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?

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 =