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

enter image description here

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.

enter image description here 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.

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    $\begingroup$ I think any question about voltages and capacitances is two low-level for computer science. We assume that the zeroes and ones just work; making them happen is for electrical engineers. $\endgroup$ – David Richerby Dec 30 '16 at 18:55
  • $\begingroup$ As I have come up to these diagrams on a computer science course I thought this might be relevant $\endgroup$ – Mert Can Ergün Dec 30 '16 at 19:58
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    $\begingroup$ When the transistors do not have to switch as fast (reduced frequency) the voltage can be reduced (this is called dynamic voltage frequency scaling), though the voltage range is constrained and transistor speed is not the only determiner of frequency. Approximating capacitance per core as constant is somewhat reasonable. Even better energy efficiency can be achieved if the cores are designed for lower performance. This really is more of an EE question. $\endgroup$ – Paul A. Clayton Dec 31 '16 at 1:10

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