*Question E5A06:
What is the magnitude of the circulating current within the components of a parallel LC circuit at resonance?*  

*Correct Answer is  B: It is at a maximum*  

### AI Response: (may contain errors)  

In a parallel LC circuit, resonance occurs when the inductive reactance ($X_L$) and capacitive reactance ($X_C$) are equal. At this point, the circuit can draw maximum current from the source.

1. **Correct Answer Explanation (B: It is at a maximum)**:
   - At resonance, the impedance of the circuit is minimized, which allows for maximum current to flow through the components. The formula for the resonant frequency ($f_0$) is given by:
   $$
   f_0 = \frac{1}{2\pi\sqrt{LC}}
   $$
   - At this frequency, the circulating current in the LC circuit reaches its peak value because the energy oscillates between the inductor and capacitor with minimal resistance.

2. **Incorrect Choices Explanation**:
   - **A: It is at a minimum**: This is incorrect because at resonance, the impedance is at its lowest, allowing maximum current to circulate, not minimum.
   - **C: It equals 1 divided by the quantity 2 times pi, times the square root of (inductance L multiplied by capacitance C)**: This choice describes the resonant frequency ($f_0$), not the magnitude of the circulating current. The current does not equal this value.
   - **D: It equals 2 times pi, times the square root of (inductance L multiplied by capacitance C)**: This is also incorrect as it misrepresents the relationship. The current does not equal this expression; rather, it is related to the resonant frequency.

3. **Useful Formulas**:
   - Resonant frequency:
   $$
   f_0 = \frac{1}{2\pi\sqrt{LC}}
   $$
   - Impedance at resonance for a parallel LC circuit is very low, leading to high circulating currents.

In summary, at resonance in a parallel LC circuit, the circulating current is at a maximum due to the minimized impedance, allowing for efficient energy transfer between the inductor and capacitor.