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91Ó°ÊÓ

Sketch a qualitative (no numbers) graph of the resistance as a function of temperature between \(100 \mathrm{~K}\) and \(0 \mathrm{~K}\) for (a) an ordinary conductor, such as \(\mathrm{Cu} ;\) (b) a superconductor with a transition temperature of \(30 \mathrm{~K}\).

Short Answer

Expert verified
Conductor: downward slope; Superconductor: slope then sharp drop at 30 K.

Step by step solution

01

Understand the behavior of an ordinary conductor

An ordinary conductor like copper ( Cu) typically shows a resistance that decreases gradually as the temperature decreases from 100 K to 0 K due to reduced phonon scattering. The graph has a downward slope but never reaches zero resistance.
02

Sketch the graph for an ordinary conductor

In the graph, draw a smooth, downward-sloping curve starting from the left (temperature 100 K) and heading downwards as it moves to the right towards 0 K, without touching the x-axis, indicating that resistance decreases but never hits zero.
03

Understand the behavior of a superconductor

A superconductor has a critical transition temperature, below which its resistance abruptly drops to zero. Given a transition temperature of 30 K means that above this temperature, its resistance behaves similarly to ordinary conductors, but at 30 K, the resistance becomes zero.
04

Sketch the graph for a superconductor

Draw a slightly downward-sloping curve from 100 K to 30 K, similar to a normal conductor, and then, at 30 K, draw a sharp drop straight down to the x-axis at zero resistance, continuing horizontally at zero until 0 K.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Behavior of Ordinary Conductors
Ordinary conductors like copper behave predictably when their temperature changes. When you lower the temperature, resistance decreases too. Why does this happen? Well, in conductors, electrons move through a lattice of atoms. At higher temperatures, these atoms vibrate more, causing more collisions and slowing down the electrons. This increased vibration is known as phonon scattering. As phonon scattering occurs less at lower temperatures, resistance declines.
However, it's important to note that for ordinary conductors, resistance never actually reaches zero. Unlike superconductors, normal conductors such as copper will always have some resistance no matter how low the temperature goes.
Behavior of Superconductors
Superconductors exhibit unique behavior that sets them apart from ordinary conductors. Superconductors have the remarkable property of completely losing their electrical resistance below a particular temperature. Imagine it as reaching a magical threshold. Once the temperature of the material drops below this critical point, called the transition temperature, the resistance plummets to zero.
This means that superconductors can carry electrical current indefinitely without any loss of energy when cooled below their transition temperature. It's a fascinating phenomenon that offers substantial benefits for technologies like MRI machines and magnetic levitation. However, above their transition temperature, they behave much like ordinary conductors.
Resistance vs Temperature
The relationship between resistance and temperature in materials like conductors and superconductors is vital for understanding their electrical behavior. In both ordinary conductors and superconductors, as the temperature lowers, resistance tends to decrease.
For ordinary conductors, this decrease is gradual and never reaches zero. On a graph, this is represented by a gently sloping line that doesn't touch the zero-resistance line, showing that there's always some level of resistance.
Superconductors, on the other hand, display an abrupt change. On a graph, this abruptness is shown as a steep drop to zero at the transition temperature. It's like flipping a switch – one moment there's resistance; the next, there isn't any.
Transition Temperature of Superconductors
The transition temperature of superconductors is a critical threshold. It's the temperature at which a superconductor switches from having regular resistance to exhibiting zero resistance. This temperature is distinct for each superconducting material and is fundamental to its unique properties.
The concept of transition temperature is essential for applications where superconductors can revolutionize technology, such as in energy-efficient power transmission and advanced scientific research. Before reaching this temperature, the material behaves much like an ordinary conductor. As it cools and crosses the transition temperature, its defining superconductivity feature activates.

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