# Summary Guide: Basic Circuits¶

This first section is about establishing core electrical concepts and standard vocabulary for talking about electronics. Everybody in the class is starting from a different level of experience (perhaps none) but needs to develop a common language for working together.

The following list is an informal summary of basic electrical concepts which will be used throughout the course. Please read through everything and keep this for reference. If the terminology is unfamiliar, it will become familiar through practice with the exercises. If it is review, then please help your classmates with understanding the exercises.

## Takeaway Lessons¶

Electricity is the flow of electrons through a conductor.

Electricity is invisible; we use instruments such as multimeters and oscilloscopes to measure it and render it visible.

An electrical current conveys energy.

Electric potential is measured in volts. Potential can exist between any two points in a circuit or conductor; it is a relative measure. It is a measure of potential energy, and exists whether or not a current is flowing between those two points.

Electric current is measured in amperes (amps). Current is the volume of electron flow past a point.

Electrical currents can vary with time. The simplest case is the AC (alternating current) wall power in which the voltage is formed as a 60 Hz sine wave (in the US) for transmission efficiency. In contrast, our lab power supplies and batteries will output DC (direct current) which has a constant voltage.

An electrical current can encode information.

Information can be conveyed even with very small amounts of energy. In practice there are very different kinds of electrical signals and circuits for processing information (e.g. from sensors) versus actuating mechanical systems (e.g. motors, speakers).

An electric potential across a resistance causes a current to flow through it. Resistance is measured in ohms and is measured along a pathway through a conductor.

Virtually all materials have a finite resistivity, which is a property of the material. The resistance of a path through a material is a function of the resistivity and the length and cross-section of the conductive path. Longer and thinner wires have more resistance, shorter and thicker wires have less resistance. Copper has lower resistivity than aluminum or steel; silver is better yet.

A current flowing through a resistance converts electrical energy to heat. This is commonly termed dissipation.

An insulator is a material with very high resistance, i.e., a typical voltage will cause negligible current flow through it.

The relationship between current, voltage, and resistance in an electrical path is described by Ohm’s Law: V = i * R, in which V represents a voltage measured across a resistance R through which current i is flowing. Ohm’s Law can be trivially rewritten as i = V / R and R = V / i.

Electricity flow is loosely analogous to water flow: current is analogous to the volume of flow of water through a pipe, voltage is analogous to the pressure difference between two locations, and resistance is analogous to friction. However, it is good practice to think directly in terms of electrical properties rather than relying on this comparison.

A resistor is a type of electronic component engineered for a precise and constant resistance property. Resistors are designed with a guaranteed minimum capability for dissipating energy. In general, physically larger resistors have more dissipation capacity. Resistors come in a variety of physical shapes and means of electrical connection. No resistor is precisely the specified value; resistors are specified with a tolerance range. Highly precise resistors generally cost more. In practice, resistors have no dynamic behavior.

Resistors have a constant value for any voltage and current within their rating. Ohm’s Law for a resistor means that current and voltage follow a simple linear relationship given a constant R.

Wires can be viewed as resistors with low resistance values. Ideally the resistance is low enough not to affect circuit operation, but in circuits delivering energy the wire resistance needs to be considered.

A short-circuit (or “short”) is an unintended low-resistance connection between two points, e.g. bare wires touching accidentally, a stray drop of solder bridging two pins, or a DMM probe touching two circuit board traces. The effects of a short can range from nothing to smoke and destruction, depending on the location and available energy.

In practice, resistors are used to relate current and voltage within a circuit rather than to generate heat. Heat is normally an undesirable side-effect.

There are many other types of passive and active components: capacitors, inductors, diodes, transistors, LEDs, lamps, integrated circuits, motors, solenoids, and thousands more.

Unlike resistors, most components do not have a simple constant resistance.

The DMM (digital multi-meter) measures fundamental properties of an electrical signal: voltage and current. It also measures electrical properties of materials (either components or conductors): resistance, capacitance, and inductance. The DMM is most useful for measuring relatively constant properties, as the numeric display doesn’t show rapid variation well.

Measuring voltage with a DMM requires attaching it between two points, since voltage is a relative measure.

Measuring current with a DMM requires routing a signal through the meter, since current is a measurement of flow. This frequently requires modifying the circuit by opening a connection and replacing it with the path through the meter. The meter itself has a different physical connection point for measuring current that offers a low-resistance path: for this reason it is very important not to use the current input unless actually measuring current, otherwise you will short out a circuit and potentially damage the meter.

The oscilloscope draws a dynamic graph of the voltage of an electrical signal. It is most useful for visualizing time-varying signals. The oscilloscope can plot a signal over many orders of magnitude of time scale; in the course we will generally deal with signals varying at scales ranging from microseconds to seconds, but modern electronics involves signals at nanosecond scales and shorter. In contrast, human perception operates at scales closer to tenths of a second.

Sensors are transducers which convert a physical signal to an electrical signal. Some common transducers have variable resistance, e.g., for a given voltage across them, the current through them will vary depending upon physical state. Two examples: a switch has a resistance near zero or near infinity depending on position, a CdS photocell has a resistance varying from about 1000 ohms to millions of ohms depending on light intensity. Sensors can have a time-varying response: the switch changes resistance near-instantly, the CdS photocell can take hundreds of milliseconds to respond to a sudden change. There exists a vast variety of sensors to couple nearly any physical process of interest into electrical information. Optical sensors are especially useful building blocks since many other physical effects can be transduced to a variation in light, and then transduced from light to a variation in electricity.

Circuits are arrangements of components and conductors engineered for a particular purpose. You must learn to recognize certain fundamental circuit structures which will be used throughout the course.

A circuit is a graph; circuit topology matters more than exact physical layout. This becomes less true at the extremes: low-voltage, high-current, or high-frequency circuits require more attention to physical layout. For this course this will come into play with DC motor circuits.

Electrical engineering has been wildly successful at providing means for converting energy and information to and from electrical form and providing tools for manipulating electrical energy and information. Historically, computation and signal processing has also been performed in other domains. The first closed-loop control system was actually a mechanical computation performed with a flyball governor. Elaborate mechanical computers were constructed to represent mathematical functions before the advent of electronic computing. Analog electronic computers were used before digital electronic computers were developed. None of these methods have scaled to the complexity of digital computing, but all still have application for particular problems.

Analog circuits refer to systems in which the energy or information is represented by continuously varying electrical signals. E.g. a photoresistor exhibits a continuously varying resistance as a function of the incident light, and in a circuit can be wired to produce a continuously varying voltage or current. A microphone produces a voltage proportional to air pressure and represents sound as an oscillating voltage.

Digital signals are discretized signals in which specific values of voltage or current are defined to represent specific symbols. In the most common case, only two symbols are represented, labeled zero and one. This encodes a single binary digit, or bit, as the current or voltage on a wire.

The specific values of voltage or current representing a digital symbol depend on the specific components. The Arduino follows the 5V CMOS convention, so voltages below 1.5V are considered zero or LOW and voltages above 3.7V are considered one or HIGH. Voltages in-between are potentially ambiguous but will be arbitrated into a distinct value when passing through a digital input. Please note that other microcontrollers such as the Arduino Due operate at 3.3V and circuits in laptops and cell phones at even lower voltages, so these thresholds will be different. Connecting between different logic families can require level-translation circuitry if the values are not compatible.

Schematics are circuit diagrams showing the logical connection of electronic components. A schematic does not define the physical layout of components or conductors, so constructing a circuit from a schematic requires applying additional knowledge. However, a good schematic contains enough information to construct a functional circuit assuming common engineering experience.

Schematic signals are often named to convey intended purpose of a connection. In digital circuits, a bar over a name or a slash in front of it indicates an active-low signal in which the low-voltage state is the active state. The meaning of active is relative to the specific case: for example, an input labeled /RESET is active-low, so a zero-voltage input is “active” in the sense that the circuit is reset (and hence not operating).