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Do multi-core processors reduce power consumption?

lets say if I have a processor that operates at frequency f. The output power is $$ CV^2f $$ where V is the voltage, and C is the capacitance. … And for each of the processor, voltage will be V (they are in parallel). And the Capacitance will be 2C (C1+C2) for parallel. …
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Do multi-core processors reduce power consumption?

Since we can keep cramming transistors into a processor (Moore’s law has slowed … but it’s not dead) but the power delivered to a socket is fixed, the industry has no choice but to add cores. … And This link explains the relation between voltage and frequency: How does power consumption vary with the processor frequency in a typical computer? Hope it helps everyone reading this. …
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