You might be wondering whether reducing the clock rate actually reduces total energy consumption, since after all any given task has to do a certain amount of work, which is going to require the same number of clock cycles regardless of the speed.
The answer is yes, though the reason isn't obvious: it's because reducing the frequency of a modern CPU also reduces the voltage, which among other things reduces the energy needed to charge the various capacitances in the system, most of which ultimately gets wasted. Or, to put it another way, in any given clock cycle a certain number of electrons need to flow in various parts of the CPU regardless of the voltage, so lower voltage means less energy, since electrical energy is voltage times charge, or joules = volts * coulombs.
Speaking of, what is the symbol for energy in electronics, since voltage is E (electromotive force)? Since Q is charge, I guess you could just use V for voltage and say E = V • Q? Of course, Q is also reactance. I'm so confused. Physics is a lot more consistent.