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Saturday, September 21, 2019

The diameter of a wire XY varies linearly with distance along the wire as shown in Fig. 7.1.


Question 14
(a) The current I in a metal wire is given by the expression
I = Anve.

State what is meant by the symbols A and n. [2]


(b) The diameter of a wire XY varies linearly with distance along the wire as shown in Fig. 7.1.


Fig. 7.1

There is a current I in the wire. At end X of the wire, the diameter is d and the average drift speed of the free electrons is vx. At end Y of the wire, the diameter is d / 2.

On Fig. 7.2, sketch a graph to show the variation of the average drift speed with position
along the wire between X and Y.


Fig. 7.2
[2]
[Total: 4]





Reference: Past Exam Paper – November 2018 Paper 22 Q7





Solution:
(a)
A: (cross-sectional) area (of wire)
n: number of free electrons per unit volume or number density of free electrons


(b)
line drawn between (X, vx) and (Y, 4vx)
line has increasing gradient


{I = Anve
Cross-sectional area A = πd2 / 2

I = (Ï€d2 / 2) nve
As we move from X to Y, the cross-sectional area (and hence, the diameter) decreases linearly. So, we need to understand the relationship between drift velocity vx and the diameter.

I = (Ï€d2 / 2) nve
v = 2I / πd2e
So, v 1 / d2

The drift velocity v is inversely proportional to the square of the diameter. If the diameter decreases, the drift velocity increases.

Initially at X, drift velocity = vx. On the graph, we have the point (X, vx)

If the diameter is halved, the the drift velocity is would increase by a factor of 4. On the graph, we have the point (Y, 4vx).

Since v 1 / d2, the graph of drift velocity against position (diameter) would resemble the reflection of the graph of y = 1/x2 about the x-axis (since here, from X to Y, the diameter is decreasing).}

2 comments:

  1. Hi. I have a doubt in 9702_s19_qp_23 Q6. Any help would be thankful

    ReplyDelete
    Replies
    1. go to
      http://physics-ref.blogspot.com/2019/09/a-battery-of-electromotive-force-emf-e.html

      Delete

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