Umair Gaines
Electrical resistance is the measure of how much a material resists the flow of electric charges. It is influenced by the material's shape and composition, as well as the temperature. Resistivity, an intrinsic property of a material, determines how difficult it is for electric current to flow through an object. Conductors have the lowest resistivity, while insulators have the highest. Ohm's Law, which relates electrical current to voltage difference, is often used to calculate resistance. The resistance of a wire can be calculated using its length, cross-sectional area, and temperature.
| Characteristics | Values |
|---|---|
| Definition of Resistance | Describes how strongly a given cable opposes the flow of an electric current |
| Factors Affecting Resistance | Length, Resistivity, Temperature, Material, Geometry, Voltage, Current |
| Ohm's Law | Relates electrical current (I) to the voltage difference (V) between two points of an electrical conductor |
| Ohm's Law Formula | Divide voltage by the current (V/I) |
| Pouillet's Law | A formula for estimating a wire's resistance |
| Units of Resistance | Ohms (Ω) |
| Units of Resistivity | Ohm meter (Ω x m) |
| Units of Conductivity | Siemens per meter (S/m) |
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What You'll Learn
Ohm's Law
The formula for Ohm's Law is V = IR, where V is voltage, I is current, and R is resistance. This means voltage = current x resistance, or volts = amps x ohms, or V = A x Ω. If you know any two of the values for voltage, current, and resistance, you can use Ohm's Law to calculate the third. For example, if you know voltage and current and want to know resistance, you can calculate the remaining equation by crossing out the variable you want to find in the pyramid and solving for it.
It is important to note that resistance cannot be measured in an operating circuit, so Ohm's Law is particularly useful in such cases.
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Resistivity
The resistivity of a material is dependent on its temperature. Resistivity tabulations usually list values at 20° C. Resistivity of metallic conductors generally increases with a rise in temperature; but resistivity of semiconductors, such as carbon and silicon, generally decreases with a temperature rise. Conductivity is the reciprocal of resistivity, and it, too, characterizes materials on the basis of how well electric current flows in them. The metre-kilogram-second unit of conductivity is mho per metre, or ampere per volt-metre. Good electrical conductors have high conductivities and low resistivities. Good insulators, or dielectrics, have high resistivities and low conductivities. Semiconductors have intermediate values of both.
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Temperature
For pure metals, the temperature coefficient is positive, signifying that resistance increases with temperature. This relationship can be linear, as observed in copper, or follow a power function, depending on the material. The increase in resistance with temperature is due to the heightened vibrational motion of atoms in the material, leading to increased collisions between free and captive electrons, which impedes the flow of current.
On the other hand, insulators tend to show a decrease in resistance as temperature rises. This decrease in resistance is attributed to the liberation of captive electrons due to atomic vibrations at higher temperatures. Materials commonly used as insulators, such as glass and plastic, maintain their insulating properties over the typical temperature ranges they are subjected to, only exhibiting a noticeable drop in resistance at very high temperatures.
The selection of materials for resistors in electronic circuits takes into account their temperature coefficients. Conductors with very low positive temperature coefficients are chosen to ensure that resistance remains relatively constant over varying temperatures. Conversely, insulators are selected for their low negative temperature coefficients, ensuring stable insulating behaviour across their working temperature ranges.
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Length
The resistance of a wire is directly proportional to its length. The longer the wire, the more resistance there will be. This relationship can be expressed by the equation: R = ρL/A, where R is the resistance, L is the length, A is the cross-sectional area, and ρ is the resistivity of the material.
Resistance describes how strongly a given cable opposes the flow of an electric current. The higher the resistance, the more difficult it is for the current to flow. Conversely, the higher the conductivity, the more smoothly the electrical current can flow through the wire.
Resistivity is an intrinsic property of a material. It remains the same regardless of the wire's dimensions. The higher the resistivity, the larger the field needed to produce a given current density. The resistivity of some materials is affected by temperature. For example, the resistivity of copper increases with increasing temperature.
The resistance of a wire can be calculated by first determining the wire's length and cross-sectional area. Then, divide the length of the wire by its cross-sectional area. Finally, multiply the result by the resistivity of the material.
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Cross-sectional area
The resistance of an object depends on its shape and the material it is made of. The cross-sectional area of an object is one of the factors that influence its electrical resistance.
Resistance is a measure of how much a material resists the flow of charges. The higher the resistance, the harder it is for current to flow through the conductor, and the more voltage is required. This property depends on the cable material and geometry. The resistance of an object is inversely proportional to its cross-sectional area. This means that as the cross-sectional area of an object increases, its resistance decreases, and vice versa.
The relationship between cross-sectional area and resistance can be observed in a cylindrical resistor. The resistance of a cylinder is directly proportional to its length. A longer cylinder will result in more collisions between charges and its atoms, leading to increased resistance. On the other hand, the diameter of the cylinder affects its cross-sectional area, which in turn influences its current-carrying capacity. A cylinder with a larger diameter will have a greater cross-sectional area, allowing for a higher current flow.
The cross-sectional area of a wire also impacts its resistance and conductance. A wire with a larger cross-sectional area will offer less resistance to the flow of electric current, while a wire with a smaller cross-sectional area will have higher resistance. This relationship between cross-sectional area and resistance is crucial in designing electrical components and circuits, as it helps determine the appropriate wire sizes and configurations to achieve the desired electrical properties.
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