3.8 - TEMPERATURE DEPENDENCE OF RESISTIVITY
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Resistivity Basics
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Today we'll explore resistivity, a crucial concept in electronics. Can anyone tell me what resistivity is?
Isn't it a measure of how difficult it is for current to pass through a material?
Exactly! And it's influenced by several factors, one of which is temperature. Remember this: as temperature increases in conductors, resistivity typically increases. We can use the acronym PIM - Positive Increasing Metal.
So, all metals show increased resistivity with temperature?
That's right! Let's summarize: metals have positive temperature coefficients, meaning their resistivity increases with temperature.
Temperature Coefficient of Resistivity
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Who can remember the formula that relates resistivity to temperature?
It’s \\( r = r_0 [1 + a(T - T_0)] \\$ for metals, right?
Good job! The term \\$ a \\$ is the temperature coefficient. For metals, \\$ a \\$ is positive, indicating that resistance increases with temperature. What about semiconductors?
Their resistivity decreases with increasing temperature because more electrons can move.
Correct! Remember: semiconductors are like sponges, soaking up thermal energy, which helps them conduct better.
Practical Applications
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Can anyone think of a use for these resistivity principles in everyday devices?
How about resistors in circuits? They need to be stable across temperatures.
Exactly! And technologies like thermistors rely on these principles. Remember the acronym CMC - Control-Material-Change, which reflects how temperature can control resistance.
So, would Nichrome be used for heating elements because its resistivity changes very little with temperature?
Correct again! Nichrome is chosen as it exhibits minimal change in resistivity, making it suitable for heating applications.
Introduction & Overview
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Quick Overview
Standard
This section discusses how resistivity changes with temperature for different materials. It specifically focuses on the temperature coefficient of resistivity for metals, semiconductors, and insulating materials and shows how these factors affect their practical applications.
Detailed
The resistivity \( r \) of a material is an essential property that indicates how strongly it opposes the flow of electric current; this property is temperature dependent. For metallic conductors, the general formula for resistivity as it relates to temperature is given by \( r = r_0 [1 + a(T - T_0)] \), where \( r_0 \$ is the resistivity at the reference temperature \$ T_0 \$ and \$ a \$ is the temperature coefficient of resistivity. This relationship indicates that for metals, the resistivity increases linearly with temperature, leading to a positive temperature coefficient \$ (a > 0) \$ due to increased thermal vibrations of atoms at higher temperatures, which impedes the flow of electrons. Conversely, semiconductors exhibit a negative temperature coefficient where their resistivity decreases with increasing temperature, owing to the increased mobility of charge carriers as thermal energy facilitates electron movement across the band gap. The section is significant as it outlines the implications of temperature on material properties, especially in applications such as resistors, sensors, and electrical components utilized in various temperatures.
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Effect of Temperature on Resistivity
Chapter 1 of 5
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Chapter Content
The resistivity of a material is found to be dependent on the temperature. Different materials do not exhibit the same dependence on temperatures.
Detailed Explanation
The resistivity of materials is influenced by temperature changes. As the temperature varies, the structure of the material and how easily electrons can move through it also change. This means that heating a conductor often makes it more resistant to the flow of electricity.
Examples & Analogies
Think of it like a group of people trying to walk through a hallway. If the hallway is cold, people move slowly without bumping into each other too much. However, if you heat it, more people can enter, but they start bumping into each other more frequently, causing delays – this is akin to how temperature affects the resistivity of materials.
Mathematical Relation
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Chapter Content
Over a limited range of temperatures, that is not too large, the resistivity of a metallic conductor is approximately given by, r = r0[1 + a(T - T0)] where r is the resistivity at a temperature T and r0 is the same at a reference temperature T0. a is called the temperature co-efficient of resistivity, and from Eq. (3.26), the dimension of a is (Temperature)–1. For metals, a is positive.
Detailed Explanation
This formula explains how to calculate the resistivity at different temperatures. The term 'a' represents the temperature coefficient, which tells us how much the resistivity increases as the temperature rises from a reference point (T0). This means that for most metals, as we heat them, their resistivity increases linearly within certain temperature limits.
Examples & Analogies
Imagine filling a balloon with water. If you start heating the balloon, the water expands and pushes against the sides. The temperature coefficient would be like measuring how fast the water level rises relative to the amount of heat applied. Just as the water gets harder to push through as it expands, the electricity faces more resistance in the metal as it gets warmer.
Graphical Representation
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Chapter Content
The relation of Eq. (3.26) implies that a graph of r plotted against T would be a straight line. At temperatures much lower than 0°C, the graph, however, deviates considerably from a straight line.
Detailed Explanation
When plotting the resistivity against temperature for most metals, the result is a linear graph up to a certain point. However, at very low temperatures (below 0°C), this linearity breaks down, indicating that other factors may begin to affect resistivity, possibly due to changes in electron mobility or the lattice structure of the atoms.
Examples & Analogies
Think of walking your dog on a leash. When the weather is mild (ideal temperature), you can walk in a straight line easily. But if it’s extremely cold, maybe your dog starts bouncing around more, or other obstacles appear, making it challenging. Similarly, at very low temperatures, the behavior of electrons in metals is not as predictable.
Resistivity of Specific Materials
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Chapter Content
Some materials like Nichrome (which is an alloy of nickel, iron and chromium) exhibit a very weak dependence of resistivity with temperature. Manganin and constantan have similar properties. These materials are thus widely used in wire bound standard resistors since their resistance values would change very little with temperatures.
Detailed Explanation
Certain materials are specifically chosen for their stability across a range of temperatures, which makes them ideal for applications requiring precision, such as in resistors. The weak dependence of their resistivity on temperature means that their performance remains consistent, reducing errors in measurements.
Examples & Analogies
Consider a well-insulated thermos bottle that keeps drinks cold or hot regardless of the outside temperature. Just as the thermos maintains the temperature of the liquid within, materials like Nichrome maintain their resistivity, remaining reliable across temperature variations.
Behavior of Semiconductors
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Chapter Content
Unlike metals, the resistivities of semiconductors decrease with increasing temperatures. A typical dependence is shown in Fig. 3.10. We can qualitatively understand the temperature dependence of resistivity, in the light of our derivation of Eq. (3.23).
Detailed Explanation
Semiconductors behave differently than metals; as their temperature rises, their resistivity decreases. This means they can conduct electricity better at higher temperatures as more charge carriers become available. This is particularly important for devices like transistors and diodes, which rely on semiconductor materials.
Examples & Analogies
If you think of a crowded room where people are dancing (representing electrons), it may be difficult to move through at first. But as the music gets faster and the dancing heats up, more people start moving around, creating gaps – just like how increased temperature in semiconductors enhances conductivity.
Key Concepts
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Resistivity: The intrinsic property of a material that quantifies its ability to resist electric current.
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Temperature Coefficient: A parameter that describes how resistivity changes with temperature, affecting the material's performance in different conditions.
Examples & Applications
For metallic conductors, resistivity typically increases with temperature, impacting devices such as resistors and heating elements.
Semiconductors show the opposite effect, where increasing temperature lowers resistivity, enhancing their conductivity.
Memory Aids
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Rhymes
Resistivity grows, as heat it shows; metals creep slow, in hot they won’t flow.
Stories
Imagine a metal wire getting hot in the sun, at first it flows easily, but as heat comes in, the atoms shiver, blocking the way for the current to win!
Memory Tools
Metallic metals might melt (MMM) - Metals increase resistivity with heat.
Acronyms
For temperature Coefficient
Remember PIM - Positive Increasing Metal indicates increase with temperature.
Flash Cards
Glossary
- Resistivity
A measure of how strongly a material opposes the flow of electric current, typically expressed in ohm-meters (Ω·m).
- Temperature Coefficient of Resistivity
A factor that quantifies how much a material's resistivity changes with temperature.
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