Ohm's Law for a series circuit is \(I = \frac{V}{R}\), with \(V\) representing voltage and \(R\) representing resistance. When resistance is doubled (\(R \to 2R\)) while voltage is held constant, the new current is calculated as:
\[
I_{\text{new}} = \frac{V}{2R} = \frac{1}{2} \cdot \frac{V}{R} = \frac{I}{2}
\]
Consequently, the current is halved, making option (2) the correct choice.