Question

what is the relationship between the amount of electric current passed and the heat produced.....

Answer 1

electric current = I
heat = H
Resistance = R
time = t
potential velocity= V

relationship :
H= V×I×t

and also,

H = I^2 × R × t

Answer 2

when electricity is passed  through a conductor it generates heat. this is known as heating effect of electric current.according to joules law of heating effect the amount of electric current passing through a conductor is directly proportional to the amount of heat generated.if the electric current passing through the conductor is more then the amount of heat generated will also be more.