Simple circuits

Describe the behavior of a circuit.

A circuit is composed of electrical loops, which can include wires, batteries, resistors, lightbulbs, capacitors, inductors, switches, ammeters, and voltmeters.

A closed electrical loop is a closed path through which charges may flow.

A closed circuit is one in which charges would be able to flow.

An open circuit is one in which charges would not be able to flow.

A short circuit is one in which charges would be able to flow with no change in potential difference.

A single circuit element may be part of multiple electrical loops.

Circuit schematics are representations used to describe an analyze electric circuits.

The properties of an electric circuit are dependent on the physical arrangement of its constituent elements.

Circuit elements have common symbols that are used to create schematic diagrams. Variable elements are indicated by a diagonal strikethrough arrow across the standard symbol for that element.

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  1. Circuitry basics

  2. 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 \(e_{ac}=E\sin{\omega t}\)).

(0,2) to [V=ein] (0,0); (2,0) to [I=iin] (2,2); (4,2) to [battery=Vbatt] (4,0); (6,2) to [sV=eac] (6,0);

Sources. From left to right, a generic voltage source that supplies voltage ein, a current source that supplies iin, a battery that provides DC voltage Vbatt, and an AC source that might model a wall voltage eac, for example

See also

References