Circuit Theory/Circuit Basics

Circuits
Circuits (also known as "networks") are collections of circuit elements and wires. Wires are designated on a schematic as being straight lines. Nodes are locations on a schematic where 2 or more wires connect, and are usually marked with a dark black dot. Circuit Elements are "everything else" in a sense. Most basic circuit elements have their own symbols so as to be easily recognizable, although some will be drawn as a simple box image, with the specifications of the box written somewhere that is easy to find. We will discuss several types of basic circuit components in this book.

Ideal Wires
For the purposes of this book, we will assume that an ideal wire has zero total resistance, no capacitance, and no inductance. A consequence of these assumptions is that these ideal wires have infinite bandwidth, are immune to interference, and are — in essence — completely uncomplicated. This is not the case in real wires, because all wires have at least some amount of associated resistance. Also, placing multiple real wires together, or bending real wires in certain patterns will produce small amounts of capacitance and inductance, which can play a role in circuit design and analysis. This book will assume that all wires are ideal.

Ideal Junctions or Nodes


Nodes are also called "junctions" in this book in order to make a distinction between Node analysis, Kirchhoff's current law and discussions about a physical node itself. Here a physical node is discussed.

A junction is a group of wires that share the same electromotive force (not voltage). Wires ideally have no resistance, thus all wires that touch wire to wire somewhere are part of the same node. The diagram on the right shows two big blue nodes, two smaller green nodes and two trivial (one wire touching another) red nodes.

Sometimes a node is described as where two or more wires touch and students circle where wires intersect and call this a node. This only works on simple circuits.

One node has to be labeled ground in any circuit drawn before voltage can be computed or the circuit simulated. Typically this is the node having the most components connected to it. Logically it is normally placed at the bottom of the circuit logic diagram.

Ground is not always needed physically. Some circuits are floated on purpose.

Node Quiz

Measuring instruments
Voltmeters and Ammeters are devices that are used to measure the voltage across an element, and the current flowing through a wire, respectively.

Ideal Voltmeters
An ideal voltmeter has an infinite resistance (in reality, several megaohms), and acts like an open circuit. A voltmeter is placed across the terminals of a circuit element, to determine the voltage across that element. In practice the voltmeter siphons enough energy to move a needle, cause thin strips of metal to separate or turn on a transistor so a number is displayed.

Ideal Ammeters
An ideal ammeter has zero resistance and acts like a short circuit. Ammeters require cutting a wire and plugging the two ends into the Ammeter. In practice an ammeter places a tiny resistor in a wire and measures the tiny voltage across it or the ammeter measures the magnetic field strength generated by current flowing through a wire. Ammeters are not used that much because of the wire cutting, or wire disconnecting they require.

Active, Passive & ReActive
The elements which are capable of delivering energy or which are capable to amplify the signal are called "Active elements". All power supplies fit into this category.

The elements which will receive the energy and dissipate it are called "Passive elements". Resistors model these devices.

Reactive elements store and release energy into a circuit. Ideally they don't either consume or generate energy. Capacitors, and inductors fall into this category.

Open
No current flows through an open. Normally an open is created by a bad connector. Dust, bad solder joints, bad crimping, cracks in circuit board traces, create an open. Capacitors respond to DC by turning into opens after charging up. Uncharged inductors appear as opens immediately after powering up a circuit. The word open can refer to a problem description. The word open can also help develop an intuition about circuits.

Typically the circuit stops working with opens because 99% of all circuits are driven by voltage power sources. Voltage sources respond to an open with no current. Opens are the equivalent of clogs in plumbing .. which stop water from flowing.

On one side of the open, EMF will build up, just like water pressure will build up on one side of a clogged pipe. Typically a voltage will appear across the open.

Short
A voltage source responds to a short by delivering as much current as possible. An extreme example of this can be seen in this ball bearing motor video. The motor appears as a short to the battery. Notice he only completes the short for a short time because he is worried about the car battery exploding.

Maximum current flows through a short. Normally a short is created by a wire, a nail, or some loose screw touching parts of the circuit unintentionally. Most component failures start with heat build up. The heat destroys varnish, paint, or thin insulation creating a short. The short causes more current to flow which causes more heat. This cycle repeats faster and faster until there is a puff of smoke and everything breaks creating an open. Most component failures start with a short and end in an open as they burn up. Feel the air temperature above each circuit component after power on. Build a memory of what normal operating temperatures are. Cold can indicate a short that has already turned into an open.

An uncharged capacitor initially appears as a short immediately after powering on a circuit. An inductor appears as a short to DC after charging up. The short concept also helps build our intuition, provides an opportunity to talk about electrical safety and helps describe component failure modes.

A closed switch can be thought of as short. Switches are surprisingly complicated. It is in a study of switches that the term closed begins to dominate that of short.