Question

Consider two cuboidal blocks of volume 1 cm\(^3\) each, one made of gold and the other of undoped silicon. What will happen to the resistivity of these blocks if the temperature is increased from 300 K to 350 K? Choose one of the following.

• A. Resistivity of gold increases and undoped silicon decreases
• B. Resistivity of gold decreases and undoped silicon increases
• C. Resistivity of gold remains same and undoped silicon increases
• D. Resistivity of gold decreases and undoped silicon remains same

Hint:

A simple rule to remember: For metals, Temperature \(\uparrow\) \(\implies\) Resistivity \(\uparrow\). For semiconductors, Temperature \(\uparrow\) \(\implies\) Resistivity \(\downarrow\).

Answer 1

The Correct Option is A

Step 1: Concept:
Electrical resistivity depends on charge carrier concentration and mobility. The temperature effect differs for metals and semiconductors.
Step 2: Behaviour of Gold (Metal):
In metals, the number of free electrons remains almost constant with temperature. When temperature increases, lattice vibrations increase, which causes more scattering of electrons and reduces mobility. As a result, resistivity increases with temperature.
Step 3: Behaviour of Undoped Silicon (Intrinsic Semiconductor):
In intrinsic semiconductors, increasing temperature generates more electron-hole pairs. This significantly increases the carrier concentration, which increases conductivity and decreases resistivity, even though mobility slightly reduces.
Final Conclusion:
Therefore, with an increase in temperature, the resistivity of gold increases, while the resistivity of undoped silicon decreases.