Skip to content Skip to navigation

Connexions

You are here: Home » Content » Solving Circuits with Impedances

Navigation

Recently Viewed

This feature requires Javascript to be enabled.

Solving Circuits with Impedances

Module by: Don Johnson. E-mail the author

User rating (How does the rating system work?)
Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

:
(0 ratings)

Summary: Introducing the advantages of using impedance and how to use it.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

As we unfold the impedance story, we'll see that the powerful use of impedances suggested by Steinmetz greatly simplifies solving circuits, alleviates us from solving differential equations, and suggests a general way of thinking about circuits. Because of the importance of this approach, let's go over how it works.

  1. Even though it's not, pretend the source is a complex exponential. We do this because the impedance approach simplifies finding how input and output are related. If it were a voltage source having voltage v in =pt v in p t (a pulse), still let v in = V in ⅇⅈ2πft v in V in 2 f t . We'll learn how to "get the pulse back" later.
  2. With a source equaling a complex exponential, all variables in a linear circuit will also be complex exponentials having the same frequency. The circuit's only remaining "mystery" is what each variable's complex amplitude might be. To find these, we consider the source to be a complex number ( V in V in here) and the elements to be impedances.
  3. We can now solve using series and parallel combination rules how the complex amplitude of any variable relates to the sources complex amplitude.

A common error in using impedances is to keep the time-dependent part, the complex exponential, in the fray. The entire point of using impedances is to get rid of them in writing circuit equations and in the subsequent algebra. The complex exponentials are there implicitly (they're behind the scenes). Only after we find the result do we raise the curtain and put things back to together again. In short, when solving circuits using impedances, t t should not appear except for the beginning and end.

Content actions

Give Feedback:

E-mail the module author | Rate module ( How does the rating system work?)

Rating system

Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

(0 ratings)

Download:

Module PDF

Add module to:

My Favorites (?)

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

| A lens (?)

Definition of a lens

Lenses

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

What is in a lens?

Lens makers point to Connexions 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 Connexions 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