Joule’s Law of Heating, also called heating effect, is a mathematical description of rate at which resistance in a circuit converts electrical energy to heat energy.
The S.I unit of heating effect is joules.
Heating effect is directly proportional to the square of current, $H \propto I^2$
Heating effect is directly proportional to resistance, $H \propto R$
Heating effect is directly proportional to time taken, $H\propto t$
Hence,
$$ H \propto I^2Rt\\H=I^2Rt,[k = 1] $$
Substituting Ohm’s Law($I=\frac{V}R$),
$$ H=(\frac{V}R)^2Rt\\H=\frac{V^2}{R}Rt\\H=\frac{V^2}{R}t $$
Substituting Ohm’s Law($R = \frac{V}I$),
$$ H=I^2(\frac{V}I)t\\H=VIt $$
These are the three equations for heating effect. All equal, but can be used to solve for different variables.
I have restated the three formulas:
$$ \text{Formula \#1: }H=I^2Rt\\\text{Formula \#2: }H=(\frac{V^2}I)t\\\text{Formula \#3: }H=VIt $$
Power is the rate of work done($P=\frac{W}t$)