The resistance of a metal wire increases with increasing temperature on account of...

Описание: 🔥 Class 12 Physics PYQ | Why Resistance of Metal Increases with Temperature? | Current Electricity

Question [CBSE 2020]
The resistance of a metal wire increases with increasing temperature on account of —
(a) Decrease in free electron density
(b) Decrease in relaxation time
(c) Increase in mean free path
(d) Increase in mass of electron

📌 In this video, Saif Sir explains this important CBSE Board PYQ using Drude’s model of conduction, collision concept, relaxation time and temperature effect in metals. This concept is extremely important for CBSE Boards, NEET & JEE.
📚 Topics Covered
• Temperature dependence of resistance
• Relaxation time (τ) concept
• Mean free path
• Electron collision model
• Why metals show positive temperature coefficient

🎯 Best For Class 12 Physics | CBSE Boards | NEET | JEE | Competitive Exams

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Summary of Video
The video explains why the resistance of a metal wire increases with increasing temperature, as asked in a CBSE 2020 question (0:00-0:11).

Here's a breakdown of the explanation:

Resistance and Resistivity Formula (0:17-0:29): The resistance (R) is directly proportional to resistivity (ρ), given by the formula R = ρL/A. Resistivity itself is given by ρ = m/(ne²τ), where:
'm' is the mass of the electron.
'n' is the free electron density.
'e' is the charge of the electron.
'τ' (tau) is the relaxation time.

Effect of Temperature Increase (0:38-1:23):
When temperature increases, more bonds break, leading to an increase in 'n' (number of free electrons).
An increase in temperature also increases the velocity of electrons, causing them to collide more frequently. This leads to a decrease in 'τ' (relaxation time), which is the time between two successive collisions (0:51-1:16).

Conflicting Effects on Resistivity (1:23-2:00):
An increase in 'n' would tend to decrease resistivity (since ρ is inversely proportional to n), thereby decreasing resistance.
A decrease in 'τ' would tend to increase resistivity (since ρ is inversely proportional to τ), thereby increasing resistance.

Dominant Factor in Conductors (2:09-2:53):
In conductors, the number of free electrons ('n') is already very high. Therefore, the slight increase in 'n' due to temperature has a negligible effect on overall resistance.
However, the decrease in relaxation time ('τ') is the dominant factor. This decrease in 'τ' significantly increases resistivity, and consequently, the resistance of the metal wire.
Therefore, the primary reason for increased resistance in metals with increasing temperature is the decrease in relaxation time (2:56-2:58).

Contrast with Semiconductors (3:01-3:15):
In semiconductors, increasing temperature significantly increases the number of free electrons ('n'). This increase in 'n' is dominant, leading to a decrease in resistance (the opposite effect compared to metals).