Question

The resistivity of a resistor is $5\Omega m$. Its length is $1m$ and the area of cross section is $2m{m}^2$. Calculate its resistance.

• A. $2.5\times {10}^7\Omega$
• B. $2.5\times {10}^6\Omega$
• C. $3.5\times {10}^6\Omega$
• D. $3.5\times {10}^7\Omega$

Answer 1

The correct option is B $2.5\times {10}^6\Omega$

Given: Resistivity, $\rho =5\Omega m$, length, $l=1m$ and the cross sectional area, $A=2m{m}^2=2\times {10}^{-6}{m}^2$.
The resistance is given by:
$R=\frac{\rho l}{A}.\Rightarrow R=5\times \frac{1}{2\times {10}^{-6}}=2.5\times \frac{1}{{10}^{-6}}=2.5\times {10}^6\Omega .$