conductor of copper, the density of free electons is 5×10^23 electrons per unit volume, carrying current of intenisty 1.6A if the cross-sectional area of a conductor is 4mm^2 so the drift velocity of electrons is
Question
conductor of copper, the density of free electons is 5×10^23 electrons per unit volume, carrying current of intenisty 1.6A if the cross-sectional area of a conductor is 4mm^2 so the drift velocity of electrons is
Solution
The drift velocity can be calculated using the formula:
v_d = I / (nAe)
Where:
- v_d is the drift velocity
- I is the current flowing through the conductor
- n is the number density of charge carriers (such as electrons) in the conductor
- A is the cross-sectional area of the conductor
- e is the elementary charge (1.6 x 10^-19 Coulombs)
Step 1: Identify the given values.
- The current (I) is 1.6 A.
- The number density (n) is 5 x 10^23 electrons/m^3.
- The cross-sectional area (A) is 4 mm^2, which needs to be converted to m^2 for consistency with the other units. 1 mm^2 = 10^-6 m^2, so A = 4 x 10^-6 m^2.
Step 2: Substitute the given values into the formula. v_d = I / (nAe) v_d = 1.6 / (5 x 10^23 * 4 x 10^-6 * 1.6 x 10^-19)
Step 3: Calculate the drift velocity. v_d = 1.6 / (3.2 x 10^-2) v_d = 50 m/s
So, the drift velocity of the electrons is 50 m/s.
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