- The linear resistivity of this wire is equal to 3.15 × 10⁻⁸ Ωm.
- The current density in this wire is equal to 6.35 × 10⁶ A/m².
- The total current in a wire is equal to 0.0499 Amp.
- The drift speed of the conduction electrons is equal to 6.59 × 10⁻⁴ m/s.
- The potential difference between the ends of this wire is equal to 0.4 Volt.
<u>Given the following data:</u>
Diameter of aluminum wire = 0.100 mm.
Uniform electric field of aluminum wire = 0.200 V/m.
Temperature of aluminum wire = 50.0°C.
<u>Scientific data:</u>
Resistivity of aluminum, ρ = 2.82 × 10⁻⁸ Ωm
Temperature coefficient for aluminum, α = 3.9 × 10⁻³ °C⁻¹.
<h3>How to determine the resistivity?</h3>
Mathematically, the linear resistivity of a material can be calculated by using this formula:
ρ = ρ₀(1 + αΔT)
ρ = ρ₀(1 + α(T₂ - T₁)
ρ = 2.82 × 10⁻⁸ × [1 + 3.9 × 10⁻³(50 - 20)
Resistivity, ρ = 3.15 × 10⁻⁸ Ωm.
<h3>What is the current density in this wire?</h3>
Mathematically, the current density in a wire can be calculated by using this formula:
J = σE = E/ρ
J = 0.2/3.15 × 10⁻⁸
Current density, J = 6.35 × 10⁶ A/m².
<h3>What is the total current in this wire?</h3>
Mathematically, the total current in a wire can be calculated by using this formula:
I = JA = J(πr²)
I = 6.35 × 10⁶ × (3.142 × 0.00005²)
Total current, I = 0.0499 Amp.
<h3>What is the drift speed of the conduction electrons?</h3>
Mathematically, the drift speed of the conduction electrons can be calculated by using this formula:
V = I/nqA
V = (0.0499 × 0.027)/(6.023 × 10²³ × 27000 × 1.602 × 10⁻¹⁹ × (3.142 × 0.00005²)
Drift speed, V = 6.59 × 10⁻⁴ m/s.
For the the potential difference, we have:
Mathematically, the potential difference between the ends of a wire can be calculated by using this formula:
ΔV = El
ΔV = 0.2 × 2
ΔV = 0.4 Volt.
Read more on drift speed here: brainly.com/question/15219891
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Complete Question:
An aluminum wire with a diameter of 0.100 mm has a uniform electric field of 0.200 V/m imposed along its entire length. The temperature of the wire is 50.0°C. Assume one free electron per atom.
(a) Determine the resistivity.
(b) What is the current density in the wire?
(c) What is the total current in the wire?
(d) What is the drift speed of the conduction electrons?
(e) What potential difference must exist between the ends of a 2.00-m length of the wire to produce the stated electric field?
