question_answer

Dimensions of a block are \[1\,cm\times 1\text{ }cm\times 100\,cm\]. If specific resistance of its material is \[3\times {{10}^{-7}}\Omega m\], then the resistance between the opposite rectangular faces is

A)  \[3\times {{10}^{-7}}\Omega \]

B)  \[3\times {{10}^{-9}}\Omega \]

C)  \[3\times {{10}^{-5}}\Omega \]

D)  \[3\times {{10}^{-3}}\Omega \]

Correct Answer: A

Solution :

Length \[l=1\text{ }cm={{10}^{-2}}m\] Area of cross-section \[A=1\text{ }cm\times 100\text{ }cm\] \[=100\,c{{m}^{2}}\] \[={{10}^{-2}}{{m}^{2}}\] Resistance, \[R=3\times {{10}^{-7}}\times \frac{{{10}^{-2}}}{{{10}^{-2}}}\] \[=3\times {{10}^{-7}}\Omega \]