What is the resistance of a cylindrical metal rod $1.0 \mathrm {~cm}$ in diameter and $45 \mathrm {~m}$ long, if the resistivity of the metal is $1.4 \times 10 ^ { - 8 } \Omega \cdot \mathrm { m }$ ?

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The resistance of a cylindrical metal rod is given by:$$R = \frac{\rho L}{A}$$where:* $R$ is the resistance in ohms ($\Omega$)* $\rho$ is the resistivity of the metal in ohm-meters ($\Omega \cdot \mathrm { m }$)* $L$ is the length of the rod in meters (m)* $A$ is the cross-sectional area of the rod in square meters (m²)The cross-sectional area of a circle is given by:$$A = \pi r^2$$where:* $r$ is the radius of the circle in meters (m)In this problem, we are given the following information:* $\rho = 1.4 \times 10 ^ { - 8 } \Omega \cdot \mathrm { m }$* $L = 45 \mathrm {~m}$* $d = 1.0 \mathrm {~cm} = 0.01 \mathrm {~m}$First, we need to find the radius of the rod:$$r = \frac{d}{2} = \frac{0.01 \mathrm {~m}}{2} = 0.005 \mathrm {~m}$$Now we can calculate the cross-sectional area:$$A = \pi r^2 = \pi (0.005 \mathrm {~m})^2 = 7.85 \times 10 ^ { - 5 } \mathrm {~m}^2$$Finally, we can calculate the resistance:$$R = \frac{\rho L}{A} = \frac{(1.4 \times 10 ^ { - 8 } \Omega \cdot \mathrm { m })(45 \mathrm {~m})}{7.85 \times 10 ^ { - 5 } \mathrm {~m}^2} = 0.0080 \Omega$$Therefore, the resistance of the rod is $0.0080 \Omega$.

What Is the Resistance of a Cylindrical Metal Rod 1.0 cm1.0 \mathrm {~cm}1.0 cm

What Is the Resistance of a Cylindrical Metal Rod $1.0 \mathrm {~cm}$