Statement-I: At resonance. LCR circuit have a minimum current.
Statement-II: At resonance, in LCR circuit, the current and e.m.f are in phase with each other.

Options

A. If both Statement- I and Statement- II are true, and Statement - II is the correct explanation of Statement– I.
B. If both Statement - I and Statement-II are true but Statement - II is not the correct explanation of Statement – I.
C. If Statement-I is true but Statement-II is false.
D. If Statement-I is false but Statement-II is true.

Answer

To analyze the statements provided in the question regarding the LCR circuit at resonance, let's break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding the LCR Circuit**:
- An LCR circuit consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series. The behavior of this circuit is influenced by the frequency of the alternating current (AC) supplied to it.

**Hint**: Remember that the LCR circuit's behavior is defined by the relationship between inductive reactance (XL), capacitive reactance (XC), and resistance (R).

2. **Resonance Condition**:
- The resonance condition in an LCR circuit occurs when the inductive reactance (XL) equals the capacitive reactance (XC). Mathematically, this is expressed as:
\[ XL = XC \]
- At this point, the circuit is said to be at resonance.

**Hint**: Recall that at resonance, the reactances cancel each other out, leading to a simplified analysis of the circuit.

3. **Impedance at Resonance**:
- The total impedance (Z) of the circuit is given by:
\[ Z = \sqrt{(XL - XC)^2 + R^2} \]
- When XL = XC, the equation simplifies to:
\[ Z = R \]
- This indicates that the impedance is at its minimum value, which is equal to the resistance R.

**Hint**: Impedance is crucial in determining the current in the circuit; lower impedance means higher current.

4. **Current Calculation**:
- The current (I) in the circuit can be calculated using Ohm's law for AC circuits:
\[ I = \frac{E_0}{Z} \]
- Substituting Z with R (at resonance):
\[ I = \frac{E_0}{R} \]
- This shows that at resonance, the current is maximized because Z is minimized.

**Hint**: Think about how current behaves in relation to impedance; lower impedance leads to higher current.

5. **Analysis of Statements**:
- **Statement I**: "At resonance, LCR circuit have a minimum current."
- This statement is **false** because the current is actually at its maximum at resonance.
- **Statement II**: "At resonance, in LCR circuit, the current and e.m.f are in phase with each other."
- This statement is **true** because at resonance, the circuit behaves like a purely resistive circuit, where voltage and current are in phase.

**Hint**: Evaluate each statement based on the definitions and relationships established in the analysis.

6. **Conclusion**:
- Based on the analysis, the correct answer is that Statement I is false and Statement II is true.

### Final Answer:
- **Statement I**: False
- **Statement II**: True