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Chapter 1 - Elements of Electrical Circuits: The Nuts and Bolts of Circuits Electricity, or rather electrical circuits, is the blood of our modern society. We live in a world surrounded by electrical appliances, ranging from a simple light bulb to a highly sophisticated cell phone. We will begin our study of electrical circuits here. The study of electrical circuits involves: • The understanding of how electric current arises. • The function of various electrical devices. • The design of electrical circuits to achieve certain purposes. For now we will begin by studying the important elements in an electrical circuit, namely electrical currents, voltage, electrical power and resistance. The term electricity in physics is a more broad area of study of the nature of interaction between electric charges. We will study the nature of electrical interaction in more detail later. All that we need to know is that: 1. Charges come in 2 flavors, positive and negative. Like charges repel while unlike charges attract. Further, the amount of charges is measured in coulombs with unit . 2. Matter around us can be broadly classified as electrical conductors and insulators. Conductors allow electric current to flow past them easily while insulators does not allow electric current to flow past them. We will study why this is the case later. What are electrical circuits? Electrical circuits are wires, which are made of electrical conductors, connected to various components such as battery, switches and electrical devices. The reason they are called electrical circuits is the wires must form a loop in order for current to flow. Consider a simple electrical circuit with a battery connected to a light bulb as shown on the right: The battery will push electric charges around the wire loop, resulting in a flow of positive charges from the positive terminal to the negative terminal of the battery. This flow of electric charge is called an electrical current. (This is called the conventional current flow, but in reality in metal wires, it is the negatively charged electrons flowing in the opposite direction, but this can be ignored.) We will quantify them shortly. The wire in an electrical circuit form a loop for a continuous current flow, if not charges will accumulate on its end point and prevent any more current from flowing through it. In the process the electrical current flowing through the light bulb will cause the light bulb to be switched on, giving off light in the process. In effect, the current carries electrical energy that are converted from the battery and brought into the light bulb, so it can be converted into light energy. The energy conversion cab be summarized as: Chemical Electrical Energy in Light Energy given Energy from the electrical current off by the light bulb battery This simple example is highly instructive as it illuminates some things we will have to account for in electrical circuits, which are electrical currents and energy conversion. Electrical Currents (or simply Current) In order to quantify the flow rate of an electrical current, consider a cross-sectional area of a wire with a current flowing through it as shown on the right: The electrical current is defined to be the amount of charge flowing through per unit time and it is given by: Where is the amount of charge flowing through the cross-sectional area, while is the time taken. The SI unit for current is amperes denoted by ; 1 of current means that in 1 , 1 of charge have passed through the area. Actually it needs to be mentioned that there are two forms of current flow, direct current (DC) and alternating current (AC). The simple battery with light bulb example earlier is an example of a DC circuit, where current flows steadily in one direction. AC on the other hand transmits energy by having a current that flows back and forth the circuit as shown by the following current-time graphs: From here on, we will be working exclusively with DC circuits as they are a lot simpler since the current and voltage are held constant. We will study AC circuits in more detail in Electromagnetism. Voltage: Electromotive Force and Potential Differences The other thing we have to account for in electrical circuits is the energy conversion. As we have noted earlier in the simple circuit with the light bulb, there are two different energy conversions: 1. The conversion of the stored energy in a battery into electrical energy. 2. The conversion of electrical energy into light energy by the light bulb. These energy conversions can be generalized to the following 2 types: 1. The conversion of other forms of energy into electrical energy; this conversion is not limited to batteries, other examples include the conversion of kinetic energy to electrical energy by generators. 2. The conversion of electrical energy to other forms of energy; this conversion is usually performed by electrical appliances such as light bulb, heater, speaker and so on. To account for the amount of energy used, we will have to introduce another quantity called voltage which is generally defined as the work done (the amount of energy converted) per unit charge flowing through the component: For example: • A typical 1.5 battery will convert 1.5 of its chemical potential energy into electrical energy for every 1 of charge that flows through it. • A 9 speaker will convert 9 of electrical energy into sound (and some heat due to inefficiencies) energy for every 1 of charge that flows through it. Clearly there are two different forms of voltage that we should be aware of. One is called the electromotive force or EMF for short (not a force), usually denoted by , the voltage involved in pushing the current around the circuit. The in the definition of voltage is the amount of other forms of energy converted into electrical energy. The other is potential difference (also commonly called voltage drop), usually denoted by , the voltage involved in draining the electrical energy from the circuit. The in the definition of voltage is the amount of electrical energy converted into other forms of energy. In practice, the term voltage is used which could mean either the electromotive force or potential difference, so it is important to have a clear understanding of the both of them and distinguish them clearly. Electrical Power Consider the multiplication of current with voltage: Based on their definitions, the multiplication of and results in the quantity , which is the amount of work done per unit time. In physics, this quantity is called power, which is the rate of work done; with SI unit of watts which the rate at which 1 of work done in 1 . Hence the electrical power is given to be: Once again, electrical power can mean two things; either the rate of electrical energy generation by an electrical power source or the rate at which electrical energy is drained by an electrical device. To determine the amount of electrical energy being consumed or generated, we will have to multiply the power and the time that has elapsed: Household electrical energy usage is usually measured in kilowatt-hours, joules, . 1 ℎ rather than ℎ of energy is equivalent to the electrical energy consumed by a 1 electrical device for 1 hour, which is a total of 3.6 million joules of energy, which is a lot of energy! In other words, 1 ℎ 3.6 3.6 × 10 . Resistance: Ohmic and Non-Ohmic Devices Going back to the example of the simple light-bulb switch. On one hand we have the battery pushing the current, supplying electrical energy; and on the other hand we have the light-bulb draining away electrical energy. How does this affect the current flowing through it? Of course, the stronger the electromotive force, the larger the current. Another factor that affects the amount of current flowing through depends on the device as well (its construction and its material). The less conductive the device is, the lesser the current. The degree of conductance of a device is measured by its resistance . The higher the resistance, the less conductive it is, making it difficult for current to flow through. For most conductors, the amount of current flowing through it is directly proportional to the applied electromotive force, with the constant of proportionality being used is that for a given voltage, the larger the ! (the reason ! is being value, the lower the current is, reflecting the nature of electrical resistance): Such conductors are called ohmic conductors, where if a graph of applied voltage and current flowing through it is plotted, it will result in a straight line through the origin. The gradient is then ! as shown: Non-ohmic conductors on the other hand, have a non-linear graph, so it does not have a well-defined resistance. Nonetheless, non-ohmic conductors are also important in practice, such as diodes. graphs are called characteristic graphs as it highlights how is current flowing through the device based on the voltage applied to it, displaying its electrical characteristic. The following sketch contrast their characteristics: To find , we can rearrange the equation " ! to obtain the following formula to calculate resistance as a ratio to the voltage applied and the current flowing through it: Using this formula, we can measure a device’s resistance, which can be used to predict the amount of current flowing through it for any given applied voltage (assume any device is ohmic unless told otherwise). The unit of resistance is ohms, denoted by Ω. Finally by rearranging the equation " $ , the potential difference of the electrical device can be found by knowing its resistance and the current flowing through it by . This equation will be used often when we cover and apply Kirchhoff’s law later. To calculate the power consumed by a device given its resistance, the following equations can be used (which can be shown easily by combining the equation % % and " $ ): It is important to note that in these equations are the potential difference across the electrical device, not the electromotive force of the connected battery. It is implicitly assumed that the potential difference is equal to the electromotive force when a single device is connected to one single battery. We will see why this is the case when we look at Kirchhoff’s law later. Any devices that has a resistance to them are called resistors. Their function in the circuits are mainly, but not restricted, to restrict the amount of current flowing and draining away electrical energy. The electrical energy converted can either be useful such as heat (a heater is just a giant resistor) and light, or waste energy to be dumped into the surroundings.