A wire 10 m long with a diameter of 1.0 mm has a resistance of 5.0 $\Omega$.The resistance of a second wire made of the same material,but 3.0 m long with a diameter of 4.0 mm,is approximately
A)0.38 $\Omega$
B)0.094 $\Omega$
C)0.75 $\Omega$
D)1.7 $\Omega$
E)0.27 k$\Omega$

Question

Quizplus · Accepted Answer

The resistance of a wire is given by the formula:
$R=\frac{ho l}{A}$ where $ho$ is the resistivity of the material, $l$ is the length of the wire, $A$ is the cross-sectional area of the wire.
The cross-sectional area of wire 1 is given by:
$A=\frac{\pi d^2}{4}=\frac{\pi}{4}(0.001)^2=7.85	imes 10^{-7}m^2$
Substituting the values, we get:
$5\ \Omega=\frac{ho(10)}{7.85	imes 10^{-7}}$
$ho=6.36	imes 10^{-7}\ \Omega m$ (resistivity of wire 1)
For wire 2, the cross-sectional area is:
$A=\frac{\pi d^2}{4}=\frac{\pi}{4}(0.004)^2=1.26	imes 10^{-5}m^2$
Substituting the values, we get:
$R=\frac{ho(3)}{1.26	imes 10^{-5}}\approx0.094\ \Omega$

A Wire 10 M Long with a Diameter of 1 Ω\OmegaΩ

A Wire 10 M Long with a Diameter of 1 $\Omega$