Which of the following statements are correct about the electrical resistance and resistivity of a wire?

1. Both quantities depend on the area of cross-section of the wire

2. Both depend on the temperature

3. Resistance of the wire is directly proportional to the resistivity of the wire

4. Resistivity of the wire is directly proportional to the length of the
wire

Select the correct answer using the code given below:

This question was previously asked in
UPSC NDA-II (General Ability) Official Paper-I (Held On: 03 Sept, 2023)
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  1. 1 and 2
  2. 1 and 3
  3. 2 and 3
  4. 2 and 4

Answer (Detailed Solution Below)

Option 3 : 2 and 3
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NDA 01/2025: English Subject Test
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Detailed Solution

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The correct answer is 2 and 3.

Key Points

  • Resistance depends inversely on the area, not directly. Resistivity directly depends on the area of the cross-section of the wire. Hence, statement 1 is incorrect.
  • The electrical resistance of a wire generally increases with temperature. This phenomenon is described by the temperature coefficient of resistance. Hence, statement 2 is correct.
  •  The resistance (R) is directly proportional to the resistivity (ρ) and the length (L), and inversely proportional to the cross-sectional area (A), as mentioned in the formula R = ρL/A. Hence, statement 3 is correct.
  • The resistivity of the wire is inversely proportional to the length of the wire. Hence, statement 4 is incorrect.

Additional Information

  • Resistance:
    • The property of any conductor which opposes the flow of electric current through it is called resistance.
    • It is represented by R and the SI unit is Ohm (Ω).
    • The resistance of a metallic wire is directly proportional to its length and inversely proportional to the area of its cross-section.
      • The resistance (R) is given by:
        • R = ρL / A
        • where ρ is resistivity, L is the length and A is the area of the cross-section.
  • Effect of Temperature on Resistance:
    • For pure metals, resistance increases with an increase in temperature, this is called the positive temperature coefficient of resistance.
    • For semiconductors and insulators, resistance increases with a decrease in temperature and vice versa, this is called negative temperature coefficient of resistance.
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