The diameter of a wire ST varies linearly with distance along the wire as shown in Fig. 6.1.

Question 13

(a) Define the coulomb. [1]

(b) An electric current is a flow of charge carriers.

In the following list, underline the possible charges for a charge carrier.

8.0 × 10^-19 C                4.0 × 10^-19 C                1.6 × 10^-19 C                1.6 × 10^-20 C    [1]

(c) The diameter of a wire ST varies linearly with distance along the wire as shown in Fig. 6.1.

Fig. 6.1

There is a current I in the wire. At end S of the wire, the diameter is d and the average drift speed of the free electrons is vs. At end T of the wire, the diameter is 2d.

On Fig. 6.2, sketch a graph to show the variation of the average drift speed with position

along the wire between S and T.

Fig. 6.2

[2]

 [Total: 4]

Reference: Past Exam Paper – November 2018 Paper 23 Q6

Solution:

(a) The coulomb is the charge that passes a point in a circuit when there is a current of 1 A for 1 s.

(b) 8.0 × 10^-19 C and 1.6 × 10^-19 C both underlined (and no others underlined)

{The charge can only have an integer value times the elementary charge (charge of electron = 1.6×10^-19 C)

8.0 × 10^-19 C / 1.6×10^-19 C = 5}

(c)

line drawn between (S, 1.00vs) and (T, 0.25vs)

line with decreasing magnitude of gradient

{At end S of the wire, the average drift speed of the free electrons = v_s. This corresponds to point (S, 1.00vs) on the graph.

Electric current: I = Anvq

Average drift speed v = I / Anq

The current I flowing in the wire, the number density n of electrons in the wire and the charge q of an electron are constants.

So, v is inversely proportional to cross-sectional area A.

Area A = πd² / 4

At end T of the wire, the diameter is doubled (= 2d). This means that the area A is 4 times greater.

Since v is inversely proportional to area A, when the area at T is 4 times that at S, the average drift speed at T would be ¼ (= 0.25) that at S. This corresponds to point (T, 0.25vs) on the graph.

As we move from S to T, the diameter varies linearly with the position (the diameter increases linearly).

We have seen that v ∝ 1/A     and A ∝ d²

So, v ∝ 1/d²

The average drift velocity is inversely proportional to the square of the diameter.

This resembles the graph of y = 1/x² which has a decreasing gradient.}