Introductory Circuit Analysis—power ratings

[JessicaHelena]

TL;DR

If you calculate the power dissipated as 0.1 watts, then a 0.25-watt resistor can handle this amount of power. A 0.125-watt resistor should be able to handle that amount as well. Given P=0.1, how do you get these numbers (0.25 and 0.125)?

I am going through "Circuit Analysis for Dummies". On pg 18, it says, "If you calculate the power dissipated as 0.1 watts, then a 0.25-watt resistor can handle this amount of power. A 0.125-watt resistor should be able to handle that amount as well, but when it comes to power ratings, err on the larger side."

The only information they had provided prior to this are these two well-known equations, P=i^2*R and p = v^2/R. Given P = 0.1, how do I get the resistance without the voltage or current? I've gone far back into the book to ascertain that I'm not really missing other values...

 

[Borek]

Given P = 0.1, how do I get the resistance without the voltage or current?

You can't.

But I feel like you are trying to approach the problem from the wrong side. In a typical situation, when you design the circuit, you know what kind of load to expect - you either know what its the voltage applied, you know what is the resistance, or you know what current will be flowing - you always have some kind of data that allows you to predict power that will be involved. THEN you choose the rating, not the other way around.

 

[BvU]

Hi,

how do I get the resistance

You don't. This is about the product of current and voltage, not about their ratio.

So, while e.g. designing a circuit with a resistance of 1 k$\Omega$, you know that a 0.1 W resistor can handle up to 10 mA (I²R) and 10 Volt (V²/R).

( a lot slower than Borek )

 

[anorlunda]

You can hear it the third time. You don't. Resistance is defined as the ratio of voltage to current.

The max power of a device depends on how well it gets rid of heat, and how high it's temperature can get. Those things have nothing to do with the circuit analysis.

The heat produced that you have to get rid of is P=I²R.

 

[NascentOxygen]

Summary: If you calculate the power dissipated as 0.1 watts, then a 0.25-watt resistor can handle this amount of power. A 0.125-watt resistor should be able to handle that amount as well. Given P=0.1, how do you get these numbers (0.25 and 0.125)?

When resistors are manufactured, not only are they made to have certain resistance values (measured in ohms), they are also produced in a range of physical sizes. The larger the physical size, the more power (measured in watts) it can dissipate into the air without its temperature getting so hot that it melts or its paint starts smoking. So a 100 ohm resistor of tiny physical size cannot handle more than a tiny fraction of a watt before getting damaged by the heat, whereas a physically bigger 100 ohm resistor can dissipate more watts before it starts smoking. Manufacturers make resistors in a wide range of physical sizes to offer designers standard power ratings that include one-eighth watt (0.125 W), ¼ watt (0.25 W), ½ watt, 1 watt, 5 watts, and so on. A resistor that can handle more wattage is physically bigger and bulkier and it costs more.

 

[Tom.G]

Summary: If you calculate the power dissipated as 0.1 watts, then a 0.25-watt resistor can handle this amount of power. A 0.125-watt resistor should be able to handle that amount as well. Given P=0.1, how do you get these numbers (0.25 and 0.125)?

how do I get the resistance without the voltage or current?

That question is a bit unclear.
Did you mean

• "...without both the voltage or current?"
• "...without either the voltage or current?"

There are a total of four values involved, W, E, I, R. Given any two, the other two can be found.
W=E⋅I,
W=I²⋅R
W= E²/R

And of course the commonly known:
E=I⋅R

Common resistor power ratings in Watts are:
0.125, 0.250, 0.5, 1, 2, 3, 5, 7, 10, 15, 25, 50.
Those are the 'Standard' wattage ratings, the values that manufacturers decided were adequate to cover most applications without much of a size or cost penalty for the user.

By the way, for general-use, the common rule-of-thumb is "choose dissipation capability not less than twice the expected dissipation." For instance if you calculate 230mW dissipation, use a 1/2W resistor.

This keeps the operating temperature down. And since electrical (and physical) lifetime halves for every 10°C rise in temperature, that yields an acceptable lifetime and failure rate.

Hope this helps!

Cheers,
Tom

 

[Windadct]

Also - the way Resistors are rated has to do with assumptions about their environment, where they are located and how much heat they can get rid off ( dissipate). If you were to wrap a 0.125 W resistor in tape ( or conformal coating) and then have it operate in the range of 0.1W -- it is much more likely likely that the resistor will overheat and fail than a 0.25W one.

So the standard ratings of 0.125, 0.25 ... etc - correlate to their PHYSICAL size and construction of the resistors. The physical system must be able to get rid of the heat.