Question

1. Compute the resistance of a hardened copper rod 2 meters long and 8 mm
in diameter 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
meters squared is found to have
a resistance of 2.53 x 10-3
ohms. According to the resistivity chart, from what material is the wire
made?
3. The resistance of a uniform copper wire 50.0 meters long and 1.15 mm in
diameter is 0.830 ohms at
20° C. What is the resistivity of the copper at this temperature?
4. At 20° C, 33 meters of copper wire has a resistance of 0.639 ohms. What is
the resistance of 165
meters?
5. A 200 m long aluminum wire has the same resistance and cross-sectional
area as a carbon wire. What is
the length of the carbon wire?
6. A wire of radius R and length L has a resistance of 14 Ω. What is the
resistance of a wire made from
the same material that has twice the radius and five times the length?

Answer 1

Resistance of Wire = 7 mΩ

Step-by-step explanation:

resistance  R

ρ = Resistivity

L = length

A = Cross sectional Area

L = 2 m

ρ = 1.756 x 10⁻⁸ ohm-meters.

Diameter = 8 mm => radius =  4 mm = 4 * 10⁻³ m

A = πr²  = 3.14 * (4 * 10⁻³)²  = 50.24 * 10⁻⁶ m

R = ρ L / A

R = 1.756 x 10⁻⁸   * 2 / 50.24 * 10⁻⁶ m

=> R = 0.699    x 10⁻³ Ω

=> R = 0.699   mΩ

=> R ≈ 7 mΩ

Resistance of Wire = 7 mΩ

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