How to use the lessons

On this page: The Board · The icons · Links in the text · Buttons and sliders · Movable labels · Contents · Notation · If something goes wrong

The interactive lessons on this site have two parts side by side: the text, which explains, and the Board, which shows. They work together: you control the Board from the text, and the Board shows, step by step, what the text describes.

The Board

We call Board the panel next to the text that holds the interactive figures: circuits, graphs, vectors, animations. You can act on the Board directly, by dragging points and sliders, or from the text, with the icons and links described below.

The Board can change within a lesson: depending on the paragraph, the same panel holds different figures.

The icons

Hover over an icon to see a short tooltip that says what it does, for example “Initial board”, “Board: purely inductive load” or “New board: capacitive reactance with finite differences”. You can always start over with the “Initial board” icon.

Links in the text

There are two kinds of links in the text:

• red links, like this one, act on the Board: they show or hide an element (a vector, a curve, a slider) or change a value. When you hover over them they get darker and a light background appears; often a tooltip explains what they do;
• the other links take you, as usual, to another page or to another part of the lesson.

A double click on a red link usually does the opposite of a single click: if the click shows an element, the double click hides it.

Buttons and sliders

Below the Board there are sometimes buttons, such as Start Stop Time, that start or stop an animation or change what the Board shows.

Inside the Board, you drag the sliders with the mouse or a finger; the chosen value appears next to the slider. Highlighted points can often be dragged too: it is the best way to see how one quantity changes as another one varies.

For fine adjustment, click a slider and use the arrow keys: each press moves the value by one step (Shift+arrow by 10 steps, Page Up and Page Down by 100). Or hold down Shift while dragging the slider: the value then changes much more slowly.

Movable labels

If a label covers something else on the Board (say, the label of a vector that, as it rotates, ends up on top of another vector), you can drag it out of the way with the mouse or a finger, just as in GeoGebra: when you hover over it, the cursor turns into a four-headed arrow. Only the label moves, not the object, and the label keeps following it. Fixed captions, such as the component names on a circuit, stay where they are. The Board’s reset button (the circular arrow in the top right corner) or the “Initial board” icon puts everything back.

Contents

At the start of the longer lessons, a table of contents lists the chapters and sections: one click takes you straight to the part you want.

Notation

• Dotted letters, for example \(\dot{V},\, \dot{I},\, \dot{Z}\), denote phasors and complex operators. The same notation also stands for the corresponding complex numbers (for example \(\dot{Z} = R + j\,X\)). Rotating vectors use the standard vector notation instead, for example \(\vec{I},\, \vec{V}\).
• Undotted letters denote the magnitudes of complex or vector quantities (for example \(Z = \sqrt{R^2 + X^2}\)).
• The imaginary unit is written \(j = \sqrt{-1}\) instead of the \(i\) used in mathematics, since in electrical engineering \(i\) stands for current.
• Lowercase letters highlight the dependence on another quantity, usually time, for example \(v(t) = V_M \sin(\omega t)\).

If something goes wrong

• If a Board looks outdated or does not respond, reload the page bypassing the cache: Ctrl+F5 on Windows and Linux, Cmd+Shift+R on Mac.
• On a smartphone the lessons are easier to read in landscape; on a wider screen the text and the Board sit side by side.
• The lessons work in all recent browsers and need nothing installed, but JavaScript must be enabled.

Found a mistake or have a suggestion? Write to me: info@sandroronca.it.