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Given the data:

- Current, [tex]f = 160 \text{ Amperes}[/tex]
- Charge of an electron, [tex]\theta = 1.6 \times 10^{-19} \text{ Coulombs}[/tex]
- Cross-sectional area of the cable, [tex]A = 0.25 \text{ cm}^2[/tex]

Calculate the number of free electrons per [tex]m^3[/tex] in the cable.

A. [tex]n = 10^{31} \text{ electrons/m}^3[/tex]

B. [tex]10^{30} \text{ electrons/m}^3[/tex]

C. [tex]10^{29} \text{ electrons/m}^3[/tex]

D. [tex]10^{28} \text{ electrons/m}^3[/tex]

Answer :

Final answer:

The number of free electrons per m3 in the cable is approximately 2.5 * (10^23) electrons/m3.

Explanation:

To calculate the number of free electrons per m3 in the cable, we can use the formula:

n = I / (A * q)

Where:

  • n is the number of free electrons per unit volume
  • I is the current flowing through the conductor
  • A is the cross-sectional area of the conductor
  • q is the charge of a single electron

Given:

  • I = 160 Ampere
  • A = 0.25 cm2
  • q = 1.6×10−19 Coulomb

First, we need to convert the cross-sectional area from cm2 to m2:

A = 0.25 cm2 = 0.25 * (10^-4) m2 = 2.5 * (10^-5) m2

Now, we can substitute the values into the formula:

n = 160 / (2.5 * (10^-5) * 1.6×10−19)

Simplifying the expression:

n = 160 / (4 * (10^-5) * 1.6×10−19)

n = 160 / (6.4 * (10^-24))

n ≈ 2.5 * (10^23) electrons/m3

Therefore, the number of free electrons per m3 in the cable is approximately 2.5 * (10^23) electrons/m3.

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