Assertion : At resonance, LCR series circuit have a minimum current.
Reason : At resonance, in LCR series circuit, the current and e.m.f. are not in phase with each other.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Answer

To solve the given problem, we need to analyze the assertion and reason provided in the context of an LCR series circuit at resonance.

### 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 the circuit changes with frequency, particularly at resonance.

2. **Resonance Condition**:
At resonance, the inductive reactance (X_L) equals the capacitive reactance (X_C). This can be expressed mathematically as:
\[ X_L = X_C \quad \Rightarrow \quad \omega L = \frac{1}{\omega C} \]
where \(\omega\) is the angular frequency.

3. **Impedance at Resonance**:
The total impedance (Z) of the circuit at resonance can be calculated as:
\[ Z = R \quad \text{(since \(X_L = X_C\) cancels out)} \]

4. **Current Calculation**:
The current (I) in the circuit can be calculated using Ohm's law:
\[ I = \frac{E}{Z} = \frac{E}{R} \]
At resonance, the current is at its maximum because the impedance is minimized (equal to R).

5. **Phase Relationship**:
The phase angle (\(\phi\)) between the current and the voltage (e.m.f.) is given by:
\[ \tan \phi = \frac{X_L - X_C}{R} \]
At resonance, since \(X_L = X_C\), we have:
\[ \tan \phi = 0 \quad \Rightarrow \quad \phi = 0 \]
This means that the current and e.m.f. are in phase with each other at resonance.

6. **Evaluating the Assertion and Reason**:
- **Assertion**: "At resonance, LCR series circuit have a minimum current."
- This is **false**; the current is actually at a maximum at resonance.
- **Reason**: "At resonance, in LCR series circuit, the current and e.m.f. are not in phase with each other."
- This is also **false**; they are in phase at resonance.

7. **Conclusion**:
Both the assertion and the reason are false. Therefore, the correct option is that both the assertion and reason are incorrect.

### Final Answer:
Both the assertion and the reason are false.