At resosnance in a series LCR circuit, which of the following statements is true:-

Options

A. Current in the circuit is maximum and phase difference between E and I is `pi//2`
B. Current in the circuit is maximum and phase difference between E and I is zero
C. Voltage is maximum and phase difference between E and I is `pi//2`
D. Current is minimum and phase difference between E and I is zero

Answer

To solve the question regarding the behavior of a series LCR circuit at resonance, we will analyze the conditions and characteristics of the circuit step by step.

### Step-by-Step Solution:

1. **Understanding Resonance in LCR Circuit:**
- In a series LCR circuit, resonance occurs when the inductive reactance (XL) equals the capacitive reactance (XC). This means that the circuit can oscillate at its natural frequency without any net reactance.

2. **Condition for Resonance:**
- At resonance, the condition is given by:
\[ X_L = X_C \]
- This leads to the cancellation of the reactance, resulting in the circuit behaving like a purely resistive circuit.

3. **Impedance at Resonance:**
- The total impedance (Z) of the circuit at resonance is minimized and is equal to the resistance (R) of the circuit:
\[ Z = R \]
- Since the impedance is at its minimum, the current (I) in the circuit is at its maximum:
\[ I = \frac{E}{Z} = \frac{E}{R} \]

4. **Phase Difference Between Voltage and Current:**
- In a purely resistive circuit, the current and voltage are in phase. This means that the phase difference (φ) between the voltage (E) and the current (I) is:
\[ \phi = 0 \]

5. **Analyzing the Options:**
- Now, we will evaluate the provided statements:
- **Option A:** Current in the circuit is maximum and phase difference between E and I is π/2.
- This is incorrect because, at resonance, the phase difference is 0.
- **Option B:** Current in the circuit is maximum and phase difference between E and I is 0.
- This is correct.
- **Option C:** Voltage is maximum and phase difference between E and I is π/2.
- This is incorrect because the phase difference is 0.
- **Option D:** Current is minimum and phase difference between E and I is 0.
- This is incorrect because the current is maximum at resonance.

6. **Conclusion:**
- The correct statement is **Option B:** Current in the circuit is maximum and phase difference between E and I is 0.