You're thinking about alternating current (AC) and not direct current (DC) that all electronics work in. I'm not sure about high-end electronics, like a motherboard, but the IoT products we have designed use an oscillator crystal (usually a high frequency and a low frequency) to keep everything in sync / set the clock rate. I'm sure high-end products are similar.

Calin said:
Does increasing the frequency by using the oscillator will also increase the power consumption?

Afaict, the main reason high frequency needs more power is to compensate for leakage. Meaning, higher frequency makes the signals less defined, resulting noise causes errors, so you use higher power to ‘override’ the noise.
You can also make smaller circuits, so less power is needed, but smaller circuits also increase leakage. So there is some sweet spot.

I don't know much about electronics, so can't explain better with proper terminology.

A pseudo-random website from my search engine about power consumption broken down by components.

https://www.buildcomputers.net/power-consumption-of-pc-components.html​

Eventually all power is converted to heat (except a bit to to move air (fans), spin hard-disks, or emit light (screen)).

Overclocking makes the CPU more hot, so yeah, more power is converted to heat.

Of course to dissipate that heat you also need power for cooling your CPU(s).

Calin said:
Does overclocking the CPU will make the motherboard drain more power?

Yes. The CPU needs more power for higher clocks, you need bigger fans as well for better cooling, etc. Overclocking goes beyond the sweet spot.
Contrary, Undervolting attempts to get the sweet spot of maximum efficiency at minimized power draw. (But this might need better cooling as well.)

Calin said:

Does overclocking the CPU will make the motherboard drain more power? The number of transistors on the Cpu die remains the same in this case, so is the size of transistors.

Electrical components all have operating ranges, usually called “absolute maximum ratings” (that can be viewed on their datasheets) that show what the component can handle. As an example, a transistor could have a VDD (power voltage) of minimum 2.5v to a maximum 5.5v. Hardware, like RAM, may default operating at 3.5v. When you overclock hardware you're simply providing more voltage, so let's say 4.5v. Now it's not only consuming more power, but it's also generating more heat. It also shortens the life of the hardware since your pushing the components harder (think of a light bulb; the more voltage the brighter, but it will burn out much quicker). They are improving components all the time to be smaller, run cooler, etc. Engineers are also finding ways to utilize the wasted energy, aka the heat, back into something useful. So a lot of things are becoming a lot more efficient.

On a side note, there are a lot of different ways to save energy as well. For instance, if you have 4 8-segment displays to show a clock, as an example, then each digit needs updated fast enough that it doesn't flicker (you update one digit at a time), which is around 4 ms every “digit”. This is the same as game development since you need a good FPS to now show screen tearing. Anyway, if you have ever programed any firmware you would know that 4 ms is an eternity for a CPU (some things are computed in microseconds). So, between updating the digits you can actually utilize that time for other things (known as time slicing). You can poll button inputs, run state machines, put the device to sleep, etc. If you are using something fast enough, and with enough inputs (aka pins) you can simply put the device to sleep in between updates since no time slicing is needed. If your digit updates every 750 microseconds then you can sleep for the other 3.25 milliseconds since there is nothing to do. That 3.5 milliseconds is huge (we have devices that run on 2 AA's that can last for several years).

I could ramble all night, but I don't want to bore you. I think those are hypothetical enough to give you an idea.