Wiktor Wise
In physics, the term 'small r' is used to denote the internal resistance of a battery. This is differentiated from the total resistance of a circuit, which is represented by the capital letter 'R'. The internal resistance of a battery is a result of its intrinsic resistance and is added to the resistance of the wire and other circuit elements to determine the total resistance. Ohm's law, a fundamental concept in electrical engineering, describes the relationship between voltage, current, and resistance in a circuit. It states that the electromotive force (emf) is proportional to the current produced and provides a quantitative understanding of how these electrical properties are interconnected.
| Characteristics | Values |
|---|---|
| Definition | Small r in the context of physics and electricity typically refers to the radial coordinate of a cylinder or spherical coordinate system. |
| Symbol | r |
| Unit | Meters (m) or centimeters (cm), depending on the context |
| Context | Small r is used in electrical engineering and physics to describe the distribution of electric charges and the resulting electric fields and potentials. |
| Applications | - Calculating electric fields and potentials in cylindrical or spherical systems - Understanding charge distributions and their effects - Solving for electric field and potential due to charged conductors or distributions |
| Related Concepts | - Large R (radial coordinate for cylindrical systems) - Theta (angular coordinate) - Phi (azimuthal angle in spherical coordinates) |
| Example Usage | In a cylindrical system, small r would represent the radial distance from the central axis, while large R would be the height or length of the cylinder. |
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What You'll Learn
Internal resistance (r) is the intrinsic resistance of the battery
In electrical engineering, a practical electric power source represented as a linear circuit may, according to Thévenin's theorem, be modelled as an ideal voltage source in series with an impedance. This impedance is called the internal resistance of the source. When the power source delivers current, the measured voltage output is lower than the no-load voltage; the difference is the voltage drop caused by the internal resistance.
The internal resistance of a battery can be calculated using its open-circuit voltage, load voltage, and load resistance. It can also be expressed in terms of the Overpotential and the current. As a battery ages, its internal resistance increases due to the degradation of components, electrolytes, and other factors. This increase in internal resistance leads to a decrease in the battery's voltage output.
Measuring the internal resistance of a battery is important for quality control during production and maintenance. It helps ensure consistent battery quality and allows for the identification and replacement of degraded batteries. Additionally, internal resistance can impact the safety of a battery. According to the Joule effect, the resistance hinders the current's passage, generating thermal heating. If the temperature becomes too high, it can lead to thermal runaway, causing harm to the system and its surroundings.
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Resistors and other circuit elements enable voltage harvesting
In the context of physics and electricity, "r" often denotes resistance, which is the capacity of a material to resist or prevent the flow of electric current within a circuit. Resistance is measured in Ohms, represented by the Greek symbol Omega (Ω).
Resistors and other circuit elements play a crucial role in voltage harvesting through a concept known as voltage division or the Voltage Divider Rule. Voltage dividers are passive circuits that utilise voltage division to produce different voltage levels from a single supply. This is achieved by connecting resistors, capacitors, and inductors in series, taking advantage of the voltage drops across each component.
The Voltage Divider Rule allows us to calculate the voltage drops across each series resistor. When two resistors, R1 and R2, are connected in series, the same electric current, I, must flow through each resistive element, resulting in an I*R voltage drop across each. By applying Kirchhoff's Voltage Law (KVL) and Ohm's Law, we can determine the voltage drop across each resistor using the equation V = IR.
Additionally, the voltage divider equation can be used to calculate the output voltage, Vout, based on the input voltage, Vin, and the values of R1 and R2. This equation states that Vout is directly proportional to Vin and the ratio of R1 to R2. By manipulating this equation, we can determine the required resistance value at R2 to achieve a desired Vout.
The behaviour of voltage dividers can be further understood through simplifications. For instance, when R1 and R2 are equal, the output voltage is half of the input voltage. If R2 is significantly larger than R1, the output voltage approximates the input voltage, with minimal voltage across R1. Conversely, if R2 is much smaller than R1, the output voltage becomes negligible compared to the input.
In summary, resistors, capacitors, and inductors, when combined in voltage divider circuits, enable voltage harvesting by providing the ability to generate specific output voltages from a single supply. These circuits find extensive applications in electrical engineering, showcasing the importance of resistors and other circuit elements in voltage manipulation and control.
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Resistivity of conductors increases with temperature
In physics, the letter "r" is often used to denote resistivity, which is a measure of how strongly a substance resists the flow of electric current. It is represented by the Greek letter rho (ρ) and is defined as the ratio of the voltage applied across a conductor to the current flowing through it.
Resistivity is influenced by temperature, and in general, the resistivity of conductors tends to increase with rising temperatures. This relationship can be described by the equation for the resistivity of a metallic conductor, where a graph of ρ (resistivity) against temperature would show a positive correlation, indicating that as temperature rises, so does resistivity.
This phenomenon can be explained by examining the atomic structure of conductors. Conductors typically have a large number of free electrons that facilitate the flow of electric current. When the temperature increases, the atoms in the conductor vibrate more vigorously, causing more collisions between the free electrons and the captive electrons. Each collision results in energy loss for the free electron, and this increased resistance to current flow is what defines higher resistivity.
However, it is important to note that not all materials exhibit the same behaviour. While conductors generally display positive temperature coefficients, indicating an increase in resistivity with temperature, insulators tend to show the opposite trend. As insulators are heated, their resistance may decrease due to the liberation of captive electrons, resulting in a higher number of free electrons available to carry the current.
The choice of materials for specific applications, such as resistors in electronic circuits, carefully considers the temperature dependence of resistivity. Materials with very low positive temperature coefficients are selected for resistors to ensure that their resistivity and resistance values change only slightly over a given temperature range.
Additionally, certain materials like Nichrome, Manganin, and constantan exhibit minimal changes in resistivity with temperature variations, making them ideal for use in wire-bound standard resistors.
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The relationship between voltage, current and resistance
The relationship between voltage, current, and resistance is fundamental to understanding electrical circuits. This relationship is described by Ohm's Law, which was discovered by Georg Simon Ohm and published in his 1827 paper, "The Galvanic Circuit Investigated Mathematically".
Ohm's Law states that the electrical current in a circuit can be calculated by dividing the voltage by the resistance. In other words, the current is directly proportional to the voltage and inversely proportional to the resistance. Mathematically, this can be expressed as I = V/R, where I represents the current in amperes, V represents the voltage in volts, and R represents the resistance in ohms.
According to Ohm's Law, if the voltage in a circuit is increased while the resistance remains constant, the current will also increase. Similarly, if the voltage is decreased, the current will decrease. This relationship can be understood by thinking of voltage as the force that motivates charge carriers to "flow" in a circuit, with the current being the continuous movement of electric charge through the conductors.
The amount of resistance in a circuit determines whether it is a good conductor or a bad conductor. Resistance is measured in ohms (Ω), with low resistance implying a good conductor made from materials such as copper, aluminium, or carbon, and high resistance implying a bad conductor made from insulating materials such as glass, porcelain, or plastic.
Ohm's Law also allows us to calculate the voltage or resistance in a circuit if the current and resistance or the current and voltage are known. For example, if the current and resistance in a circuit are known, we can calculate the voltage by rearranging Ohm's Law as V = IR. Similarly, if the current and voltage are known, we can calculate the resistance as R = V/I.
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The role of resistors in electronic devices
A resistor is a passive electrical component that creates resistance in the flow of electric current. They are indispensable to the proper functioning of electrical circuits and are ubiquitous in electronic equipment. Resistors regulate electrical current, protect sensitive components from voltage spikes, and ensure devices work as intended.
Resistance is measured in ohms (Ω). An ohm is the resistance that occurs when a current of one ampere (A) passes through a resistor with a one-volt (V) drop across its terminals. The current is proportional to the voltage across the terminal ends, and this ratio is represented by Ohm's law. Resistors are commercially available with resistance values over a range of more than nine orders of magnitude.
Resistors are rated according to their maximum power dissipation. Discrete resistors in solid-state electronic systems are typically rated at 1/10, ... 1/4 watt. They usually absorb much less than a watt of electrical power and require little attention to their power rating. Power resistors, on the other hand, are required to dissipate substantial amounts of power and are used in power supplies, power conversion circuits, and power amplifiers. These resistors have power ratings of 1 watt or greater and are physically larger.
In high-frequency applications, such as radio electronics, the parasitic capacitance and inductance of resistors can lead to undesired effects. Foil resistors generally have low parasitic reactance, while wire-wound resistors are among the worst. For accurate applications like audio amplifiers, the electric noise of the resistor must be minimal. The power rating is important in high-power applications as it specifies the maximum operating power the component can handle without sustaining damage or altering its properties.
Resistors have a wide range of applications in electronic devices. They can be used for limiting electric current, voltage division, heat generation, matching and loading circuits, gain control, and setting time constants. For example, LED load resistors are required when upgrading incandescent turn signals to LED lights. These resistors create a voltage drop, ensuring that the LED turn signals blink at a proper speed and are not destroyed by high voltage. Resistors can also be used as electric brakes to dissipate kinetic energy from trains or be smaller than a square millimeter for use in electronics. Variable resistors can adjust circuit elements, such as volume control or lamp dimmers, or act as sensing devices for heat, light, humidity, force, or chemical activity.
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Frequently asked questions
Small r in physics electricity refers to the internal resistance of a battery. It is denoted by 'r' and is used in the equation I = emf/(R + r).
Internal resistance (r) is the resistance that arises from within the battery itself. It is a result of the intrinsic resistance of the battery.
The internal resistance of a battery can be calculated by measuring the voltage drop when a small current is drawn from the battery.
R refers to the total resistance of the circuit, which includes the resistance of the wire and other circuit elements, while r refers specifically to the internal resistance of the battery.
