Alternating Current

To determine the phase difference between current and voltage in a series LCR circuit at resonance, we need to analyze the circuit's behavior at the resonant frequency.

1. Understanding Series LCR Circuit at Resonance:
In a series LCR circuit:
- Inductor (L) causes voltage to lead current by π/2
- Capacitor (C) causes voltage to lag current by π/2
- Resistor (R) has current and voltage in phase (0 phase difference)

2. At Resonant Frequency:
The inductive reactance (X_L) and capacitive reactance (X_C) become equal:
X_L = X_C
This causes their effects to cancel each other out.

3. Resulting Phase Relationship:
Since:
- The phase lead by L (+π/2)
- The phase lag by C (-π/2)
- Sum to zero phase shift (π/2 - π/2 = 0)
Only the resistive component remains, which has 0 phase difference.

4. Mathematical Representation:
The phase angle (φ) is given by:
tanφ = (X_L - X_C)/R
At resonance, X_L = X_C, so:
tanφ = 0 → φ = 0

5. Physical Interpretation:
This means the current and voltage waveforms are perfectly aligned (in phase) at resonance, reaching their peaks and zero crossings simultaneously.

Final Answer:
The phase difference between current and voltage in a series LCR circuit at resonance is 0.