6.2: Source Voltage
- Page ID
- 100359
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- Define source voltage.
- Explain the basic operation of a battery.
- Define an ideal battery.
If you forget to turn off your car lights, they slowly dim as the battery runs down. Why don’t they suddenly blink off when the battery’s energy is gone? Their gradual dimming implies that the battery output voltage decreases as the battery is depleted. The reason for the decrease in output voltage for depleted batteries is that all voltage sources have two fundamental parts—a source of electrical energy and an internal resistance. In this section, we examine the energy source and the internal resistance.
Introduction to Source Voltage
Voltage has many sources, a few of which are shown in Figure \(\PageIndex{1}\). All such devices create a potential difference and can supply current if connected to a circuit. A special type of potential difference is known as source voltage. (Note: Source voltage is called electromotive force (emf) in some texts, but this usage is deprecated because emf is not a force and does not have dimensions of newtons in the SI system.)
Consider a simple circuit of a 12-V lamp attached to a 12-V battery, as shown in Figure \(\PageIndex{2}\). The battery can be modeled as a two-terminal device that keeps one terminal at a higher electric potential than the second terminal. The higher electric potential is sometimes called the positive terminal and is labeled with a plus sign. The lower-potential terminal is sometimes called the negative terminal and labeled with a minus sign.
When the battery is not connected to the lamp, there is no net flow of charge within the battery. Once the battery is connected to the lamp, charges flow from one terminal of the battery, through the lamp (causing the lamp to light), and back to the other terminal of the battery. If we consider positive (conventional) current flow, positive charges leave the positive terminal, travel through the lamp, and enter the negative terminal.
Positive current flow is useful for most of the circuit analysis in this chapter, but in metallic wires and resistors, electrons contribute the most to current, flowing in the opposite direction of positive current flow. Therefore, it is more realistic to consider the movement of electrons for the analysis of the circuit in Figure \(\PageIndex{2}\). The electrons leave the negative terminal, travel through the lamp, and return to the positive terminal. For the battery to maintain the potential difference between the two terminals, negative charges (electrons) must be moved from the positive terminal to the negative terminal. The battery acts as a charge pump, moving negative charges from the positive terminal to the negative terminal to maintain the potential difference. This increases the potential energy of the charges and, therefore, the electric potential of the charges.
The force on the negative charge from the electric field is in the opposite direction of the electric field, as shown in Figure \(\PageIndex{2}\). For the negative charges to be moved to the negative terminal, work must be done on the negative charges. This requires energy, which comes from chemical reactions in the battery. The potential is kept high on the positive terminal and low on the negative terminal to maintain the potential difference between the two terminals. The source voltage is equal to the work done on the charge per unit charge \(\left(\varepsilon = \frac{dW}{dq}\right)\) when there is no current flowing. Since the unit for work is the joule and the unit for charge is the coulomb, the unit for source voltage is the volt \((1 \, \mathrm{V} = 1 \, \mathrm{J}/\mathrm{C})\).
The Origin of Battery Potential
The first battery was invented in 1799 by Alessandro Volta and was also known as the voltaic pile. Modern batteries have improved considerably since those early times, but often still retain the concept of a series of cells, each of which creates a potential difference. The combination of chemicals and the makeup of the terminals in a battery determine its source voltage. The lead acid battery used in cars and other vehicles is one of the most common combinations of chemicals. Figure \(\PageIndex{3}\) shows a single cell (one of six) of this battery. The cathode (positive) terminal of the cell is connected to a lead oxide plate, whereas the anode (negative) terminal is connected to a lead plate. Both plates are immersed in sulfuric acid, the electrolyte for the system.
Knowing a little about how the chemicals in a lead-acid battery interact helps in understanding the potential created by the battery. Figure \(\PageIndex{4}\) shows the result of a single chemical reaction. Two electrons are placed on the anode, making it negative, provided that the cathode supplies two electrons. This leaves the cathode positively charged, because it has lost two electrons. In short, a separation of charge has been driven by a chemical reaction.
Note that the reaction does not take place unless there is a complete circuit to allow two electrons to be supplied to the cathode. Under many circumstances, these electrons come from the anode, flow through a resistance, and return to the cathode. Note also that since the chemical reactions involve substances with resistance, it is not possible to create the source voltage without an internal resistance.
Terminal Voltage and Ideal Batteries
The terminal voltage \(V_{\mathrm{terminal}}\) of a battery is the voltage measured across the terminals of the battery when there is no load connected to the terminal. An ideal battery maintains a constant terminal voltage, independent of the current between the two terminals. An ideal battery has no internal resistance, and the terminal voltage is equal to the source voltage of the battery \(\varepsilon = V_{\mathrm{terminal}}\). While all real batteries will have some internal resistance, if the internal resistance is small compared to the external load resistance in the circuit, the internal resistance will have a negligible effect on the current in the circuit and modeling the battery as ideal can yield accurate results. As we start to learning to analyze circuits, we will commonly make this model assumption in subsequent problems.
In a subsequent section, we will show that a real battery does have internal resistance and the terminal voltage is always less than the source voltage of the battery.