## Practical Resistors: Power Rating (Wattage)

### Resistor Self-Heating

As discussed in the section on Resistance and Ohm's Law, inelastic collisions between electrons and resistive materials mean that within a resistor, electrical energy is transformed (briefly) into the kinetic energy of an electron, which is then transformed into heat by the collision.

This causes the mass of the resistor itself to heat up.

If that heat is not removed, the temperature of the resistor will rise.

As the resistor's temperature rises, heat is naturally removed faster in three ways:

• Conduction. A resistor can conduct heat out through its metallic leads to the nearby substrate. This naturally happens faster at higher temperature differences.
• Convection. A resistor will cause convection to the surrounding air, which also naturally happens faster at higher temperature differences.
• Radiation. A resistor's exterior will radiate heat from its surface, which is an extremely temperature-dependent effect.

(Additionally, as the resistor's temperature rises, the resistance itself changes, which we will discuss in the next section on resistor temperature coefficient.)

Over time, equilibrium at some higher-than-ambient temperature is achieved. At this equilibrium point, the resistor is converting electrical energy to heat at the same rate that heat is being removed by one or more of the heat transfer pathways listed above.

Or, if an equilibrium is not established, then the resistor's temperature keeps increasing until the resistor fails.

### Fuses and Resistor Failure

If a resistor's temperature keeps rising, the material within eventually reaches its melting or vaporization point. Poof! The resistor burns itself out and becomes an open circuit.

At any point of localized overheating (or weaker material), the loss of material causes an increase in the local resistance. This causes even further heating at that exact weak point, which causes a cascade of further loss of material, until the resistor burns through completely, open circuit.

This failure can be undesirable: for example, a circuit board trace can break due to overcurrent, leaving a damaged circuit.

Alternatively, this failure can be intentional and desirable: a fuse is a resistor that's designed to fail at a particular current. In design practice, we want to put intentional easy-to-replace fuses (or resettable circuit breakers) in places where they will protect undesired fuses (like permanent circuit board traces or other valuable or hard-to-replace components).

### Resistor Power Rating

Every resistor is sold with a nominal power rating. This power might be $\frac {1} {4} \ \text{W}$ or it might be $10\ \text{W}$. This value is related to the size of the resistor, and in particular, how much area it has to dissipate heat. It's also related to the materials of the resistor.

While a resistor is sold with a power rating, this power rating is really based on a temperature rating -- a temperature at which bad things will start to happen to the resistor.

Usually, this power rating is calculated assuming that heat is dissipated by natural convection to otherwise still air. But, for example, if you're operating this resistor in a vacuum, the true maximum power may be lower because there's no air to move heat away. Or, if you have good cooling (like a huge heatsink and/or a big fan), the true maximum power may be higher because the temperature will be lower.

We haven't talked about time constants yet, but in the case of a resistor, the time constant of interest is the thermal time constant, which has to do with the mass, material, shape, and heat transfer situation. In many cases, this could be on the order of a second or so. This indicates that you may be able to briefly exceed the power rating as long as you don't don't exceed it on average.

For example, if you have a resistor rated for $\frac {1} {4} \ \text{W}$, you can probably discharge through it at $10\ \text{W}$ for just $1 \ \text{ms}$ once per second, with the resistor off for the rest of the second. The average power is just $10 \ \text{mW}$, far less than the $250 \ \text{mW}$ power rating, and this happens for much shorter than the thermal time constant, so the temperature never gets very high. Beware, though, that this kind of cycling may cause stresses in the material: see the Physical Stresses of Mode Transition discussion in the Steady State & Transient section.

If you find yourself in a design situation where you need a certain resistance but need to exceed the power rating, you generally have three options:

• Buy higher-power-rated resistors. These are usually physically larger and more expensive.
• Divide into multiple resistors. You may be able to use multiple resistors in series and parallel to achieve the same effect, and spread the heating across multiple components.
• Redesign circuit to avoid. From an energy efficiency standpoint, it's never great to be burning up lots of energy in a resistor. Consider other ways to accomplish your design goal.

### Fuse Current Rating

Unlike resistors, fuses are usually sold with a specified current rating. Above this current, they will "pop" and become open-circuit.

Fuses nominally have near zero on-resistance, but it's actually often a few milliohms to tens of milliohms. This non-zero resistance is important: it creates the self-heating that causes the fuse to do its job.

(Resettable circuit breakers use a related effect where a bimetallic strip bends when heated, instead of being heating to the point of melting or vaporization.)

### What's Next

In the next section, Practical Resistors: Temperature Coefficient, we'll discuss how resistance changes with temperature before the point of failure.

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