What is a Circuit?

A circuit is a circular route in which something travels. In a circuit race cars, bikes, or runners race through a looping course and end where they started. In the circulatory system blood starts in the heart makes its way through the lungs and body back to where it started in the heart. In physics, a circuit is the circular path of charge through a wire from one terminal of a power source to the other.

For MCAT physics, we will be focusing on the last in our list above and dive deeper into electrodynamics a fancy way of saying moving charges.

Why Does Charge Move?

First and foremost we need to understand why charges move. From our foray into electrostatics, we learned that opposites attract and that similar charges repel. Additionally, we talked about voltage or the desire for a charge to move either towards its opposite or away from similarly charged particles. Where a higher voltage indicates a greater desire to move.

Batteries supply voltage to circuits causing charges to move. However, charges can’t simply move through the air they need a specific path or medium to flow through. Not any old medium will do though. Charges can only move through conductive materials like the metals or solutions formed from salts or strong acids. While insulating materials like the air trap charges preventing them from flowing.

Types of Conductivity

We already explored conductivity in electrostatics but it is worth reviewing the material now and going through the two types of conductivity described above.

Quick Review

Conductors allow for the movement of charge along their surface and from material to material. If we were to place 10C of charge on the surface of a conductive material it would spread out evenly along the outer surface.

Common conductors include metals because the electrons, which carry negative charges, within the elements are able to move around. Even still not all materials are equal and some are better at conducting charges than others. We call this ability to move charges conductivity (σ; Ω^-1⋅m^-1) and the higher your conductivity the more easily charges move.

This is why most wires are made out of copper or in special cases silver. It is highly conductive and can easily transfer charges from place to place.

Insulators

Insulators are the opposite of conductors in that they don’t allow charge to flow from place to place. If we were to place 10C of charge on an insulator it would be stuck right where we put it.

Common insulators include non-metals because their electrons are stuck and can’t move freely. Just like conductors, some materials are better insulators than others. While we could measure an insulator’s conductivity we don’t. Instead, we measure their resistivity (ρ; Ω⋅m), how well they resist the movement of charge.

Metallic Conductivity

The quick review above only describes one of the two types of conductivity, metallic conductivity, or the movement of electrons within metals. Since metals hold onto their electrons loosely they can freely flow and allow charges to move from one place to the other.

Electrolytic Conductivity

Electrolytic conductivity, on the other hand, results from the movement of charged ions within a solution instead of the flow of metallic electrons from place to place. This is why strong acids and bases are good electrolytes the freely dissociate into charged particles than can conduct electricity from place to place.

This means that liquids can act either as insulators or conductors depending on what has been dissolved into them. Ocean water would be a great conductor whereas deionized water from the grocery store would be a great insulator.

Current Flow in A Circuit

Regardless of the type of conductivity a circuit used or what produced the voltage in the first place the end result is current. Current (I) measured by the Ampere (A; C/s) is the flow of positive charge. In many ways current is identical to fluid flow except instead of measuring what volume passes through a space in a particular time we measure the amount of charge (C) that passes through our circuit per unit time (s).

Thus current is quantified with the following equation:

[Latexpage]
\[ I=\frac{Q}{\Delta t}\]

Here we can see that current (I) is the amount of charge (Q) per amount of time (Δt).

Circuit Laws

Now that we understand what a circuit is, why the charges within a circuit move, and a little bit about current let’s look at the two laws that govern circuits.

Junction Rule

The first is Kirchhoff’s junction rule, which states that the amount of current that flows through a junction is the same amount that entered the junction. Basically if 10A flows into a junction that fork into two directions the current in both forks must equal 10A.

I like to conceptualize this rule by thinking about fluid flow since it is easier to imagine. Let’s imagine that you put 10L into a pipe that then branches into 3 different pipes and into a collecting basin. How much water would be in the basin once all of the water flows into the basin? 10L. You put 10L in, you get 10L out. The same is true of electrical current.

Loop Rule

Kirchhoff’s loop rule is a bit harder to understand but here we can use a different analogy with potential energy to understand what is happening. In this scenario, we will imagine that a ball is held at the top of a large slide on the top of a hill. At this point in time, the ball has maximal potential energy or in the case of a circuit maximal voltage. Once released the ball will roll down the slide until it reaches the bottom and eventually stops. Here the ball has no potential energy and in circuit terms a voltage of zero.

Throughout this process, our ball lost all of its potential energy as it transitioned from the top of the hill to the bottom. Likewise, our voltage dropped from its maximum all the way to zero. Which is what the loop rule states, that all of the voltage is used up from the beginning to the end of a circuit. Mathematically:

[latexpage]
\[V_{battery}=V_{lost}\]
or more traditionally
\[V_{source}=V_{drop}\]

At this point our battery or voltage source transport our ball back to the start and the process starts over again.

Circuit Elements

Circuits aren’t terribly interesting without a variety of circuit elements allowing them to carry out different functions. We will explore each of the different elements in depth in the coming articles but for now, let’s briefly overview each.

Batteries

Batteries produce voltage within the circuit by carrying out electrochemical reactions. They are represented with two parallel lines one bigger than the other. Each line stands in for one of the terminals on a battery with the bigger line representing the positive terminal and the smaller line the negative terminal.

Resistors

Resistors represented as squiggly lines resist the flow of current causing a decrease in current. Additionally, resistors cause voltage drops in a circuit since they are a major source of energy loss in a circuit. Why do we want to lose energy in our circuit though? There are plenty of reasons but some of the simplest are examples of their usefulness are lightbulbs and heating elements. In a lightbulb, the energy in voltage is converted into light while in heating elements voltage is converted into heat energy.

Capacitors

Capacitors represented by parallel lines of equal size “store” charge. While a capacitor doesn’t actually store charge it is the easiest way to conceptualize them and allows circuits to discharge a large amount of charge at once. This useful for flash while taking picture or when using an AED to defibrillate someone.

Wires and Switches

Wires connect all of the circuit elements together and provide the path or route through which charge can flow. Additionally, a circuit can contain a switch that can turn on or turn off a circuit by causing a break in the path from one battery terminal to the other.