Skip to content Skip to navigation

Connexions

You are here: Home » Content » Power Dissipation in Resistor Circuits

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • OrangeGrove display tagshide tags

    This module is included inLens: Florida Orange Grove Textbooks
    By: Florida Orange GroveAs a part of collection: "Fundamentals of Electrical Engineering I"

    Click the "OrangeGrove" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Rice DSS - Braille display tagshide tags

    This module is included inLens: Rice University Disability Support Services's Lens
    By: Rice University Disability Support ServicesAs a part of collection: "Fundamentals of Electrical Engineering I"

    Comments:

    "Electrical Engineering Digital Processing Systems in Braille."

    Click the "Rice DSS - Braille" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Rice Digital Scholarship display tagshide tags

    This module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "Fundamentals of Electrical Engineering I"

    Click the "Rice Digital Scholarship" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Bookshare

    This module is included inLens: Bookshare's Lens
    By: Bookshare - A Benetech InitiativeAs a part of collection: "Fundamentals of Electrical Engineering I"

    Comments:

    "Accessible versions of this collection are available at Bookshare. DAISY and BRF provided."

    Click the "Bookshare" link to see all content affiliated with them.

  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Fundamentals of Electrical Engineering I"

    Comments:

    "The course focuses on the creation, manipulation, transmission, and reception of information by electronic means. It covers elementary signal theory, time- and frequency-domain analysis, the […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Lens for Engineering

    This module is included inLens: Lens for Engineering
    By: Sidney Burrus

    Click the "Lens for Engineering" link to see all content selected in this lens.

  • Elec Sci lens

    This module is included inLens: Electrical Science
    By: Andy Mitofsky

    Click the "Elec Sci lens" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Power Dissipation in Resistor Circuits

Module by: Don Johnson. E-mail the author

Summary: Power dissipation in resistor circuits.

We can find voltages and currents in simple circuits containing resistors and voltage or current sources. We should examine whether these circuits variables obey the Conservation of Power principle: since a circuit is a closed system, it should not dissipate or create energy. For the moment, our approach is to investigate first a resistor circuit's power consumption/creation. Later, we will prove that because of KVL and KCL all circuits conserve power.

As defined on (Reference), the instantaneous power consumed/created by every circuit element equals the product of its voltage and current. The total power consumed/created by a circuit equals the sum of each element's power. P=kvkik P k k vk ik Recall that each element's current and voltage must obey the convention that positive current is defined to enter the positive-voltage terminal. With this convention, a positive value of vkik vk ik corresponds to consumed power, a negative value to created power. Because the total power in a circuit must be zero ( P=0 P 0 ), some circuit elements must create power while others consume it.

Consider the simple series circuit should in (Reference). In performing our calculations, we defined the current iout iout to flow through the positive-voltage terminals of both resistors and found it to equal iout=vinR1+R2 iout vin R1 R2 . The voltage across the resistor R2 R2 is the output voltage and we found it to equal vout=R2R1+R2vin vout R2 R1 R2 vin . Consequently, calculating the power for this resistor yields P2=R2R1+R22vin2 P2 R2 R1 R2 2 vin 2 Consequently, this resistor dissipates power because P2 P2 is positive. This result should not be surprising since we showed that the power consumed by any resistor equals either of the following.

v2R   or   i2R v 2 R   or   i 2 R
(1)
Since resistors are positive-valued, resistors always dissipate power. But where does a resistor's power go? By Conservation of Power, the dissipated power must be absorbed somewhere. The answer is not directly predicted by circuit theory, but is by physics. Current flowing through a resistor makes it hot; its power is dissipated by heat.

Note:

A physical wire has a resistance and hence dissipates power (it gets warm just like a resistor in a circuit). In fact, the resistance of a wire of length L L and cross-sectional area A A is given by R=ρLA R ρ L A The quantity ρ ρ is known as the resistivity and presents the resistance of a unit-length, unit cross-sectional area material constituting the wire. Resistivity has units of ohm-meters. Most materials have a positive value for ρ ρ, which means the longer the wire, the greater the resistance and thus the power dissipated. The thicker the wire, the smaller the resistance. Superconductors have zero resistivity and hence do not dissipate power. If a room-temperature superconductor could be found, electric power could be sent through power lines without loss!

Exercise 1

Calculate the power consumed/created by the resistor R1 R1 in our simple circuit example.

Solution

The power consumed by the resistor R1 R1 can be expressed as (vinvout)iout=R1R1+R22vin2 vin vout iout R1 R1 R2 2 vin 2

We conclude that both resistors in our example circuit consume power, which points to the voltage source as the producer of power. The current flowing into the source's positive terminal is iout iout . Consequently, the power calculation for the source yields (viniout)=(1R1+R2vin2) vin iout 1 R1 R2 vin 2 We conclude that the source provides the power consumed by the resistors, no more, no less.

Exercise 2

Confirm that the source produces exactly the total power consumed by both resistors.

Solution

1R1+R2vin2=R1R1+R22vin2+R2R1+R22vin2 1 R1 R2 vin 2 R1 R1 R2 2 vin 2 R2 R1 R2 2 vin 2

This result is quite general: sources produce power and the circuit elements, especially resistors, consume it. But where do sources get their power? Again, circuit theory does not model how sources are constructed, but the theory decrees that all sources must be provided energy to work.

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks