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Understanding the time required by electrons to travel 1 m in a copper wire is essential for mastering concepts like drift velocity in current electricity. This concept connects microscopic electron motion with macroscopic current, helping students solve numerical problems accurately for exams and practical applications.

Problem Statement

A copper wire of cross-sectional area 6.62×10^-6 m² carrying a current of 20 A will require about 4.2 minutes for electrons to drift a distance of 1 m</strong).

Concept Recap for Students

• Drift velocity is extremely small compared with the speed of electric signals in a circuit.
• It depends on current, charge density of electrons, and cross-sectional area of the conductor.
• For a copper wire with given dimensions and 20 A current, the calculated drift speed leads to a travel time of about 4.2 minutes for electrons to move 1 m.

Drift Velocity Calculation

To find the time taken by electrons to travel 1 m, first calculate the drift velocity using:

where:

• I = current = 20 A
• n = number of free electrons per unit volume
• e = charge of electron = 1.6×10^-19 C
• A = cross-sectional area = 6.62×10^-6 m²
• v_d = drift velocity

Step 1: Calculate Electron Density

Given:

• Density of copper = 8.92 g/cm³ = 8.92×10³ kg/m³
• Molar mass of copper = 63.5 g/mol = 63.5×10^-3 kg/mol
• Avogadro number N_A = 6.02×10²³ mol^-1

Number of moles of Cu per m³:

Number of atoms (and hence free electrons, assuming one per atom):

Step 2: Drift Velocity

So electrons move with a drift speed of about 4×10^-3 m/s.

Time Calculation

Use t = distance/v_d:

Convert seconds to minutes: t ≈ 250/60 ≈ 4.2 min

Thus, the time required is approximately 4.2 minutes.