question_answer

Dimensions of a block are \[1\,cm\times 1\,cm\times 100\,cm\]. If specific resistance of its material is \[3\times {{10}^{-7}}ohm-m\], then the resistance between the opposite rectangular faces is                                                                                            [MP PET 1993]

A)                    \[3\times {{10}^{-9}}ohm\]                                       

B)            \[3\times {{10}^{-7}}ohm\]

C)                    \[3\times {{10}^{-5}}ohm\]                                       

D)            \[3\times {{10}^{-3}}ohm\]

Correct Answer: B

Solution :

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