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Current Electricity

Question
CBSEENPH12037918
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Write the mathematical relation for the resistivity of a material in terms of relaxation time, number density and mass and charge of charge carriers in it. Explain, using this relation, why the resistivity of a metal increases and that of a semi-conductor decreases with rise in temperature. 

Solution

Resistivity (ρ) of a material in terms of it's relaxation time (τ) , number density (n), mass (m) and charge carriers (e) is given by
                     ρ = mne2τ  

(i) Case of metals: As temperature increases, the thermal speed of electrons increases and consequently, free electrons collide more frequently with the positive metal ions thereby, decreasing the relaxation time τ. And, since resistivity has an inverse dependence on relaxation time, resistivity ρ of the metal increases. 

(ii) Case of semiconductors: The relaxation time τ does not change with temperature in semiconductor. But, the number density (n) of free electrons increases exponentially with increasing temperature. As a result, the resistivity of semiconductor decreases exponentially with the increase in temperature.

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

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