - In a capacitor, the current ($I$) leads the voltage ($V$) by a quarter of a cycle, or 90 degrees. This means that when the voltage across the capacitor reaches its maximum value, the current is already at its maximum value. This relationship can be expressed mathematically as:
   $$ I(t) = C \frac{dV(t)}{dt} $$
   where:
   - $I(t)$ = instantaneous current
   - $C$ = capacitance in farads
   - $V(t)$ = instantaneous voltage

2. **Why the other choices are incorrect:**
   - **A: Voltage and current are in phase**  
     This is true for resistive circuits, where voltage and current reach their maximum values simultaneously. In a capacitive circuit, this is not the case.
   
   - **B: Voltage and current are 180 degrees out of phase**  
     This describes a purely resistive load where the current and voltage are equal in magnitude but opposite in direction at any given time. This does not apply to capacitors.
   
   - **C: Voltage leads current by 90 degrees**  
     This is the opposite of the correct relationship. In capacitors, it is the current that leads the voltage, not the other way around.

3. **Useful formulas and rules of thumb:**
   - For capacitors in AC circuits, remember:
     - Current leads voltage by 90 degrees.
     - The relationship can be visualized using phasor diagrams, where the current phasor is rotated ahead of the voltage phasor by 90 degrees.
   - The capacitive reactance ($X_C$) can be calculated using:
   $$ X_C = \frac{1}{2 \pi f C} $$
   where:
   - $f$ = frequency in hertz
   - $C$ = capacitance in farads

Understanding these relationships is crucial for analyzing AC circuits involving capacitors, especially for the Extra Class exam.