
Electrical resistance is a property of a material or circuit that transforms electric energy into heat energy by impeding the flow of electric current. It is denoted by the symbol R and measured in ohms. The resistance of an object depends on several factors, including the material it is made of, its shape, and its temperature. Objects made of electrical insulators like rubber tend to have high resistance, while electrical conductors like metals have low resistance. Resistance is also influenced by the length and cross-sectional area of the conductor, with longer and thinner objects having higher resistance. Understanding electrical resistance is crucial for controlling and optimizing the performance of electrical circuits and devices.
| Characteristics | Values |
|---|---|
| Material | Objects made of electrical insulators like rubber have high resistance and low conductance, while electrical conductors like metals have low resistance and high conductance. |
| Size and Shape | Resistance is higher in long and thin wires and lower in short and thick wires. |
| Temperature | Resistance increases with temperature in conductors. In insulators, resistance decreases with increasing temperature. |
| Voltage and Current | Resistance is defined as the ratio of voltage to current. |
| Superconductors | Superconductors have zero resistance. |
| Resistivity | A property of materials related to the number of free electrons present. |
| Geometry | Resistance is higher in a long, narrow pipe compared to a wide, short pipe. |
| Frequency | Resistance and conductance can be frequency-dependent in AC circuits. |
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What You'll Learn

Material
The material from which an object is made is a key factor in determining its electrical resistance. Electrical resistance refers to a material's opposition to the flow of electric current. It is a fundamental property of conductive materials, such as metals and semiconductors, and is measured in ohms (Ω).
Different materials have different levels of resistance due to the arrangement and density of their atoms. Materials with a high number of "delocalized" electrons, which are not stuck in any one place, have low resistance as these electrons are free to move across large distances. Examples of such materials include gold, silver, copper, and aluminium. On the other hand, materials with tightly bound electrons, such as Teflon, rubber, plastic, and glass, have high resistance as a great force is required to pull the electrons away.
The geometry of an object also affects its resistance. For instance, a long, thin copper wire has higher resistance than a short, thick wire of the same material. This is because longer conductors have higher resistance as electrons must travel a greater distance, increasing the likelihood of collisions with atoms. Similarly, smaller wires have more resistance than larger-diameter wires as they contain fewer atoms for electrons to flow through.
The temperature of a material also influences its resistance. In general, resistance increases with temperature as higher temperatures cause atoms to vibrate more, increasing the likelihood of collisions with electrons. However, the resistivity of insulators decreases as temperature increases, as the movement of electrons from the conduction band to the valence band increases due to the large energy gap between these two bands.
Superconductors are materials that have zero resistance and infinite conductance. They require cooling to extremely low temperatures, usually with liquid helium or liquid nitrogen.
Understanding and managing electrical resistance is essential for energy efficiency and safety. Reducing resistance in electronic circuits and devices minimises energy loss as heat, thereby increasing energy efficiency. Additionally, excessive heat generated by high resistance can pose a risk to both electronic components and users.
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Geometry
The geometry of an object plays a significant role in determining its electrical resistance. This is similar to how water flows through pipes: it is harder to push water through a long, narrow pipe than a wide, short one. In the same way, a long, thin copper wire has higher resistance than a short, thick one.
The resistance of an object is directly proportional to its length. For example, a cylinder's resistance is directly proportional to its length, and its diameter determines how much current it can carry. The longer the cylinder, the more collisions charges will make with its atoms. Therefore, the resistance of an object can be decreased by increasing its cross-sectional area.
The relationship between resistance and geometry is also evident in wires. The resistance of a wire is influenced by its length and thickness. A long and thin wire has higher resistance than a short and thick one. This relationship between geometry and resistance is not limited to wires; it applies to objects of various shapes and sizes.
The geometry of a conductor also affects its resistivity, which is a measure of its ability to oppose electric current. The formula for resistivity assumes a uniform current density in the conductor, but in practical situations, this may not always be the case. For long, thin conductors like wires, this formula still provides a good approximation. However, for alternating current (AC), the skin effect and the related proximity effect impact the current flow near the centre of the conductor, resulting in a higher-than-expected resistance.
In conclusion, the geometry of an object is a critical factor in determining its electrical resistance. The length, thickness, and cross-sectional area of an object influence its resistance, and these geometric properties interact with the material's composition to determine its overall resistance. Understanding the relationship between geometry and resistance is essential for designing and analysing electrical systems, ensuring efficient energy transmission, and preventing issues such as overheating or electrical fires.
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Temperature
The relationship between electrical resistance and temperature is an important concept in physics, and it varies depending on the material being considered. Resistance is influenced by the design and material composition of a conductor, but temperature also plays a significant role.
Atoms and molecules within a conductor obstruct the flow of electrons, and as temperature increases, these atoms and molecules vibrate more, making it harder for electrons to pass through. This results in increased resistance as temperature rises. This relationship is particularly notable in metallic conductors, where resistance is directly proportional to temperature.
However, the relationship between resistance and temperature is more complex in semiconductors. As temperature rises, more electrons are freed from their valence duties and become available for conducting electricity. This increase in electrons improves the conductivity of the semiconductor, leading to a decrease in resistance.
The temperature coefficient of resistance, α, quantifies the relationship between temperature and resistance. It represents the fractional increase in resistivity per unit rise in temperature. In some materials, like silicon, the temperature coefficient of resistivity is negative, indicating that resistance decreases as temperature increases. This complexity has led to the development of devices like thermistors, which are specifically designed to measure or control temperature based on the principle of varying resistance with changes in temperature.
Additionally, it is possible to create a resistor with minimal temperature dependence by combining two resistors in series, one with a positive temperature coefficient and the other with a negative temperature coefficient. This design ensures that changes in temperature have a negligible impact on the overall resistance.
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Voltage
The relationship between voltage, electrical resistance, and current forms the basis of Ohm's Law, a fundamental principle in electrical engineering and physics. This law states that voltage (V) is equal to the product of current (I) and resistance (R), expressed as V = IR.
Ohm's Law shows that voltage (or electrical pressure) is the driving force behind the flow of current in a circuit. The current in a circuit is directly proportional to the voltage applied and inversely proportional to the resistance of the circuit, provided the temperature remains constant. This means that if the voltage is high, the current is high, and if the voltage is low, the current is low.
For example, if a circuit has a resistance of 10 ohms and the voltage supplied is 5 volts, the current can be calculated using Ohm's Law as follows: I = V/R = 5V/10Ω = 0.5A. If the resistance is increased to 20 ohms while keeping the voltage constant, the current decreases to I = 5V/20Ω = 0.25A.
The relationship between voltage, current, and resistance is crucial for understanding how electrical devices work and for designing circuits effectively. It is also important for various electrical applications, including electronics and troubleshooting electrical systems.
Additionally, the resistance of an object depends on the material it is made of and its size and shape. Objects made of electrical insulators like rubber tend to have high resistance, while conductors like metals have low resistance. The larger the cross-section of a conductor, the lower its resistance.
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Current
Electrical resistance is closely related to current. Current refers to the flow of electricity through an object, such as a wire, and is measured in amps (A). The driving force behind the flow of current is known as voltage, which is measured in volts (V).
The amount of current in a circuit depends on the amount of voltage and the amount of resistance in the circuit to oppose current flow. Voltage can be thought of as the force that pushes electrons through a conductor, and the greater the voltage, the greater its ability to push electrons through a circuit.
Ohm's Law states that the current flowing in a circuit is directly proportional to the applied voltage and inversely proportional to the resistance of the circuit, provided the temperature remains constant. In other words, to increase the current flowing in a circuit, the voltage must be increased, or the resistance decreased.
The relationship between voltage, current, and resistance can be expressed algebraically as: voltage (E) is equal to current (I) multiplied by resistance (R). This equation can be manipulated to solve for I and R.
The SI unit of electrical resistance is the ohm (Ω), and it measures the opposition to the flow of electric current. The unit of electrical resistance is ohms, defined as one volt per ampere.
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