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 assertion and reason question, we need to analyze both the assertion and the reason in the context of an LCR series circuit at resonance.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that "At resonance, LCR series circuit have a minimum current."
- In an LCR series circuit, resonance occurs when the inductive reactance (XL) equals the capacitive reactance (XC). At this point, the impedance (Z) of the circuit is minimized and is equal to the resistance (R) of the circuit.

2. **Analyzing the Impedance**:
- The impedance of an LCR circuit is given by the formula:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
- At resonance, since \(X_L = X_C\), the impedance simplifies to:
\[ Z = R \]
- Therefore, at resonance, the impedance is at its minimum value, which is equal to R.

3. **Current at Resonance**:
- According to Ohm's Law, the current (I) in the circuit can be expressed as:
\[ I = \frac{V}{Z} \]
- Since Z is minimized at resonance (Z = R), the current is maximized:
\[ I = \frac{V}{R} \]
- Thus, the assertion that the current is minimum at resonance is **false**.

4. **Understanding the Reason**:
- The reason states that "At resonance, in LCR series circuit, the current and e.m.f. are not in phase with each other."
- At resonance, the voltage (e.m.f.) and current are indeed in phase. This means that the phase difference (φ) between the voltage and current is zero:
\[ \tan(\phi) = \frac{X_L - X_C}{R} = 0 \quad \Rightarrow \quad \phi = 0 \]
- Therefore, the reason that the current and e.m.f. are not in phase is also **false**.

5. **Conclusion**:
- Both the assertion and the reason are incorrect. Therefore, the correct answer is that both the assertion and the reason are false.

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