Yes, an induction cooker will generally use less power if the pan's area is smaller than the area of the cooktop (the coil area). This is because induction cookers are designed to heat only the area in direct contact with the pan.
Induction cookers work by creating an electromagnetic field that generates heat directly in the pan. The magnetic field induces electrical currents in the pan, which in turn generates heat. Since the heat is generated in the pan itself, any area of the cooktop that is not covered by the pan will not receive direct heating.
If the pan's area is smaller than the cooktop, the unused portions of the cooktop will not generate heat, resulting in reduced energy consumption. The cooker's energy usage is typically proportional to the heat required to warm the food or liquid in the pan, so using a smaller pan will require less energy.
However, it's worth noting that using a significantly smaller pan than the cooktop's area may lead to some energy loss due to heat dissipation around the edges of the pan. To maximize energy efficiency, it's generally recommended to use a pan that is reasonably sized and covers a substantial portion of the cooktop.