The dimensions of a block are 1 cm × 1 cm × 100 cm. If the specific resistance of its material is \( 3\times10^{-7}\,\Omega\,\mathrm{m} \), then the resistance between the two opposite faces of size 1 cm × 100 cm is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 3\times10^{-7}\,\Omega \)
The specific resistance is the resistivity \( \rho \). The resistance between two opposite faces is \( R=\rho l/A \). Here \( A \) is the area of each face and \( l \) is the distance between the faces. The faces of size 1 cm × 100 cm are 1 cm apart.
\( \begin{aligned} A &= 1\,\mathrm{cm}\times100\,\mathrm{cm} \\ &= 0.01\,\mathrm{m}\times1\,\mathrm{m} \\ &= 10^{-2}\,\mathrm{m^{2}} \end{aligned} \)
\( l=1\,\mathrm{cm}=10^{-2}\,\mathrm{m} \)
\( \begin{aligned} R &= \frac{\rho l}{A} \\ &= \frac{3\times10^{-7}\,\Omega\,\mathrm{m}\times10^{-2}\,\mathrm{m}}{10^{-2}\,\mathrm{m^{2}}} \\ &= 3\times10^{-7}\,\Omega \end{aligned} \)