Step 1: Recall the condition of parallel resonance.
At resonance,
\[
X_L=X_C.
\]
The inductive and capacitive branch currents are equal and opposite, so they cancel each other.
Step 2: Determine the line current.
Since the reactive currents cancel,
\[
\boxed{\text{The source (line) current becomes minimum.}}
\]
Hence,
\[
\boxed{(B)}
\]
is the correct answer.