Step 1: Understand the question.
We have an ideal step down transformer. We must pick which quantity becomes larger in the secondary coil out of power, voltage, current, and frequency.
Step 2: Check the power.
An ideal transformer wastes no energy. So the power going in equals the power coming out. Power stays the same, it does not increase.
Step 3: Check the frequency.
A transformer works by changing magnetic field, and it does not change how fast the AC swings. So the frequency stays the same in both coils.
Step 4: Check the voltage.
The words step down mean the transformer lowers the voltage. So the secondary voltage is smaller than the primary voltage. Voltage decreases, not increases.
Step 5: Check the current.
Since power $P = V \times I$ stays the same, if the voltage drops then the current must rise to keep the product the same:
\[ V_p I_p = V_s I_s \]
Because $V_s$ is smaller, $I_s$ must be larger. So the current increases.
Step 6: Write the answer.
The quantity that increases is the current. This matches option (3).
\[ \boxed{\text{Current increases in the secondary}} \]