a conductor having a cross sectional area of 0.00161 sq. in. carries a current of 4.5 amp. Calculate the electron velocity, assuming the wire to be a copper.

To calculate the electron velocity in the given conductor, we can follow these steps:

1. Find the number of electrons per unit volume:
- The atomic weight of copper is approximately 63.55 grams/mole.
- The density of copper is around 8.96 grams/cm³.
- Convert the density to grams/mm³ by dividing by 1,000: 8.96 grams/cm³ ÷ 1,000 = 0.00896 grams/mm³.
- Calculate the atomic weight per volume by dividing the atomic weight by the density: 63.55 grams/mole ÷ 0.00896 grams/mm³ = 7,085.67 moles/mm³.
- Since copper has one free electron per atom, the number of electrons per unit volume is the same as the number of moles per unit volume: 7,085.67 electrons/mm³.

2. Calculate the volume of the conductor:
- The cross-sectional area of the conductor is given as 0.00161 sq. in.
- Convert the area to square mm by multiplying it by 645.16 (since 1 sq. in. = 645.16 sq. mm): 0.00161 sq. in. × 645.16 sq. mm/sq. in. = 1.039136 sq. mm.
- Assume the length of the conductor is 1 mm, so the volume is equal to the cross-sectional area: 1.039136 mm³.

3. Calculate the number of electrons in the conductor:
- Multiply the volume of the conductor by the number of electrons per unit volume: 1.039136 mm³ × 7,085.67 electrons/mm³ = 7,355.32 electrons.

4. Calculate the electron velocity:
- The electron velocity can be determined using the formula v = I / (n × A × q), where v represents the electron velocity, I is the current, n is the number of electrons, A is the cross-sectional area, and q is the charge of an electron.
- The charge of an electron is approximately 1.602 × 10⁻¹⁹ Coulombs.
- Substituting the values into the formula: v = 4.5 amp / (7,355.32 electrons × 1.039136 mm³ × 0.00161 sq. in. × 645.16 sq. mm/sq. in. × 1.602 × 10⁻¹⁹ Coulombs).
- Calculate the electron velocity using the above expression.

By following the steps above, you should be able to calculate the electron velocity in the given conductor.