Otis Singleton
Electrical resistance is the obstruction offered by the material in the flowing of the current or charge through the material. It is denoted by the letter R and is measured in ohms, represented by the symbol Ω. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S). The equation for electrical resistance is derived from Ohm's law, which states that the voltage (V) across a circuit is equal to the current (I) multiplied by the resistance (R). This can be rearranged to give the equation for resistance: R = V/I.
| Characteristics | Values |
|---|---|
| Definition | Electrical resistance is the obstruction offered by the material in the flowing of the current or charge through the material. |
| Symbol | R |
| Unit | Ohm (Ω) |
| Formula | V = IR, R = V/I, R = ρ*L/A |
| Factors | Material, Length, Area, Temperature, Voltage, Current |
| Ohm's Law | The law states that the voltage of a circuit is equal to the current multiplied by the resistance, or V = IR in equation form, with R = V / I. |
| Examples | Silver, copper, gold, and aluminium are conductors. Rubber, paper, glass, wood, and plastic are insulators. |
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What You'll Learn
The formula for electrical resistance
Ohm's law applies to a wide variety of materials and conditions, where V and I are directly proportional to each other, and therefore R and G (conductance) are constants. However, this is not always the case, and some components and materials used in electronics are nonlinear or non-ohmic, meaning the current is not proportional to the voltage. In these cases, the resistance varies with the voltage and current, and the formula cannot be used.
The resistance of a given object depends primarily on two factors: the material it is made of and its shape. For a given material, the resistance is inversely proportional to the cross-sectional area and directly proportional to the length. For example, a thick copper wire has lower resistance than a thin copper wire, and a long copper wire has higher resistance than a short copper wire.
The resistance of a resistor, which is a piece of material that impedes the electric current, can be calculated using the formula R = ρLA, where ρ is the Greek letter "rho" representing the resistivity of the material, L is the length of the resistor, and A is the area of a cross-section of the resistor.
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How to measure electrical resistance
Electrical resistance is the ratio between voltage and current, and is denoted by the capital letter R. The unit of electrical resistance is ohms, and resistance is always equal to voltage divided by current.
Ohm's Law states that the voltage of a circuit is equal to the current multiplied by the resistance, or V = IR, with R = V/I. This law applies to all circuits that conduct electricity.
Resistance can be measured using analog or digital multimeters, which also measure current and voltage. There are two methods for measuring resistance: constant current or constant voltage. The constant current technique involves sourcing a known current through an unknown resistance and measuring the resulting voltage. This technique is generally used for resistance values below 200M ohms. The constant voltage technique involves sourcing a known voltage across an unknown resistance and measuring the resulting current. This approach is used for high resistance (1e8 to 1e16) measurement applications.
When using a digital multimeter, turn the dial to resistance or ohms. The display should show OLΩ because, in Resistance mode, the multimeter automatically begins taking a resistance measurement even before test leads are connected. When the leads are connected, the multimeter will automatically adjust to the best range. Pressing the Range button allows for a manual range selection.
For very low-resistance measurements, use the relative mode (REL). This mode automatically subtracts test lead resistance. If the test leads touch, the display should show 0 Ω. Avoid touching the metal parts of the test leads, as the human body can become a parallel resistance path, lowering total circuit resistance.
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The relationship between voltage, current and resistance
The relationship between voltage, current, and resistance is defined by Ohm's Law, which states that the voltage (V) of a circuit is equal to the current (I) multiplied by the resistance (R), or V = IR. This law applies to all circuits that conduct electricity.
Ohm's Law can also be rearranged to solve for resistance, with the formula R = V/I. This formula tells us that resistance is always equal to voltage divided by the current. For example, if a resistor in a circuit has a resistance of 100 ohms and a current of 0.5 amps, we can calculate the voltage of the circuit as 50 volts.
The electrical resistance of an object is a measure of how much it opposes the flow of electric current. It is influenced by two main factors: the material it is made of and its shape. Objects made of electrical insulators like rubber tend to have higher resistance, while conductors like metals have lower resistance. This relationship is quantified by resistivity, which is the resistance offered per unit length and unit cross-sectional area. Resistivity is denoted by the Greek letter rho (ρ).
The geometry of an object also affects its resistance. For example, a long, thin copper wire has higher resistance than a short, thick wire of the same material. This is because it is more difficult for electric current to flow through a longer, narrower path.
Other factors such as temperature can also influence resistance. For instance, as the temperature of pure metals increases, their resistance also increases due to a reduction in electron mobility. On the other hand, insulators exhibit a decrease in resistance with increasing temperature as more electrons move from the conduction band to the valence band, resulting in increased conductance.
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Factors affecting electrical resistance
The equation for electrical resistance, R, is defined by Ohm's Law, which relates voltage, V, current, I, and resistance in a circuit:
$$R = \frac{V}{I}$$
There are four main factors that affect electrical resistance: length, cross-sectional area, type of material, and temperature.
Firstly, the length of a conductor affects its resistance. As the length of a conductor increases, so does its resistance. This relationship can be observed experimentally and is analogous to the increased risk of collision when driving a longer distance.
Secondly, resistance is inversely proportional to the cross-sectional area of a conductor. Increasing the cross-sectional area of a conductor leads to a decrease in resistance. This is because an increase in area provides more space for electric current to flow, reducing the obstruction.
Thirdly, the type of material used in a conductor influences its resistance. Materials with high electrical resistivity, such as insulators, impede the flow of electric current more than materials with low resistivity, such as conductors. Metals, for example, are typically good conductors, but they are not perfect, as evidenced by the heating of toaster wires.
Lastly, temperature plays a significant role in determining resistance. An increase in temperature leads to an increase in resistance for pure metals due to a higher number of electrons in the conduction band, reducing their mobility. Conversely, an increase in temperature causes a decrease in resistance for insulators. This is because the energy gap between the conduction and valence bands is large, allowing for increased electron movement from the conduction band to the valence band, resulting in enhanced conductance and reduced resistance.
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How electrical resistance generates heat
The equation for electrical resistance is given by Ohm's law, which states that resistance (R), voltage (V), and current (I) are related as follows: V = IR, or R = V/I. Resistance is measured in ohms, voltage in volts, and current in amps.
Now, onto how electrical resistance generates heat. Electrical resistance directly influences the heating effect in a circuit by determining the amount of heat produced. This is explained by Joule's law of heating, which states that the heat produced in a conductor is directly proportional to the square of the current (I), the resistance (R), and the time (t) for which the current passes through the circuit. This can be represented mathematically as H = I^2Rt, where H is the heat produced.
Resistance is essentially a measure of the difficulty faced by the current in passing through a conductor. When a current passes through a conductor, the electrons in motion collide with the atoms of the conductor. These collisions cause the electrons to lose energy, which is then converted into heat. Therefore, a higher resistance results in more collisions and, consequently, more heat generation.
The heating effect of resistance is utilized in various everyday appliances, such as electric heaters, toasters, and incandescent light bulbs. These devices use high-resistance wires, and the resistance impedes the flow of current, generating heat that serves the intended purpose of the appliance.
On the other hand, excessive heat generation due to resistance can be undesirable in certain applications, such as in electronic devices, where it can damage components and reduce their lifespan. In such cases, materials with low resistance, like copper and aluminum, are used in wiring to minimize the heating effect.
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Frequently asked questions
The equation for electrical resistance is V = IR, with R = V/I. In this equation, R stands for resistance, V stands for voltage, and I stands for current.
Voltage is measured in volts, current in amps, and resistance in ohms.
Resistance depends on the material and its shape. For example, a long, thin copper wire has higher resistance than a short, thick wire of the same material.
Resistivity is a property of a material that measures how strongly it resists electric current. It is defined as the resistance offered per unit length and unit cross-sectional area. The SI unit of resistivity is the ohm-meter (Ωm), and it is related to resistance by the formula ρ = RA, where ρ is resistivity, R is resistance, and A is the cross-sectional area.
