Step 1: Understanding transformers.
In an ideal transformer, the voltage and current are related through the turns ratio. For a step-up transformer, the voltage in the secondary coil is higher than that in the primary coil.
Step 2: Current and voltage relation.
According to the law of conservation of energy and the transformer equation, when the voltage increases in the secondary coil, the current decreases. This inverse relationship ensures that the power transferred remains constant.
Step 3: Conclusion.
Thus, in a step-up transformer, the current in the secondary coil is less than the current in the primary coil.
\[
\boxed{\text{Correct Answer: Less}}
\]