The correct answer is C. High thermal conductivity.
A transformer core is a magnetic material that is used to confine the magnetic field produced by the current flowing through the windings of the transformer. The core is typically made of a ferromagnetic material, such as iron or steel, which has a high permeability and a low hysteresis loss.
The permeability of a material is a measure of how easily a magnetic field can be established in the material. A high permeability is desirable for a transformer core because it allows the core to be used to produce a strong magnetic field with a small amount of current.
The hysteresis loss of a material is a measure of the energy that is lost in the material when the magnetic field is changed. A low hysteresis loss is desirable for a transformer core because it reduces the amount of energy that is wasted in the core.
Thermal conductivity is a measure of how easily heat can be transferred through a material. A high thermal conductivity is not necessarily desirable for a transformer core because it can lead to the core overheating.
In conclusion, the correct answer is C. High thermal conductivity.