I don't understand what causes the heating effect in a wireElectrons are charge carriers for current, they move (opposite to current, remember, that's the flow of positive charge, odd I know but that's the convention, it makes sense in some places) through the wire. The wire itself is a lattice of atoms, and it's rare, but electrons may "collide" with these lattice atoms. "Collide" because they're just deflected, but we're judging a collision as a very
close deflection, one which transfers a notable amount of the electrons kinetic energy to the nucleus. The more current, the more electrons, the more collisions, the more the atoms get this KE. And we know that lattice vibration <-> temperature of the material.
tl;dr electrons collide, transfer KE, material heats up.
or a higher powerPower dissipated in the wire is given by
i2R where
i is the current. You can say that an increase in current will give rise to more power dissipation across the wire. Alternatively if you give the above wordy argument, you won't need to resort to using equations.