Cambridge A Level Physics AS I = Anvq Current Equation Questions

[Maximum number: 5]

(a)

A metal wire has length L and cross-sectional area A, as shown in Fig. 6.1.

Fig. 6.1

I is the current in the wire,
n is the number of free electrons per unit volume in the wire,
v is the average drift speed of a free electron and
e is the charge on an electron.

[ 3 ]

(i)

State, in terms of A, e, L and n, an expression for the total charge of the free electrons in the wire.

[ 1 ]

(ii)

Use your answer in (i) to show that the current I is given by the equation

I = nAve.

[ 2 ]

( t is time taken for electrons to move length L )
I=Q / tI=n A L e / t

or
I=n A L e /(L / v)

or
$I=n A \text { vte } / t \text { and } I=n A \text { ve }$

(b)

A metal wire in a circuit is damaged. The resistivity of the metal is unchanged but the cross

sectional area of the wire is reduced over a length of 3.0 mm , as shown in Fig. 6.2.

Fig. 6.2

The wire has diameter d at cross-section X and diameter 0.69 d at cross-section Y . The current in the wire is 0.50 A .

[ 2 ]

(i)

Determine the ratio
$\frac{\text { average drift speed of free electrons at cross-section } \mathrm{Y}}{\text { average drift speed of free electrons at cross-section } \mathrm{X}}$ .
ratio =

[ 2 ]

ratio = area at X/area at Y
$=\left[\pi d^{2} / 4\right] /\left[\pi(0.69 d)^{2} / 4\right] \text { or } d^{2} /(0.69 d)^{2} \text { or } 1 / 0.69^{2}$
= 2.1

CAIE A-Level Physics AS 9.1.4 Use for a Current Carrying Conductor the Expression I Anvq Questions

Exam points

CAIE A-Level Physics AS 9.1.4 Use for a Current Carrying Conductor the Expression I Anvq Questions question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)