B

Step 1: Understand resonance in an LCR circuit.
A series LCR circuit achieves resonance when the inductive reactance ($X_L$) equals the capacitive reactance ($X_C$). This condition is given by:
$$X_L = rac{1}{rac{1}{ u^2 LC}} = X_C$$
where $L$ is the inductance, $C$ is the capacitance, and $ u$ is the resonant frequency.

Step 2: Analyze the implications of resonance.
At resonance, the total impedance ($Z$) of the circuit is at its minimum, which is equal to the resistance $R$. The impedance of the circuit can be represented as:
$$Z = R + j(X_L - X_C)$$
At resonance, since $X_L = X_C$, the overall impedance simplifies to:
$$Z = R$$
Thus, when the impedance is minimal, it only consists of the resistive part.

Step 3: Evaluate the other options:
- Option A: Voltage across R is not minimum; it is typically maximum due to the minimum impedance.
- Option C: The power transferred is maximum at resonance because power ($P$) is given by:
$$P = rac{V^2}{Z}$$
- Option D: The current amplitude ($I$) is maximum at resonance because $I = rac{V}{Z}$.

Conclusion: Therefore, the correct answer is that the impedance is minimum at resonance.
Hence, the answer is Option B.