What happens when voltage is too high?

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Things like resistors will fail from excessive power dissipation- they get too hot and the materials they are made from suffer irreversible degradation. For example, the lacquer on the outside of a through-hole resistor may discolor or burn off, the resistance value change as the element oxidizes until finally it changes out of spec or opens up and starts arcing. Wires and PCB traces behave like resistors- too much current and the insulation burns off, the PCB delaminates or the trace opens up.

In low voltage circuits usually the voltage rating is not an issue- but if you were to take (say) an ordinary 0805 20M resistor and apply 2kV to it the power would be (in theory) only 200mW (which might be in spec or slightly outside of it) but the resistor could arc over and cause irreversible damage almost instantly. Similarly, you can have arcing between traces.

Things like capacitors and MOSFET gate oxide can fail when they are exposed to excessive potential which causes irreversible damage to the insulation. There will be some very localized heating (or more depending on what happens after the insulation is punctured) but that's not the main cause.

Things like diode and transistor junctions have breakdown voltages above which the current increases rapidly with voltage (sometimes they snap on with an avalanche/negative resistance characteristic). If the current is limited to that the heating is kept to a sensible amount (and doesn't increase too fast so that the heating is not localized to tiny areas) then this can be non-destructive. Otherwise the junctions can heat until they are not longer good semiconductor junctions any longer (in the hundreds of degrees C to destroy a silicon junction).

Getting back to your specific question about resistors- none of the voltages you mention is likely to run into a maximum voltage specification on the resistors (anything under about 25V you can forget about for resistors that are not an inhalation hazard).

So you're left with maximum power dissipation (and maybe maximum current if the resistance value is stupidly low, but let's ignore that). Here is a datasheet for a series of resistors, say we have a 10\$\Omega\$ resistor 0805 size. Rated power is shown as 0.125W and maximum working voltage as 150V. If you look at the "Power Derating Curve":

.. you can see that the rated power holds for ambient temperatures up to 70°C, but above that you must consider the rating to be less, according to the curve. Why does it level off at 70 degrees? Most likely the resistor would survive okay at >100% power if the ambient is kept cool, but the manufacturer does not want us testing that.

Recall that power dissipation of a resistor is $$P=I^2R$$ or $$P=V^2/R$$

(since power is $$V\cdot I $$ and Ohm's law).

In your first example, the resistance is fixed and you double the voltage- so the power should go up by 4:1. (from 20W to 80W) If your resistor is rated for 80W or more (under the conditions it sees in your box) then all will be fine. Otherwise, it may not be. Damage is caused by the heating, which is the product of voltage and current (obviously the current increases because the voltage is increased).

In your second example, you've doubled the resistance and the power is now 40W rather than 20W. If the resistor is rated for 40W then all will be fine.

The third example also results in 40W of dissipation. So if the resistor is good for 40W you're fine.

Voltage Too High, Too Low

Voltage that is too high can cause premature failure of electrical and electronic components (e.g. circuit boards) due to overheating. The damage caused by overheating is cumulative and irreversible. Frequent episodes of mild overheating can result in the same amount of component damage as a few episodes of severe overheating. Like slicing a loaf of bread – you can have many thin slices or a few really thick slices – but when you get to the end, you’re done.

Motors can, on the other hand, often benefit from voltages that tend to be a little bit high. The reason is fairly simple. As the voltage level goes up, the current is reduced and lower current usually equates to less heat generation within the motor windings. There is a point where the voltage level supplied can be so high as to damage a motor but this level is far higher than that for electronics.

Keeping electrical and electronic components cool tends to insure their longevity. Slight reductions in voltage levels may permit many electronics to perform perfectly well while minimizing their temperature. Of course, the same is not true of motors.

Just as higher voltages can help reduce motor operating temperatures, low voltage is a major cause of motor overheating and premature failure. A low voltage forces a motor to draw extra current to deliver the power expected of it thus overheating the motor windings. The rule of thumb for motors is “for every 10 degrees C (50 degrees F) a motor is operated above its rated temperature, motor life will be decreased by 50%”.

More than motors and circuit boards are at risk for damage when voltage levels are bad, but chronic problems with either is often an indication of a voltage problem.