Skip to content Skip to navigation

Connexions

You are here: Home » Content » Ideal Circuit Elements

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.
 

Ideal Circuit Elements

Module by: Don Johnson. E-mail the author

Summary: This module provides examples of the elementary circuit elements; the resistor, the capacitor,and the inductor, which provide linear relationships between voltage and current.

The elementary circuit elements—the resistor, capacitor, and inductor— impose linear relationships between voltage and current.

Resistor

Figure 1: Resistor. v=R⁢i v R i
Resistor
Resistor (resistor.png)

The resistor is far and away the simplest circuit element. In a resistor, the voltage is proportional to the current, with the constant of proportionality R R, known as the resistance. v⁢t=R⁢i⁢t vt R it Resistance has units of ohms, denoted by ΩΩ, named for the German electrical scientist Georg Ohm. Sometimes, the v-i relation for the resistor is written i=G⁢v i G v , with G G, the conductance, equal to 1R 1 R . Conductance has units of Siemens (S), and is named for the German electronics industrialist Werner von Siemens.

When resistance is positive, as it is in most cases, a resistor consumes power. A resistor's instantaneous power consumption can be written one of two ways. p⁢t=R⁢i2t=1R⁢v2t pt R it 2 1 R vt 2

As the resistance approaches infinity, we have what is known as an open circuit: No current flows but a non-zero voltage can appear across the open circuit. As the resistance becomes zero, the voltage goes to zero for a non-zero current flow. This situation corresponds to a short circuit. A superconductor physically realizes a short circuit.

Capacitor

Figure 2: Capacitor. i=C⁢dv⁢td t i C t v t
Capacitor
Capacitor (capacitor.png)

The capacitor stores charge and the relationship between the charge stored and the resultant voltage is q=C⁢v q C v . The constant of proportionality, the capacitance, has units of farads (F), and is named for the English experimental physicist Michael Faraday. As current is the rate of change of charge, the v-i relation can be expressed in differential or integral form.

i⁢t=C⁢dv⁢tdt   or   v⁢t=1C⁢∫−∞ti⁢αdα it C t vt   or   vt 1 C α t iα
(1)
If the voltage across a capacitor is constant, then the current flowing into it equals zero. In this situation, the capacitor is equivalent to an open circuit. The power consumed/produced by a voltage applied to a capacitor depends on the product of the voltage and its derivative. p⁢t=C⁢v⁢t⁢dv⁢tdt pt C vt t vt This result means that a capacitor's total energy expenditure up to time tt is concisely given by E⁢t=12⁢C⁢v2t Et 1 2 C vt 2 This expression presumes the fundamental assumption of circuit theory: all voltages and currents in any circuit were zero in the far distant past ( t=−∞ t ).

Inductor

Figure 3: Inductor. v=L⁢di⁢td t v L t i t
Inductor
Inductor (inductor.png)

The inductor stores magnetic flux, with larger valued inductors capable of storing more flux. Inductance has units of henries (H), and is named for the American physicist Joseph Henry. The differential and integral forms of the inductor's v-i relation are

v⁢t=L⁢di⁢tdt   or   i⁢t=1L⁢∫−∞tv⁢αdα vt L t it   or   it 1 L α t vα
(2)
The power consumed/produced by an inductor depends on the product of the inductor current and its derivative p⁢t=L⁢i⁢t⁢di⁢tdt pt L it t it and its total energy expenditure up to time tt is given by E⁢t=12⁢L⁢i2t Et 1 2 L it 2

Sources

Figure 4: The voltage source on the left and current source on the right are like all circuit elements in that they have a particular relationship between the voltage and current defined for them. For the voltage source, v= v s v v s for any current ii; for the current source, i=− i s i i s for any voltage vv.
Sources
(a) (b)
Figure 4(a) (vsource.png)Figure 4(b) (isource.png)

Sources of voltage and current are also circuit elements, but they are not linear in the strict sense of linear systems. For example, the voltage source's v-i relation is v= v s v v s regardless of what the current might be. As for the current source, i=− i s i i s regardless of the voltage. Another name for a constant-valued voltage source is a battery, and can be purchased in any supermarket. Current sources, on the other hand, are much harder to acquire; we'll learn why later.

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