Short Note: Understanding equation through a mechanical analogue

Lets intuitively understand why Power(P) = Voltage(V) x Current(I) through a mechanical analogue. Power means delivering some amount of energy per second. In electricity, energy is delivered to a system when electrons passing through it move from a higher potential (high energy) to a lower potential (low energy). Total energy delivered per electron is proportional to potential difference (V).

Consider a ball of mass falling from height . Energy is . Lets say that 1 such ball comes to your door at the ground level every second and gives all of its energy (It can give you its energy by moving a turbine blade, a windmill etc. Lets assume perfect energy conversion). So Power is (Note t=1 sec). Another equivalent scenario is you have a ball that starts out at height i.e it has energy . Lets assume that 2 such balls appear at your door every second and give you all their energy.

as before.

So:
Power=Potential energy of each ball x No of balls giving up energy per second

In the electrical case:

Power=Energy lost by the electron(U) x No of electrons passing per-second(N)

If is the potential difference, the Energy difference is . is the electron charge. So

Here:

Current(I)=charge of electron(e) x No of electrons passing per second(N)

So you can double your current (double the “balls”) and halve the potential difference (decrease height of “balls” by half) and still have the same power. Current in our mechanical analogue represents the number of balls you get per second while potential(V) represents the gravitational potential.