Introduction
Electricity is literally omnipresent- we can use it at our homes, at our factories, and in our gadgets that we carry with us day in day out. But have you ever wondered why some things have electricity flowing through them like it is butter and some things just keep it out completely? This is answered by an attribute known as resistivity.
Resistivity informs us of the resistance of a substance to electricity. Silver and copper are cool metals that are good conductors, but are blocked by insulators such as glass and rubber. In between them are semiconductors, which are the lifeblood of our technology.
We will consider the resistivity of various materials using the values given in the Table in this work, and we will also observe the working of resistors in real circuits.
Understanding Resistivity
Fundamentally, it is resistivity that informs us about the degree of resistance of a certain material to electric current. It is represented by the Greek character ρ (rho) and we quantify it in ohm-meters ( Ω m).
Formula for Resistivity
Resistivity is mathematically expressed as:
Where:
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R = Resistance of the conductor (Ω)
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A = Cross-sectional area of the conductor (m²)
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l = Length of the conductor (m)
Simply, resistivity is dependent upon the material and temperature of the material rather than on its size.
Classification of Materials Based on Resistivity
The common groupings of materials based on their resistance to electricity are conductors, semiconductors, and insulators.
Conductors
Resistive conductors are materials that do not resist electricity in any way; they have resistivity in the 10⁻⁸ 10⁻⁶ m. Due to the ease with which electrons can move through them, they are the preferred choice in wiring and electrical circuits.
Examples of Conductors
| Material | Resistivity (Ω·m at 0°C) | Temperature Coefficient (°C⁻¹) |
|---|---|---|
| Silver | 1.6 × 10⁻⁸ | 0.0041 |
| Copper | 1.7 × 10⁻⁸ | 0.0068 |
| Aluminium | 2.7 × 10⁻⁸ | 0.0043 |
| Tungsten | 5.6 × 10⁻⁸ | 0.0045 |
| Iron | 10 × 10⁻⁸ | 0.0065 |
| Platinum | 11 × 10⁻⁸ | 0.0039 |
| Mercury | 98 × 10⁻⁸ | 0.0009 |
| Nichrome | ~100 × 10⁻⁸ | 0.0004 |
| Manganin (alloy) | 48 × 10⁻⁸ | 0.002 × 10⁻³ |
Key Takeaways:
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Silver is the most conductive, but too expensive for general wiring.
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Copper, thanks to its high conductivity and cost-effectiveness, is extensively used in electrical systems.
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Aluminium is light and hence ideal for overhead power cables.
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Nichrome and Manganin are employed in resistors and heating coils because of their resistance against changes in resistivity with temperature.
Temperature Dependence of Conductors
The vast majority of conductors have a positive temperature coefficient, i.e. their resistivity increases with temperature. The reason is that the atoms move faster on the higher temperatures, which decelerates electrons.
Semiconductors
Semiconductors lie between conductors and insulators. Their resistivity is more than in metals but less than in insulators. The neat thing is that their resistivity decreases with temperature and this is the opposite of conductors.
Examples of Semiconductors (From Table 3.1)
| Material | Resistivity (Ω·m at 0°C) | Temperature Coefficient (°C⁻¹) |
|---|---|---|
| Carbon (graphite) | 3.5 × 10⁻⁵ | -0.0005 |
| Germanium | 0.46 | -0.05 |
| Silicon | 2300 | -0.07 |
Key Takeaways:
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Graphite is somewhat a good conductor of electricity and is used in carbon resistors.
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Diodes, transistors, and microchips contain Germanium and silicon.
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They have a negative temperature coefficient and are therefore very useful in devices that are sensitive to temperature.
Insulators
Insulators are the reverse; they are of such large resistivity, 10¹⁰ to 10¹⁶ Ω m. They do not conduct any electricity, and hence we use them to prevent electric leakage.
Examples of Insulators
| Material | Resistivity (Ω·m at 0°C) |
|---|---|
| Pure Water | 2.5 × 10⁵ |
| Glass | 10¹⁰ – 10¹⁴ |
| Hard Rubber | 10¹³ – 10¹⁶ |
| NaCl (Sodium Chloride) | ~10¹⁴ |
| Fused Quartz | ~10¹⁶ |
Key Takeaways:
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Glass and rubber are common insulators used in everyday applications.
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Fused Quartz has exceptional resistance, thus it is ideal when completing special insulating work.
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Pure water is also not a good conductor, but by adding a small amount of salt to it, the resistivity of the water can be reduced significantly.
Practical Applications of Resistivity
Resistivity isn't some abstract idea—its effects have a very real application in the design of electrical devices. No better example exists than the resistor, an engineered device whose sole purpose is to resist electric current.
Resistors in Circuits
Resistors assist in regulating the circulation of electricity, dividing voltage, and maintaining other components of the circuit safe. The material you choose is determined by what you want it to accomplish, since various materials have varied resistivity.
Types of Resistors
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Wire-Wound Resistors: We prepare them by putting an alloy wire, such as nichrome or manganin, around a ceramic core. They are very precise and constant hence their frequent appearances in the labs.
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Carbon Resistors: They are constructed from carbon, they are small, cheap, and are commonly used in consumer electronics.
Resistor Colour Coding
Since resistors are often tiny, their resistance values are marked using a colour band system instead of printed numbers. Each colour corresponds to a digit, a multiplier, and sometimes a tolerance value.
| Colour | Digit | Multiplier | Tolerance (%) |
|---|---|---|---|
| Black | 0 | 1 | – |
| Brown | 1 | 10 | – |
| Red | 2 | 10² | – |
| Orange | 3 | 10³ | – |
| Yellow | 4 | 10⁴ | – |
| Green | 5 | 10⁵ | – |
| Blue | 6 | 10⁶ | – |
| Violet | 7 | 10⁷ | – |
| Gray | 8 | 10⁸ | – |
| White | 9 | 10⁹ | – |
| Gold | – | 10⁻¹ | 5 |
| Silver | – | 10⁻² | 10 |
| No colour | – | – | 20 |
Example Calculation
Suppose a resistor has four colour bands: Red, Red, Silver. The first two bands (Red, Red) correspond to the digits 2 and 2. The third band (Silver) is the multiplier (10⁻²). So, the resistance value is:
22×10⁻² Ω=0.22 Ω
If the fourth band is Silver, the tolerance is ±10%.
Another example: A resistor with Violet, Yellow, Brown, and Gold translates to:
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Violet (7), Yellow (4), Brown (10 multiplier) = 74 × 10 = 740 Ω
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Gold band = ±5% tolerance
This is exactly how Figure illustrates real-world color-coded resistors.
Conclusion
The theory of resistivity nicely describes why certain materials carry electricity with ease and others fight it. Conductors such as copper and aluminum are the veins of our power infrastructure, semiconductors such as silicon power the information revolution, and insulators such as glass provide safety and reliability.
In addition, by using resistivity in real devices like resistors, we are able to control and govern electric current in specific manners. Due to the color coding system, even small resistors are able to express their values at a glance.
From home wiring to sophisticated microchips, resistivity is a characteristic that determines how our world is powered and networked. It is a property that, when comprehended, provides a better understanding of the hidden science of contemporary life.