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Which of the following statements is/are true regarding resistance of a conducting metal wire?
1. Resistance decreases with decrease in length of the wire
2. Resistance increases with increase in thickness of the wire
3. Resistance decreases with increase in temperature of the wire
4. All of the above

1 Answer

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Correct Answer - Option 1 : Resistance decreases with decrease in length of the wire

The correct answer is option 1) i.e. Resistance decreases with decrease in length of the wire

CONCEPT:

  • Resistance: The hindrance to the flow of current offered by a material is called electrical resistance.
    • The SI unit of electrical resistance is the ohm (Ω)

 The resistance of a conducting wire is given by the equation:

\(R = \rho\frac{l}{A}\)

Where R is the resistance, l is the length of the wire and A is the cross-sectional area of the material.

EXPLANATION:

R ∝ l

  • Therefore, resistance decreases with a decrease in the length of the wire.

\(R \propto \frac{1}{A}\)

  • The thickness of the wire is a measure of the cross-sectional area. Hence, the increasing thickness increases the cross-sectional area of the material.
  • Therefore, resistance increases with a decrease in the thickness of the material.

  • On increasing the temperature of the wire, the kinetic energy of the electrons in the material increases and they collide vigorously with each other.
  • Each collision uses some of the energy of electrons and thus electron flow slows down. This increases resistance. However, this is only true for metals.
  • In insulators and semiconductors, the number of free electrons increases with an increase in temperature. Thus, resistance decreases.

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