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Current Electricity question

2020 · 2 Sep · Shift 1 · Q41
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Current Electricity question

2020 · 2 Sep · Shift 1 · Q41

JEE MainPhysicsCurrent ElectricityMCQ+4 / −1
Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity ρ\rhoρ C, ρ\rhoρ T, ρ\rhoρ M and ρ\rhoρ A respectively. Then :
  1. A
    ρ\rhoρ C > ρ\rhoρ A > ρ\rhoρ T
  2. B
    ρ\rhoρ M > ρ\rhoρ A > ρ\rhoρ C
  3. C
    ρ\rhoρ A > ρ\rhoρ T > ρ\rhoρ C
  4. D
    ρ\rhoρ A > ρ\rhoρ M > ρ\rhoρ C
View written solutionFree

Correct answer: B

  1. Recall the relative resistivities of the given conductors

    At room temperature, the approximate resistivities are:

    ρCu≈1.7×10−8 Ω m\rho_{\text{Cu}} \approx 1.7 \times 10^{-8}\ \Omega\,\text{m}ρCu​≈1.7×10−8 Ωm ρAl≈2.7×10−8 Ω m\rho_{\text{Al}} \approx 2.7 \times 10^{-8}\ \Omega\,\text{m}ρAl​≈2.7×10−8 Ωm ρW≈5.6×10−8 Ω m\rho_{\text{W}} \approx 5.6 \times 10^{-8}\ \Omega\,\text{m}ρW​≈5.6×10−8 Ωm ρHg≈9.6×10−7 Ω m\rho_{\text{Hg}} \approx 9.6 \times 10^{-7}\ \Omega\,\text{m}ρHg​≈9.6×10−7 Ωm

  2. Arrange them in increasing order

    From the above values:

    ρC<ρA<ρT<ρM\rho_C < \rho_A < \rho_T < \rho_MρC​<ρA​<ρT​<ρM​

  3. Now check each option

    • Option A: ρC>ρA>ρT\rho_C > \rho_A > \rho_TρC​>ρA​>ρT​

      This is false, because actually ρC<ρA<ρT\rho_C < \rho_A < \rho_TρC​<ρA​<ρT​.

    • Option B: ρM>ρA>ρC\rho_M > \rho_A > \rho_CρM​>ρA​>ρC​

      This is true, because mercury has the highest resistivity among these, aluminium has greater resistivity than copper.

    • Option C: ρA>ρT>ρC\rho_A > \rho_T > \rho_CρA​>ρT​>ρC​

      This is false, because ρT>ρA\rho_T > \rho_AρT​>ρA​.

    • Option D: ρA>ρM>ρC\rho_A > \rho_M > \rho_CρA​>ρM​>ρC​

      This is false, because ρM>ρA\rho_M > \rho_AρM​>ρA​, not the other way around.

  4. Final answer

    The correct option is:

    B\boxed{\text{B}}B​

  5. Comparison with stored answer

    Stored correct answer: B

    My derived answer: B

    Hence, they agree.

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