Step 1: Recall the definition of resolution.
Resolution is the smallest change in the measured quantity that an instrument can detect.
Step 2: Determine the resolution.
Since the smallest scale division of the voltmeter is
\[
0.5\,\text{V},
\]
its resolution is
\[
\boxed{0.5\,\text{V}.}
\]
Therefore,
\[
\boxed{(A)}
\]
is the correct answer.