1. Compute the resistance of a hardened copper rod 2 meters long and 8 mm indiameter if the resistivity of the material is 1.756 x 10-8 ohm-meters.2. A 0.500-meter length of wire with a cross-sectional area of 3.14 x 10-6 meterssquared is found to have a resistance of 2.53 x 10-3 ohms. According to theresistivity chart, from what material is the wire made?3. The resistance of a uniform copper wire 50.0 meters long and 1.15 mm indiameter is 0.830 ohms at 20° C. What is the resistivity of the copper at thistemperature?4. A 200 m long aluminum wire has the same resistance and cross-sectional areaas a carbon wire. What is the length of the carbon wire?5. A wire of radius R and length L has a resistance of 14 Ω. What is the resistanceof a wire made from the same material that has twice the radius and five timesthe length?

The resistance (R) of a material can be calculated using the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area. The cross-sectional area of a rod (cylinder) can be calculated using the formula A = πr², where r is the radius. The radius is half the diameter, so r = 8mm/2 = 4mm = 0.004m. Therefore, A = π(0.004m)² = 5.0265 x 10^-5 m². Substituting these values into the resistance formula gives R = (1.756 x 10^-8 Ωm)(2m) / (5.0265 x 10^-5 m²) = 0.0007 Ω.

The resistivity (ρ) of a material can be calculated using the formula ρ = RA/L, where R is the resistance, A is the cross-sectional area, and L is the length. Substituting the given values into this formula gives ρ = (2.53 x 10^-3 Ω)(3.14 x 10^-6 m²) / (0.500m) = 1.59 x 10^-8 Ωm. According to the resistivity chart, this value corresponds to the resistivity of silver.

Using the same formula for resistivity as in question 2, substituting the given values gives ρ = (0.830 Ω)(π(0.00115m/2)²) / (50.0m) = 1.68 x 10^-8 Ωm.

If the aluminum and carbon wires have the same resistance and cross-sectional area, then the ratio of their lengths is equal to the ratio of their resistivities. Let Lc be the length of the carbon wire and ρa and ρc be the resistivities of aluminum and carbon, respectively. Then Lc = (ρc/ρa)(200m). The resistivities of aluminum and carbon can be found in a resistivity chart.

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Therefore, if the radius is doubled and the length is multiplied by five, the new resistance R' is given by R' = 5R/(2²) = 5(14 Ω)/4 = 17.5 Ω.