CAIE A-Level Physics 9 Electricity

Practise analysing charge flow, potential difference, resistance, power, resistivity and I-V behaviour, including temperature- and light-dependent components.

Exam points

analyse current as charge flow and apply Q = It, carrier quantisation and I = Anvq
calculate potential difference, energy transfer and electrical power from V, W, Q, I and R
apply V = IR, Ohm’s law and I–V characteristics to distinguish component behaviour
calculate resistance and resistivity from material, length and cross-sectional area
explain how temperature or light changes resistance in filament lamps, thermistors and LDRs

Covered syllabus points

9.1 Electric current 9.2 Potential difference and power 9.3 Resistance and resistivity

[Maximum number: 12]

(a)

State what is meant by an electric current.

[ 1 ]

(b)

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 / t

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I=n A L e / t

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

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

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(c)

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 .

[ 8 ]

(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
$=\left[\pi d^{2} / 4\right] /\left[\pi(0.69 d)^{2} / 4\right] \text { or } d^{2} /(0.69 d)^{2} \text { or } 1 / 0.69^{2}$

C1

= 2.1

A1

(ii)

The main part of the wire with cross-section X has a resistance per unit length of $1.7 \times 10^{-2} \Omega \mathrm{~m}^{-1}$ .

For the damaged length of the wire, calculate
1. the resistance per unit length,
resistance per unit length = $\Omega \mathrm{m}^{-1}[2]$
2. the power dissipated.
power = W

[ 4 ]

1. $R=\rho L / A$ or $R / L \propto 1 / A$

C1

$\begin{aligned} \text { resistance per unit length } =1.7 \times 10^{-2} \times(\text { area at } \mathrm{X} / \text { area at } \mathrm{Y}) =1.7 \times 10^{-2} \times 2.1 =3.6 \times 10^{-2} \Omega \mathrm{~m}^{-1} \end{aligned}$

A1

2. $\quad P=I^{2} R$ or $P=V^{2} / R$

C1

$\begin{aligned} R =3.6 \times 10^{-2} \times 3.0 \times 10^{-3}\left(=1.08 \times 10^{-4} \Omega\right) P =0.50^{2} \times 1.08 \times 10^{-4} \text { or } P=\left(5.4 \times 10^{-5}\right)^{2} / 1.08 \times 10^{-4} =2.7 \times 10^{-5} \mathrm{~W} \end{aligned}$

A1

(iii)

The diameter of the damaged length of the wire is further decreased. Assume that the current in the wire remains constant.

State and explain qualitatively the change, if any, to the power dissipated in the damaged length of the wire.

[ 2 ]

(cross-sectional area decreases so) resistance increases

M1

( $P=I^{2} R$ , so) power increases

A1

[Maximum number: 5]

(a)

Define electric potential difference (p.d.).

[ 1 ]

$\frac{\text { work (done)/energy (transferred from electrical to other forms) }}{\text { charge }}$

B1

(b)

A wire of cross-sectional area A is made from metal of resistivity $\rho$ . The wire is extended. Assume that the volume V of the wire remains constant as it extends.

Show that the resistance R of the extending wire is inversely proportional to $A^{2}$ .

[ 2 ]

$R=\rho L / A$

B1

V=L A and (so) $R=\rho V / A^{2}$ (with $\rho$ and V constant)

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(c)

An ammeter is used in the circuit in (c) to measure the current I as resistance R is varied. Fig. 6.2 is a graph of R against $\frac{1}{I}$ .

Fig. 6.2

[ 2 ]

(i)

Use Fig. 6.2 to determine the power dissipated in the variable resistor when there is a current of 2.0 A in the circuit.
power = W

[ 2 ]

$P=I^{2} R$ or P=I V or $P=V^{2} / R$

C1

$R=5.4(\Omega)$ or $V=10.8(\mathrm{~V})$

C1

$\begin{aligned} P =2.0^{2} \times 5.4 =22 \mathrm{~W} \end{aligned}$

A1

[Maximum number: 8]

(a)

Define the ohm.

[ 1 ]

(b)

Wires are used to connect a battery of negligible internal resistance to a lamp, as shown in Fig. 7.1.

Fig. 7.1

The lamp is at its normal operating temperature. Some data for the filament wire of the lamp and for the connecting wires of the circuit are shown in Fig. 7.2.

Fig. 7.2

[ 7 ]

(i)

Use the information in (i) to explain qualitatively why the power dissipated in the filament wire of the lamp is greater than the total power dissipated in the connecting wires.

[ 1 ]

(ii)

The lamp is rated as $12 \mathrm{~V}, 6.0 \mathrm{~W}$ . Use the information in (i) to determine the total resistance of the connecting wires.
total resistance of connecting wires =

[ 3 ]

$P=V^{2} / R$ or P=V I or $P=I^{2} R$

C1

(for filament wire) $R=12^{2} / 6.0$ or $R=6.0 / 0.50^{2}$ or R=12 / 0.50

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(for filament wire) $R=24 \Omega$

(for connecting wire) R=24 / 1000
$=2.4 \times 10^{-2} \Omega$

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(iii)

The diameter of the connecting wires is decreased. The total length of the connecting wires and the resistivity of the metal of the connecting wires remain the same.

State and explain the change, if any, that occurs to the resistance of the filament wire of the lamp.

[ 3 ]

[Maximum number: 1]

A spherical oil drop has a radius of $1.2 \times 10^{-6} \mathrm{~m}$ . The density of the oil is $940 \mathrm{~kg} \mathrm{~m}^{-3}$ .

The oil drop is charged. Explain why it is impossible for the magnitude of the charge to be $8.0 \times 10^{-20} \mathrm{C}$ .

minimum charge (on drop) is $1.6 \times 10^{-19} \mathrm{C}$

B1

All question bank results loaded

Covered syllabus points

9. Electricity question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (i)

Question (ii)

Question (iii)

9. Electricity question 2

Question (a)

Question (b)

Question (c)

Question (i)

9. Electricity question 3

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

9. Electricity question 4