# Power Dissipated by a Resistor? Circuit Reliability and Calculation Examples

January 14, 2020 In electronics, dissipation is a fairly common word, and those who work in the industry know it all too well, or at least they should. I say should, because obviously, that is not always the case. Well, I will elaborate in more detail as to why I said should momentarily. But for now, let's focus on the subject of dissipation.

Take, for example, a fully charged capacitor, such as a 3.0-farad capacitor, in use in an audio system. In this instance, if you are removing the capacitor for storage, replacement, or conducting maintenance on the system, you definitely want the capacitor to dissipate its charge.

That was a point that a certain gentleman failed to understand, even after providing him with meticulous details along with the necessary steps. However, failure to follow proper discharge protocols plus capacitor rolling around in trunk plus WD-40 equals the event that could have inspired one of my favorite bands (The Power Station) to write one of my favorite songs (Some Like it Hot). All jokes aside, the heat was on in his trunk, and to this day, his nick-name is still puff-smoky-smoke.

## What is Power Dissipation?

The definition of power dissipation is the process by which an electronic or electrical device produces heat (energy loss or waste) as an undesirable derivative of its primary action. Such as the case with central processing units, power dissipation is a principal concern in computer architecture.

Furthermore, power dissipation in resistors is considered a naturally occurring phenomenon. The fact remains that all resistors that are part of a circuit and has a voltage drop across it will dissipate electrical power. Moreover, this electrical power converts into heat energy, and therefore all resistors have a (power) rating. Also, a resistor’s power rating is a classification that parameterizes the maximum power that it can dissipate before it reaches critical failure.

As you may know, the unit Watt (W) is how we express power, and the formula for power is P (power) = I (current) x E (voltage). In regards to the laws of physics, if there is an increase in voltage (E), then the current (I) will also increase, and the power dissipation of a resistor, will, in turn, increase as well. However, if you increase the value of the resistor, current will decrease, and the resistor’s power dissipation will decrease as well. This correlation follows Ohm's law, which states the formula for current as I (current) = V (voltage) ÷ R (resistance).

## Calculating the Power Dissipated by a Resistor

In the field of electronics, power dissipation is also a measurement parameter that quantifies the releasing of heat within a circuit due to inefficiencies. In other words, power dissipation is a measure of how much power (P = I x E) in a circuit is converted into heat. As I mentioned earlier, each resistor has a power rating, and in terms of design, this allows designers to assess whether or not a particular resistor will meet their design needs within a circuit. So, now, let’s take a closer look at how to calculate this critical design parameter. Firstly, according to Ohm's law,

V (voltage) = I (current) × R (resistance)

I (current) = V (voltage) ÷ R (resistance)

P (power) = I (current) × V (voltage)

Therefore, to calculate the power dissipated by the resistor, the formulas are as follows:

P (power dissipated) = I2 (current) × R (resistance)

or

P (power dissipated) = V2 (voltage) ÷ R (resistance)

So, using the above circuit diagram as our reference, we can apply these formulas to determine the power dissipated by the resistor.

Voltage = 9V

Resistance = 100Ω

I (current) = 9V ÷ 100Ω or I (current) = 90 mA

P (power) = 90 mA × 9V or P (power) = .81 W or 810 mW

P (power dissipated) = V2 (voltage) ÷ R (resistance)

or

P (power dissipated) = 92 ÷ 100

or

P (power dissipated) = 81 ÷ 100 or P (power dissipated) = 810 mW

## Power Dissipation: Good or Bad?

Generally speaking, no; however, there are some instances where heat dissipation is a good thing. Take, for example, electric heaters that use resistance wire such as Nichrome. Nichrome is a unique heating element due to its cost-effectiveness, resistance to the flow of electrons, strength, flexibility, resistance to oxidation, and stability in high temperatures.

Also, another instance where heat dissipation is favorable is with incandescent light bulbs, which are in use as cost-effective heaters. Overall, under normal circumstances, heat dissipation is not desirable, but on the rare occasions that it is, it will then consist of efforts to control the heat dissipation rather than moderate it.

Now here are some essential points of emphasis when approaching power dissipation.

1. Ensure your resistor's power rating meets your circuit design needs.

2. Be sure to double-check whether your IC’s rating is contingent on the use of heatsinks.

3. If you are designing PCBs, ensure your traces are large enough to keep resistance low and avoid excessive heating.

4. When designing a switching circuit, be sure to keep your switching time short as much as possible.

To reduce switching times, make the slew rate as steep as possible, by reducing the capacitance on the line. Also, in the field of electronics, a slew rate is defined as the change of current, voltage, or other electrical measures, within a unit of time. Resistors are multi-faceted components available for your circuits.

As designers, you continuously face the ever-present challenge in electronic circuit design. One of the most critical aspects of design is finding the correct components that meet your circuit needs. Furthermore, finding these components also means that they must safely function within the given parameters of voltage, power, and current. Therefore, calculating parameters like power dissipation is critical to your overall circuit design.

Power dissipation strategies and utilizing resistors in your circuits are more than capable with Cadence’s suite of design and analysis tools. Working through any layout challenge in Allegro PCB Designer enables your designs to come out quick, clean, and ready for production. If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts

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