Question

The dimensions of the block are $1cm\times 1cm\times 100cm$. If the specific resistance of its material is $3\times {10}^{-7}ohm\times m$, then the resistance between the opposite rectangular face is

• A. $3\times {10}^{-9}ohm$
• B. $3\times {10}^{-7}ohm$
• C. $3\times {10}^{-5}ohm$
• D. $3\times {10}^{-3}ohm$

Answer 1

The correct option is B $3\times {10}^{-7}ohm$

Resistance is defined as $R=\frac{\rho l}{A}$

Length $l=1cm={10}^{-2}cm$

Area of cross-section $A=1cm\times 100cm$

$=100cm={10}^{-2}m$

Resistance $R=3\times {10}^{-7}\times \frac{{10}^{-2}}{{10}^{-2}}=3\times {10}^{-7}\Omega$