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Idle power actually decreases if you decide to switch off CPU cores, but the difference isn’t large, thanks to optimizations in Intel's architecture that shut down unused execution resources when they're not in use anyway. We measured savings of 2% between six cores and just one.
Peak power scales very linearly. If you were to switch off five out of the six cores, our Core i7-980X machine would require only 122W at peak load rather than 223W. This would be a single-core 32 nm processor with 12MB L3 cache and a 3.2 GHz clock speed running at only 54% of the peak power of six cores. Keep in mind that performance drops much more, though. This is just a hypothetical example.