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Calculate the conductivity of a conductor with resistivity of 1.7 imes 10⁻⁸ Calculate the resistance of a conductor with conductivity of 3.2 imes 107 S/m, length 15 m, and cross-sectional area 2 imes

Physics

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45.

  1. Identify the given resistivity.

    The resistivity (ρ\rho) of the conductor is given as 1.7×10−8 Ω⋅m1.7 \times 10^{-8} \, \Omega \cdot \text{m}. The length and cross-sectional area are not needed to find conductivity.

  2. Calculate the conductivity.

    Conductivity (σ\sigma) is the reciprocal of resistivity (ρ\rho).

    σ=1ρ\sigma = \frac{1}{\rho} σ=11.7×10−8 Ω⋅m\sigma = \frac{1}{1.7 \times 10^{-8} \, \Omega \cdot \text{m}} σ=0.588235×108 S/m\sigma = 0.588235 \times 10^8 \, \text{S/m} σ≈5.88×107 S/m\sigma \approx 5.88 \times 10^7 \, \text{S/m}

    The conductivity of the conductor is 5.88×107 S/m\boxed{\text{5.88} \times 10^7 \, \text{S/m}}.

    46.

  3. Calculate the resistivity from the given conductivity.

    The conductivity (σ\sigma) is 3.2×107 S/m3.2 \times 10^7 \, \text{S/m}. Resistivity (ρ\rho) is the reciprocal of conductivity.

    ρ=1σ\rho = \frac{1}{\sigma} ρ=13.2×107 S/m\rho = \frac{1}{3.2 \times 10^7 \, \text{S/m}} ρ=0.3125×10−7 Ω⋅m\rho = 0.3125 \times 10^{-7} \, \Omega \cdot \text{m} ρ=3.125×10−8 Ω⋅m\rho = 3.125 \times 10^{-8} \, \Omega \cdot \text{m}
  4. Calculate the resistance using the resistivity, length, and cross-sectional area.

    The length (LL) is 15 m15 \, \text{m} and the cross-sectional area (AA) is 2×10−6 m22 \times 10^{-6} \, \text{m}^2. The formula for resistance is:

    R=ρLAR = \rho \frac{L}{A} R=(3.125×10−8 Ω⋅m)×15 m2×10−6 m2R = (3.125 \times 10^{-8} \, \Omega \cdot \text{m}) \times \frac{15 \, \text{m}}{2 \times 10^{-6} \, \text{m}^2} R=3.125×10−8×152×10−6 ΩR = \frac{3.125 \times 10^{-8} \times 15}{2 \times 10^{-6}} \, \Omega R=46.875×10−82×10−6 ΩR = \frac{46.875 \times 10^{-8}}{2 \times 10^{-6}} \, \Omega R=23.4375×10−2 ΩR = 23.4375 \times 10^{-2} \, \Omega R=0.234375 ΩR = 0.234375 \, \Omega

    Rounding to three significant figures:

    R≈0.234 ΩR \approx 0.234 \, \Omega

    The resistance of the conductor is 0.234 Ω\boxed{\text{0.234} \, \Omega}.

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