Question 124: Current Electricity

Question

A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is $$n	imes10^{-3}\Omega$$. If the resistivity of the material is $$\mathrm{2.4	imes10^{-8}\Omega m}$$. The value of $$n$$ is ___________.

Accepted Answer

Resistance of the hollow cylindrical conductor is given by,
$R=ho \frac{l}{\pi\left(r_2^2-r_1^2ight)}$
where $r_2=$ outer radius
$$
\begin{gathered}
r_1=	ext { inner radius } \\
ho=	ext { resistivity, } l=	ext { length } \\
	herefore ho=\frac{2.4 	imes 10^{-8} 	imes 3.14}{\pi\left(\frac{8^2}{4}-\frac{4^2}{4}ight) 	imes 10^{-6}} \\
=\frac{2.4 	imes 10^{-8} 	imes 4}{48 	imes 10^{-6}}=2 	imes 10^{-3} \Omega
\end{gathered}
$$

Current Electricity

A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is $n\times10^{-3}\Omega. If the resistivity of the material is \mathrm{2.4\times10^{-8}\Omega m}. The value of n$ is ___________.

Integer / Numeric Answer Type