*Question E5A07:
What is the magnitude of the current at the input of a parallel RLC circuit at resonance?*  

*Correct Answer is  A: Minimum*  

### AI Response: (may contain errors)  

In a parallel RLC circuit at resonance, the magnitude of the current at the input is at its **minimum**. Here's why:

1. **Why the Correct Answer is Correct (Minimum):**
   - At resonance, the inductive reactance ($X_L$) and capacitive reactance ($X_C$) are equal in magnitude but opposite in phase. This causes them to cancel each other out, resulting in a purely resistive circuit.
   - The impedance of the circuit is at its maximum because the reactive components cancel, leaving only the resistance ($R$) to oppose the current.
   - Since impedance is maximum, the current, which is inversely proportional to impedance, is at its minimum.

2. **Why the Other Choices are Incorrect:**
   - **Maximum (Choice B):** This would be true for a series RLC circuit at resonance, where impedance is minimum. However, in a parallel RLC circuit, impedance is maximum at resonance, leading to minimum current.
   - **R/L (Choice C):** This expression does not relate to the current magnitude at resonance in a parallel RLC circuit. It is more relevant to time constants in RL circuits.
   - **L/R (Choice D):** Similar to Choice C, this expression is not applicable to the current magnitude at resonance in a parallel RLC circuit. It is also related to time constants in RL circuits.

3. **Useful Formulas:**
   - Impedance at resonance in a parallel RLC circuit:  
     $$Z = R$$
   - Current at resonance:  
     $$I = \frac{V}{Z} = \frac{V}{R}$$  
     Since $Z$ is maximum, $I$ is minimum.

Understanding these concepts will help you determine the behavior of parallel RLC circuits at resonance.