Question

State why the resistance of the conductor increases with the rise in temperature.

Answer 1

Here is a clear explanation of why the resistance of a conductor increases with a rise in temperature, broken down into a simple analogy and the underlying physics.

---

Simple Analogy: The Crowded Hallway

Imagine you are trying to run through a hallway.

• Low Temperature: The hallway is filled with people standing still. You can weave your way through them relatively easily. This is like a conductor at a low temperature.
• High Temperature: Now, imagine the people in the hallway start to randomly jump and move around in place. It becomes much harder for you to run through without bumping into them. Each collision slows you down and knocks you off course. This is like a conductor at a high temperature.

In this analogy:
You are an electron trying to flow.
The people are the atoms (positive ions) of the conductor.
Their movement is the atomic vibration caused by heat.
The difficulty in getting through is the electrical resistance.

---

The Physics Explained

The increase in resistance is due to what happens at the atomic level inside the conductor.

1. Structure of a Conductor: A metal conductor (like copper or aluminum) consists of a fixed, orderly structure of positive metal ions, known as a crystal lattice. Surrounding this lattice is a "sea" of free-moving electrons (delocalized electrons) that do not belong to any single atom.

2. Electrical Current: When you apply a voltage across the conductor, these free electrons are pushed to move in a general direction, creating an electrical current.

3. The Effect of Temperature: Temperature is a measure of the average kinetic energy of the particles in a substance.
   At low temperatures, the positive ions in the crystal lattice are relatively still, only vibrating slightly about their fixed positions. The free electrons can pass through the lattice with fewer obstructions.
   At high temperatures, the ions gain significant thermal energy. This causes them to vibrate much more vigorously and with a larger amplitude.

4. Increased Collisions: As the electrons try to flow through the conductor, they collide with these violently vibrating ions.
   Each collision scatters the electron, impeding its forward progress and transferring energy from the electron to the lattice (which is why current flow generates heat).
   With increased temperature and more vigorous vibrations, the frequency of these collisions increases dramatically.

5. Conclusion: Resistance is fundamentally the opposition to the flow of charge. Because higher temperatures lead to more frequent collisions between the charge-carrying electrons and the vibrating ions of the conductor, the overall opposition to the current increases. Therefore, the resistance of the conductor increases with a rise in temperature.

Summary

• Conductors have a lattice of positive ions and a sea of free electrons.
• Current is the flow of these free electrons.
• Higher temperature means the positive ions vibrate more vigorously.
• More vibration leads to more frequent collisions with the flowing electrons.
• More collisions mean more opposition to the flow, which is, by definition, higher resistance.