Why is the primary winding wire of a voltage step-up transformer usually a larger size than that of the secondary winding?

In an ideal transformer, input power equals output power. Power is the product of voltage and current (P = E x I). If a transformer steps up the voltage on the secondary side, it must proportionally step down the current to maintain the same power on both sides. Because of this inverse relationship, a step-up transformer will have a primary winding that experiences lower voltage but much higher current compared to the secondary winding. To safely handle this higher current without melting or suffering severe resistive heat losses, the primary winding requires a thicker (larger size) wire.