I was searching for OpenMP tutorials and I came up a video that showed some simple equations that promotes multiple core hierarchies against single core ones. The equations used are
Capacitance = Ability to store energy
C=q/V ⇒ q=CV
Work = Moving charge across voltage
W=Vq ⇒ W=CV^2
Power = Work over a period of time
P=Wf ⇒ P=CV^2f
It then proceeds to calculate power requirement of a single core processor as
Ps = CsVs^2fs
where Xs stands for X used on single core system.
It then goes on to calculate it for a dual core system responsible for doing the same work. But it uses following parameters (Not exactly 2 or 0.5 multipliers but they just make the problem more easier to understand):
Cd = 2Cs Vd = 0.5Vs fd = 0.5fs
Power is calculated as
Pd = 0.25Ps
I don't get why voltage and capacitance are altered.
The video is over here youtu.be/cMWGeJyrc9w?t=3m45s, if time link doesn't work for you, it starts about 3:45.