Electric current
Describe the movement of electric charges through a medium.
Current is the rate at which charge passes through a cross-sectional area of a wire \[\begin{equation} I = \dfrac{dq}{dt} \end{equation}\] Current within a conductor consists of charge carriers traveling through the conductor with an average drift velocity. \[\begin{equation} I = n q v_d A \end{equation}\]
Electric charge moves in a circuit in response to an electric potential difference, sometimes referred to as electromotive force or emf (\(\mathcal{E}\)).
If the current is zero in a section of wire, the net motion of charge carriers in the wire is also zero, although individual charge carriers will not have zero speed.
Current density is the flow of charge per unit area. \[\begin{equation} I = \int \vec{J} \cdot d\vec{A} \end{equation}\]
Current density is related to the motion of the charge carriers within a conductor. \[\begin{equation} \vec{J} = n q \vec{v_d} \end{equation}\]
Current density is a vector quantity.
A potential difference across a conductor creates an electric field within the conductor that is proportional to the resistivity of the conductor and the current density. \[\begin{equation} \vec{E} = \rho \vec{J} \end{equation}\] \[\begin{equation} \vec{J} = \sigma \vec{E} \end{equation}\]
If a function of current density is given, the total current can be determined by integrating the current density over the area. \[\begin{equation} I_{tot} = \int \vec{J}(r) \cdot d\vec{A} \end{equation}\]
Although current is a scalar quantity, it does have a direction. Because its direction is relative to the current carrier and not space, current does not obey the laws of vector addition and has no vector components.
The direction of conventional current is chosen to be the direction in which positive charge would move.
In common circuits, the current is actually due to the movement of electrons (negative charge carriers).
Circuitry basics
Prototyping: building a simple resistive circuit on a breadboard
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In ES202, we are interested in ways to perform computations in order to implement controllers. So far, we have done this digitally, by writing code and running it on a computer (mbed). An alternative way is to construct hardware (circuitry) that performs computations in analog. Before you scoff at this prospect, recognize that a large amount of legacy Navy hardware still runs in analog; analog was good enough to get us into space and to the moon... it is often a cheap alternative that is fast to develop and works. It’s also useful to understand other ways to implement controllers, as sometimes it may be desirable to implement portions of them in non-digital means (such as via analog electronics, mechanical linkages, hydraulically, etc).
Circuitry basics
Circuits are a complete path for current (e.g. moving charges) to flow. If there is not a complete path for current to flow, the circuit is incomplete or open, and (usually) nothing will happen. In future lectures, we will discuss what happens along paths and at nodes where the paths branch.
Voltage and current
Two quantities of interest in understanding circuits are voltage and current.
Voltage is the electrical potential, i.e. energy or work per charge (units of Volts, \(\qty{1}{\volt} = \qty{1}{\joule}/\qty{1}{\coulomb}\)). Voltage is given the symbol \(v\), or sometimes \(e\) or \(\phi\). It is always measured as a difference between a point or node and a reference (typically ground, defined by 0 V) or as a voltage difference across something.
Current is the amount of charge flowing through a branch in the circuit per unit time (units of Amperes, \(\qty{1}{\ampere}=\qty{1}{\coulomb\per\second}\)), given the symbol \(i\). We always speak of current flowing through something (in contrast to voltages across something).
Ideal sources
When you walk up to the workbench, you see sources that provide a specified voltage or current. The voltage or current need not be constant (it can be time varying with some function, as in an AC source given by \(e_{ac}=E\sin{\omega t}\)).
(0,0) to [V=ein] (0,-2); (2,-2) to [I=iin] (2,0); (4,0) to [battery=Vbatt] (4,-2); (6,0) to [sV=eac] (6,-2);
Prototyping: building a simple resistive circuit on a breadboard
When prototyping (developing) circuits, they are often built in a temporary and easily reconfigurable fashion using a breadboard. In the early days of electrical engineering, circuits were built by screwing them onto a wooden board (often one stolen from the kitchen and used for slicing bread) and the name stuck.
Breadboards
Modern solderless breadboards consist of a perforated block of plastic with numerous alloy spring clips under the perforations. The clips are often called contact points. The contact points are arranged on a regular (typically 0.1 inch) grid and allow plugging/unplugging of component leads and wires. The regular grid is also compatible with the pins of integrated circuits, often in a “dual inline package” (DIP). Interconnecting wires (“jumpers”) and the leads of discrete components (resistors, capacitors, inductors, diodes, transistors, etc.) can be inserted in the breadboard to complete the circuit. The breadboard spring clips are typically reated at 1 A at 5 V or 0.33 A at 15 V.
Solderless breadboards share similar layouts generally. They are typically made up of two types of areas: terminal strips and bus strips, each providing a strip of interconnected electrical terminals.
Terminal strips provide the main area to hold most of the electronic components. In the middle of a terminal strip of a breadboard you will find a notch running parallel to the long side. This provides limited airflow for cooling. The clips on the left and right of the notch run radially. Typically five clips beneath 5 perforations in a row on each side of the notch are electrically connected. Those on the left are marked A,B,C,D,E; those on the right are marked F,G,H,I,J
Bus strips provide power to the electronic components. A bus strip usually contains two columns: one for ground and one for supply voltage. The column intended for the supply voltage is usually marked with a RED + and the column for ground is usually marked with a BLACK - or BLUE - All of the terminals in a bus strip column are connected. Bus strips typically run down one or both sides of the terminal strips, and sometimes in between them.
Wires
For wires / jumpers, the material is usually solid copper, tin-plated wire at about 22 AWG (“twenty-two gauge”), coated with colored polyvinyl chloride (PVC) insulation. For wires, increasing gauge numbers indicate smaller wire diameter. Other gauges commonly encountered in lab are 26 gauge, also used as hook-up wire; and 30 gauge, finer wire used in wire-wrap prototyping, for connection to sensors like strain gauges, and during repair to jumper burned traces or mistakes in printed circuit boards. You may also see stranded wire (vice solid), useful for cabling that must bend; stranded wire must be tinned with solder before it can be plugged into a protoboard.
Wires are typically stripped to about 3/16 to 5/16 inch. Shorter stripped wires may not make proper contact with the breadboard’s spring clips. Longer stripped wires increase the likelihood of short circuits. Jumper wires are kept short and neat, to allow easily tracing connections and to reduce noise pickup. To further aid in tracing connections and debugging the circuit, a color code may be adopted for wires, e.g. red for supply voltage, black for ground, blue/green/yellow for signals. Preformed jumpers cut to pre-set lengths and with stiffened pins for repeated plugging-unplugging may also be used.
Aside from wire coated with an insulator like rubber or PVC, you may also see magnet wire, very fine wire coated with an enamel insulator that is gold or bronze in color. This type of wire is used to make magnet windings for inductors, motors, and loops for sensors like guitar pickups or RFID sensors.
See also
- list here