Power in a series, parallel resistor circuit is dissipated as

Power in a Parallel CircuitPower computations in a parallel circuit are essentially the same as those used for the series circuit. Since power dissipation in resistors consists of a heat loss, power dissipations are additive regardless of how the resistors are connected in the circuit. The total power is equal to the sum of the power dissipated by the individual resistors. Like the series circuit, the total power consumed by the parallel circuit is:

Solution:

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Equivalent Circuits
In the study of electricity, it is often necessary to reduce a complex circuit into a simpler form. Any complex circuit consisting of resistances can be redrawn (reduced) to a basic equivalent circuit containing the voltage source and a single resistor representing total resistance. This process is called reduction to an EQUIVALENT CIRCUIT.

Figure 3-49 shows a parallel circuit with three resistors of equal value and the redrawn equivalent circuit. The parallel circuit shown in part A shows the original circuit. To create the equivalent circuit, you must first calculate the equivalent resistance.

Given:

Globes connected in series

A series circuit has two or more loads connected, one after the other.

The current has only one path it can flow along.

An example of a series circuit is a set of Christmas tree lights. All the globes are placed one after the other.

There is only one path, so the current flow will be the same at any point in the circuit.

Circuit diagram showing three resistors connected in series

The total resistance in a series circuit will be equal to the sum of each individual resistance in the circuit.

The more loads placed in the circuit, the more resistance.

The total resistance for a series circuit is calculated using the following formula:

RT = R1 + R2 + R3

Voltmeter across each resistor in a series circuit

Kirchoff's law extends Ohm's law in relation to voltages across resistances in a series circuit. The total supply voltage will be equal to the sum of the voltage drop across each resistor.

Total voltage drop (VT) is calculated using the formula:

VT = V1 + V2 + V3

If both the current flow and each resistance value are known, then Ohm's law can be used to calculate the voltage drop across each resistor.

Eg:

V1 = IR1

Power dissipation

The power dissipated in a series circuit depends on the supply voltage applied to the circuit and the current flow in the circuit. The current flow depends on the total resistance of the circuit.

From the section on power you know the formula for power dissipation is:

P = VI

The power dissipated in each individual component depends on the resistance of the component. The total power dissipated will be equal to the sum of the power dissipated by each individual resistance. Depending on the values that are known, combinations of the power formula, as well as Ohm's law, can be used to calculate power dissipated (or any other unknown value).

Example

In the above circuit diagram, if the values are:

VT = 20V

R1 = 50Ω

R2 = 20Ω

R3 = 100Ω

The total resistance can be calculated as follows:

RT = R1 + R2 + R3

RT = 50 + 20 + 100

RT = 170Ω

What is the total power dissipated?

You could calculate the current flow and then calculate the power. Instead you could use substitution to get the formula.

In the formula, P = VI substitute the I with VT/RT to give the formula

PT = VT x VT/RT which is the same as

PT = VT2/RT

PT = 202/170

PT = 0.235W or 235mW

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. You can also visit our YouTube channel for videos about Simulation and System Analysis as well as check out what’s new with our suite of design and analysis tools.