• ### Unit 3: Electronic Circuit Theory

Although the study of electric and magnetic fields is interesting in and of itself, it may not seem directly useful in the real world. However, the interplay between these phenomena is responsible for much of the technology you see in your everyday life. For example, all electronics apply various features of electromagnetism, so that computers, HDTV, iMacs and iPads, smartphones, motors, fans, lights, and so on are applied electromagnetic devices. In this unit, we will take a quick look at the foundations of electronics while at the same time adding to our understanding of electromagnetism.

Completing this unit should take you approximately 8 hours.

• ### 3.1: Electric Current, Voltage and Resistance

An electric current refers to the flow of electric charge through a circuit. We measure an electric current as the net rate of flow of electric charge across an imaginary fixed surface that cuts through the region where the charge is moving. The charge can be negatively charged electrons or positive charge carriers, such as protons or positive ions.

Voltage, as defined earlier, refers to the electric potential difference between two points, and we will see that in the context of electric circuits, and can be thought of as a kind of pressure that causes the current to flow.

• ### 3.2: Ohm's Law

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points. According to Ohm's Law, the voltage drop, $V$, across a resistor when a current flows through it is calculated using the equation $V=IR$, where $I$ equals the current in amps (A) and $R$ is the resistance in ohms (Ω). Another way to think of this is that $V$ is the voltage necessary to make a current $I$ flow through a resistance $R$.

• ### 3.3: Resistance and Resistivity

Ohm's Law is an empirical relationship that applies to many different types of conductors, but not to all (e.g., incandescent light bulbs show a more complicated behavior while they heat up or cool down). This law can also be explained in more detail by making use of the microscopic picture that we introduced in the context of the drift velocity: The current through a wire is proportional to the drift velocity, so that any effect that manages to increase the drift velocity will also increase the current. One way to increase the drift velocity is to reduce the rate at which electrons undergo collisions in the material.

• ### 3.4: Power in Electric Circuits

When a current flows through a resistor, electrical potential energy of the moving charges is converted into thermal energy (as in a toaster oven) or light (as in a light bulb). This is the reason why the drift velocity stays constant in the resistor even though the potential energy of the charges does not. If you look at the label on a light bulb or most electrical appliances, you will in fact see a number that quantifies how much electrical energy they convert to other forms of energy (such as heat) every second, under normal operating conditions. That is the power rating, measured in watts.

• ### 3.5: Alternating Current vs. Direct Current

Direct current (DC) is the flow of electric charge in only one direction. It is the steady state of a constant-voltage circuit. Most well-known applications, however, use a time-varying voltage source.

Alternating current (AC) is the flow of electric charge that periodically reverses direction. If the source varies periodically, particularly sinusoidally, the circuit is known as an alternating current circuit. Examples include the commercial and residential power that serves so many of our needs.

• ### 3.6: Electric Hazards and the Human Body

The reason electric shock is so dangerous to humans is due to a trait we share with all other animals which plants do not possess: our bodies use electricity to transmit information along our nerve cells. Electricity allows us to transmit messages over long distances inside our body, much faster than would be possible if we relied on the diffusion of chemical molecules, such as hormones (a method we also use). It becomes hazardous when an electric shock interferes with these nerve signals.

• ### 3.7: Resistors in Circuits

Most circuits have more than one component (a resistor) that limits the flow of charge in a circuit. A measure of this limit on charge flow is called resistance. The total resistance of a combination of resistors depends on both their individual values and how they are connected.

• ### 3.8: Kirchhoff's Rules

The "black-box" approach of the previous section has its limitations: you cannot reduce any arbitrary combination of batteries and resistors to a single battery and a single resistor. If you could, circuit analysis would not only be boring, but it would not be able to produce all of the functionality that electronics are able to deliver in everyday life.

We need additional tools to analyze even more complicated circuits. Fortunately, the beauty of physics is that it manages to reduce the complexities of everyday life to a relatively small number of fundamental principles. In this section, we deal with two additional principles that apply to all circuits (except when they operate at the kind of frequencies that generate radio waves – more on that later).

Kirchhoff's rules for circuit analysis are basically applications of the conservation laws to circuits. The first rule applies the conservation of charge, while the second rule applies the conservation of energy. Conservation laws, even used in a specific application, such as circuit analysis, are so basic as to form the foundation of that application.

Kirchhoff's first rule, also called the junction rule, states that the sum of all currents entering a junction must equal the sum of all currents leaving the junction.

Kirchhoff's second rule, also called the loop rule, states that the algebraic sum of the changes in potential around any closed circuit path (loop) must be zero.

• ### 3.9: DC Voltmeters and Ammeters

Now that we have spent some time performing the theoretical calculations for designing an electronic circuit, we should go back and ask how to measure the currents and voltage we just calculated. Most discoveries in electromagnetism would have been impossible without measurement devices. For example, although Coulomb may have figured out the forces between charged objects, how can you determine whether those charges are sitting still or in motion?

In a circuit, voltages can exist with or without any moving charges. For example, a battery with open terminals shows a voltage even if no current is able to flow. On the other hand, electrical current is, by definition, the directed flow of charge.

In principle, it is possible to detect a voltage in the same way you detect the presence of charge: by measuring repulsive or attractive electrostatic forces between two movable objects, connected to the points whose potential difference you are trying to find. But that is difficult to do in practice, because static charges are easily lost by unintended routes, for example in humid air. Instead, the measurement of voltage and current often relies on a different effect that can only be produced by moving charges: magnetism.

Voltmeters measure voltage; ammeters measure current. Voltmeters are connected in parallel with the device whose voltage is being measured. A parallel connection is used because objects in parallel experience the same potential difference. Ammeters are connected in series with the current of the device that is being measured. A series connection is used because objects in series have the same current passing through them.