Question

A wire in the shape of frustum, have circular cross-sections of radii $r_1=2.5\text{cm}$ and $r_2=4\text{cm}$. The resistivity of the material of the wire is $\rho =2\times {10}^{-3}\Omega \text{m}$. Calculate the resistance of the wire, if the length of the wire is $10\text{cm}$.

• A. $\frac{1}{5\pi }\Omega$
• B. $\frac{2}{5\pi }\Omega$
• C. $\frac{3}{5\pi }\Omega$
• D. $\frac{4}{5\pi }\Omega$

Answer 1

The correct option is A $\frac{1}{5\pi }\Omega$

We know that the resistance of a frustum shaped wire is given by :
$R=\frac{\rho L}{\pi \left(r_1{r}_2\right)}$

According to the data given in the question,
$R=\frac{2\times {10}^{-3}\times 10\times {10}^{-2}}{\pi (2.5\times {10}^{-2}\times 4\times {10}^{-2})}$

$R=\frac{1}{5\pi }\Omega$