In the figure provided a wire consists of two segments made from the same material but with different cross sectional areas such that A2𝐴2 = 2 A1𝐴1. Which of the following is true about the strength of the electron drift velocities in the two segments?
Question
In the figure provided a wire consists of two segments made from the same material but with different cross sectional areas such that A2𝐴2 = 2 A1𝐴1. Which of the following is true about the strength of the electron drift velocities in the two segments?
Solution
The electron drift velocity in a conductor is given by the equation:
v = I / (n * A * e)
where:
- v is the drift velocity,
- I is the current,
- n is the number of charge carriers per unit volume,
- A is the cross-sectional area of the conductor, and
- e is the charge of an electron.
Given that the wire is made of the same material and is part of the same circuit, the number of charge carriers per unit volume (n) and the current (I) will be the same in both segments.
However, the cross-sectional area (A) is different. Specifically, A2 = 2 * A1.
Substituting A2 into the equation for v, we get:
v2 = I / (n * 2 * A1 * e)
Comparing this with the equation for v1:
v1 = I / (n * A1 * e)
We can see that v2 = v1 / 2.
Therefore, the electron drift velocity is smaller in the segment with the larger cross-sectional area. So, the strength of the electron drift velocities in the two segments is not the same; it is smaller in the segment with the larger cross-sectional area.
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