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In the first lesson, we saw that energy can be transformed from one form to another, and during this conversion, all the energy that we put into a device comes out. However, all the energy that we put in may not come out in the desired form. For example, we put electrical energy into a bulb and the bulb produces light (which is the desired form of output from a bulb), but we also get heat from the bulb (undesired form of energy from an electric bulb). Electrical energy conversion to light and heat. Therefore, energy flow into and out of any energy conversion device can be summarized in the diagram below:  Energy Flow Diagram for an Energy Conversion Device When all forms of energy coming out of an energy conversion device are added up, it will be equal to the energy that is put into a device. Energy output must be equal to the input. This means that energy can not be destroyed or created. It can only change its form. In the case of an electric bulb, the electrical energy is converted to light and heat.
The amount of electrical energy put into a bulb = the amount of light energy (desirable form) plus the heat energy that comes out of the bulb (undesirable form).
Gas ($15); Sandwich, fries, and a drink ($8); Lost ($5); New clothes ($62) So you spent $62 on something useful - the clothes - but you spent additional money for other things that were necessary for your trip to the mall. Self CheckInstructions: Identify the useful energy output(s) and undesirable energy output(s) in the energy conversion devices below. Enter your answers in the fields provided, and click the "Check" button to check your work. Click for text description. This will expand to provide more information.
Self Check: Energy Conversion Devices For each of the following examples, determine the types of useful energy and undesired energy for the given energy converter. Example 1: Lawnmower with a chemical energy input. (Hint: How do you know when your neighbor is mowing the lawn?) Example 2: Car with a chemical energy input. (Hint: Think about mufflers, tires, and generator.) Example 3: Television with an electrical energy input. (Hint: Have you ever felt the back of your TV after it has been on for a few hours?) Example 4: Desktop computer with an electrical energy input. (Hint: What’s in your tower and why?) Answers: Example 1: The useful energy for a lawnmower is mechanical while the undesired energy is thermal (heat) and radiation (noise). Example 2: The useful energy for a car is mechanical while the undesired energy is thermal or heat (tail pipe). Example 3: The useful energy for a TV is radiation (light and sound) and the undesirable energy is heat (from circuits). Example 4: The useful energy for a computer is radiation (light and sound) and the undesirable energy is heat (circuits – electrons moving through system) and mechanical (fan for cooling).
Energy cannot be created or destroyed, only converted between forms.
Figure 1 Fig. 1: Let there be light! The battery, shown with positive $(+)$ terminal at the top and negative $(-)$ terminal at the bottom, provides the energy that makes the light bulb shine.
Inside a battery, a chemical (redox) reaction drives positive ions towards the battery's positive terminal and negative ions towards its negative terminal. When the battery's terminals are connected through the light bulb, a pathway is created for charge to flow. Negatively charged electrons flow from the $-$ terminal to the $+$ terminal through the light bulb. This flow of charge converts chemical potential energy into electrical energy. In the light bulb, the flow of charge through the filament heats it up and causes it to glow. In this way, the light bulb converts electrical energy to heat energy and light energy.
Figure 2 Fig. 2: Conservation of energy. In the system in Fig. 1, chemical potential energy is converted to electrical energy, which is immediately converted to light energy and heat energy. By the conservation of energy, the joules of chemical potential energy input into the system equals the sum of the joules of light energy output by the system and the joules of heat energy wasted.
We now define charge, voltage and current so that we can quantify just how much energy is converted to and from electrical form.
Opposite charges attract and like charges repel.
The fact that opposite charges attract and like charges repel is why chemical potential energy is needed to separate the positive and negative charge inside the battery in Fig. 1 in order to be converted into electrical energy. It is also why electrons flow from the $-$ terminal to the $+$ terminal of the battery through the light bulb, and in the process convert electrical energy into light and heat energy. Another empirical observation about charge is that it cannot be created or destroyed. This is stated as conservation of charge: the net charge of a closed system is constant. For this reason, the flow of negatively charged electrons is electrically equivalent to an equal amount of positive charge flowing in the other direction. Because of the historical choice of electrical polarity, we base the following definitions on the idea of a mobile positive charge.A voltage drop is an amount of electrical energy per coulomb of charge. A voltage is a level like a height is a level. If you throw a paper airplane in your apartment, it will probably drop a meter or two before it hits the floor, but if it flies out the window, it could drop much farther. If it flies out the window, gets blown by a gust of wind and lands above you on the roof, the airplane has dropped by a negative height. In the same way, a voltage drop depends on its reference point.
Figure 3 Fig. 3: Voltage drop. The voltage drop $V_1$ is the drop in voltage from its $+$ label to its $-$ label. We say that $V_1$ is the voltage drop across the battery. (We could also say that $V_1$ is the voltage rise across the battery if we think of the voltage rising from the $-$ label to the $+$ label.) Just like a drop in height, a voltage drop can be negative too.
The fact that voltage is defined in terms of differences in electrical energy means that only differences in voltage (such as voltage drops or voltage rises) are meaningful. Later, we will define a node voltage which appears to be a voltage at a specific location, but even a node voltage is a difference with respect to a reference level called ground. A current is a rate of flow of charge. Current is a measure of how fast charge is moving. Remember that a flow of electrons in one direction is equivalent to an equal amount of positive charge flowing in the opposite direction. By historical convention, current is defined as the number of coulombs of positive charge that flow per second. So, current has units of coulomb/second (C/s), which are called amperes (or amps), with symbol A.
Figure 4 Fig. 4: Current direction. The current $I_1$ shown here is the rate of flow of positive charge moving through the light bulb in the direction of the arrow label. For example, $I_1 = 3\text{ mA} = 0.003\text{ A}$ means that $0.003\text{ C}$ of positive charge flows from left to right every second. This is the same as saying that every second about 19 quadrillion $(19 \times 10^{15})$ electrons with total charge $-0.003\text{ C}$ flow from right to left (in the direction opposite the arrow label). But there is no need to fixate on electrons and their incomprehensibly large numbers, so from now on we will only refer to current direction in terms of the flow of positive charge.
Figure 5 Fig. 5: Negative current. The current $I_2 = -3\text{ mA}$ means that every second $0.003\text{ C}$ of positive charge flows in the direction opposite the arrow label. That is, it flows from left to right, exactly the same as in Fig. 4. This observation makes sense because we have not changed anything physical. We only reversed the arrow label and (to compensate) changed the sign of the current value.
A capacitor can store electrical potential energy. A capacitor is a device that separates positive and negative charge when a voltage drop is applied across its terminals. The number of coulombs of charge that it separates per 1 volt applied is called its capacitance $C$. So, capacitance has units of coulombs/volt (C/V), which are called farads, with symbol F.
If an applied voltage drop of $V$ volts separates $+Q$ and $-Q$ coulombs of charge from each other, the capacitance is given by \begin{align} C=\frac{Q}{V} \label{ENE-CQV} \end{align} In this way, a capacitor continues to separate more charge as the voltage difference increases until the capacitor can no longer withstand the attraction between the separated positive and negative charges. The voltage drop at this point of breakdown is called the breakdown voltage.
Figure 7 Fig. 7: A capacitor. This capacitor is labeled as having capacitance of 100 $\mu\text{F}$ and breakdown voltage of 63 V. When a voltage drop $V$ (below the breakdown voltage) is applied to a capacitor, electrical energy is converted into electrical potential energy that keeps the charge separated. If this voltage difference is allowed to decrease, then the amount of charge separated decreases as well, and so electrical potential energy is converted back into electrical energy. In this way, the capacitor acts as storage for electrical potential energy. If $C$ is the capacitance and $V$ is the voltage drop, \begin{align} \text{Electrical potential energy stored by a capacitor}= \frac{1}{2}CV^2 \label{ENE-CEQ} \end{align} We can check equation $\eqref{ENE-CEQ}$ by verifying that $(1/2) CV^2$ has units of joules. Suppose $C=100\text{ }\mu\text{F}$ and $V=63 \text{ V}$, the capacitance and breakdown voltage of the capacitor in Fig. 7. Then equation $\eqref{ENE-CEQ}$ evaluates to \begin{aligned} \frac{1}{2}CV^2 &= \frac{1}{2} (100\text{ }\mu\text{F}) (63\text{ V})^2\\ &= \frac{1}{2} (100 \cdot 10^{-6}\text{ F}) (63^2\text{ V}^2)\\ &= \frac{1}{2} (100 \cdot 10^{-6}\frac{\text{C}}{\text{V}}) (63^2\text{ V}^2)\\ &= \frac{1}{2} (100 \cdot 10^{-6}\frac{\text{C}}{\text{J/C}}) (63^2\frac{\text{J}^2}{\text{C}^2})\\ &\approx 0.2 \text{ J}, \end{aligned}since $1\text{ F}=(1\text{ C})/(1\text{ V})$ and $1\text{ V}=(1\text{ J})/(1\text{ C})$ by definition. This calculation also shows that the maximum amount of electric potential energy stored by the capacitor in Fig. 7 is 0.2 J (to 1 significant digit). A battery is a limited source of energy. Batteries are also limited in the energy they can hold. A battery's charge capacity is often reported in milliamp-hours (mA$\cdot$h) instead of coulombs, because it is convenient to think about the capacity as a number of milliamps of current delivered during a number of hours.
We can convert the charge capacity from mA$\cdot$h to C. Then, we can calculate the energy capacity by noting that the voltage of 3.6 V means that 1 C of charge delivers 3.6 J. \begin{aligned} \text{Charge capacity } &= 1200 \text{ mA}\cdot\text{h}\\ &= 1200(0.001 \text{ A})(3600 \text{ s})\\ &= 4320 \text{ C} \\ \text{Energy capacity } &= (4320 \text{ C})(3.6 \text{ V})\\ &\approx 16000 \text{ J} \end{aligned} Therefore, the battery pack in Fig. 8 can provide energy of 16 kJ (to 2 significant digits). This amount is approximate because the voltage and charge capacity values are nominal. In reality, the voltage drop across the terminals is not constant at 3.6 V. It can vary slightly depending on what is connected to the terminals. It also decreases slowly as the energy depletes. Voltage and current sources are ideal models of energy sources. For simplicity, we want to represent a battery-like device that, unlike an actual battery, always provides a specified voltage drop across its terminals. This ideal energy source is called a voltage source and has its own symbol.
Figure 9 Fig. 9: Symbol for a voltage source. This voltage source always provides a voltage drop of $V_s$ from the $+$ terminal to the $-$ terminal, with the terminal labels indicated inside the symbol.
There is another kind of ideal energy source, called a current source, that always drives a specified current through itself. There are no simple devices that act like a current source, but the concept is useful for modeling other devices and performing circuit analysis.
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