If the resistance of 0.17 Ohms is measured across a conductive material, what is the resistivity given a diameter of 10cm and a length of 1 meter?

If the resistance of 0.17 Ohms is measured across a conductive material, what is the resistivity given a diameter of 10cm and a length of 1 meter?

• A. 0.25 Ohm cm
• B. 2.25 Ohm cm
• C. 0.13345 Ohm cm
• D. 0.29 Ohm cm

Answer: (C)

To determine the resistivity of a material from its resistance, diameter, and length, the formula used is: \[ R = \frac{\rho L}{A} \] where: - \( R \) is the resistance (in Ohms), - \( \rho \) is the resistivity (in Ohm cm), - \( L \) is the length (in cm), - \( A \) is the cross-sectional area (in cm²). First, the cross-sectional area \( A \) of the conductive material can be calculated using the diameter. The diameter given is 10 cm, which means the radius \( r \) is: \[ r = \frac{diameter}{2} = \frac{10 cm}{2} = 5 cm \] The area \( A \) can be calculated by using the formula for the area of a circle: \[ A = \pi r^2 = \pi (5 cm)^2 \approx 78.54 cm² \] Now, the given resistance \( R \) is 0.17 Ohms and the length \( L \) is 1 meter, which converts to centimeters: \[ L = 1 meter =

To determine the resistivity of a material from its resistance, diameter, and length, the formula used is:

[

R = \frac{\rho L}{A}

]

where:

• ( R ) is the resistance (in Ohms),

• ( \rho ) is the resistivity (in Ohm cm),

• ( L ) is the length (in cm),

• ( A ) is the cross-sectional area (in cm²).

First, the cross-sectional area ( A ) of the conductive material can be calculated using the diameter. The diameter given is 10 cm, which means the radius ( r ) is:

[

r = \frac{diameter}{2} = \frac{10 cm}{2} = 5 cm

]

The area ( A ) can be calculated by using the formula for the area of a circle:

[

A = \pi r^2 = \pi (5 cm)^2 \approx 78.54 cm²

]

Now, the given resistance ( R ) is 0.17 Ohms and the length ( L ) is 1 meter, which converts to centimeters:

[

L = 1 meter =