QUESTIONS
QUESTION 1 (20 MARKS)
 You are provided with the following:
 A galvanometer
 A dry cell and a cell holder
 A switch
 A wire labelled Y mounted on a piece of wood.
 Eight connecting wires each with a crocodile clip at one end.
 A resistance wire labelled AB mounted on a millimeter scale.
 Six 10 Ohm carbon resistors
 A jockey or crocodile clip
 Micrometer screw gauge (to be shared)
Proceed as follows:
 Set up the circuit as shown in figure 1 below, with X being one of the 10 ohms carbon
Figure 1  Close the switch. Tap the jockey at various points on the wire AB and locate point P at which the galvanometer shows zero deflection, measure and record in table below the length, I where L = PB.
 Repeat the procedure in (b) using X as two 10Ω resistors, three resistors, four resistors, five resistors and six resistors. X is the effective resistance for the parallel combination i.e. X = ^{10}/_{n} where n is the number of resistors in parallel.
 Record your readings in table 1 below. (6 marks)
Table 1
Number of 10Ω carbon resistor One Two Three Four Five Six X (Ω) L (cm) 1/x (Ω^{1}) 1/L (cm^{1})  Plot a graph of 1/L (yaxis) against 1/X (5 marks)
 Determine the slope m of the graph. (2 marks)
 Given that 1/L = R/KX + 1/K where K = 100cm. Use the graph to determine R. (2 marks)
 Measure the diameter d and the length L of wire Y. (2 marks)
L = .............................m d = ................................m  Determine the crosssectional area A of the wire Y. (1 mark)
A= .........................................m^{2}  Determine the resistivity p of the wire Y given that its Resistance, R =p^{L}/_{A} (2 marks)
QUESTION 2 (20 MARKS)
PART A
You are provided with the following:
 A metre rule
 A stand, boss and clamp
 A piece of string
 A 20g mass
 A 50g mass
 A measuring cylinder containing water
 A concave mirror
 A screen
 A candle
 Pieces of sewing threads
 A mirror holder (Lens holder)
 Using a string, suspend the metro rule on the stand so that it balances horizontally at its center of gravity. Record the centimetre mark at which the metre rule balances.
Centimetre mark ..................................... cm (1 mark)  With the motre rule balanced at its centre of gravity, suspend a 20 g mass at a distance of 30cm from the centre of gravity. Suspend the 50g mass on the other side of the centre of gravity and adjust its position until the rule is balanced. See figure 3.
Record the distance d of the 50 g mass from the centre of gravity,
d= .............................cm
d= ..............................m (1mk) 
 Record the volume of the water in the measuring cylinder provided.
V= ...................................  Immerse the 20g mass fully into the water and adjust the position of the 50 g mass so that the rule balances horizontally. Record the volume V1 of the water plus 20 g mass and the distance di of the 50 g mass from the centre of gravity.
V_{1} =........................................... (1mk)
d_{1} = ..........................................cm (1mk) 
 Determine the volume of the water displaced (1mk)
 Determine the weight of the water displaced. (density of water 1g/cm^{3})
 Record the volume of the water in the measuring cylinder provided.

 Use the Principle of moments to determine the apparent weight of the 20 g mass when fully immersed in water. (g = 10N/kg) (2mks)
 Calculate the weight of the 20 g mass in air. (g = 10N/kg) (1mk)
 Determine the apparent loss in weight of the 20 g mass. (1mk)
PART B
 Light the candle and place it at distance u=20 cm in front of the concave mirror. Adjust the position of the screen until a sharp image of the candle flame is obtained. See Figure below.
 Read and record the distance v between the screen and the mirror.
v = ........................................................ (1mk)  Determine:
 The magnification m of the mirror (1mk)
 The value fi given that F1 = ^{mu}/_{m + 1}
 Read and record the distance v between the screen and the mirror.
 Repeat part e) for distance u¡ 18cm
 Read and record the distance vi between the screen and the mirror.
v_{1} = ........................................................ (1mk)  determine the magnification my of the mirror (1mk)
 Hence determine f_{2}
 Read and record the distance vi between the screen and the mirror.
 Determine the average value of f. (1mk)
MARKING SCHEME
QUESTION 1 (20 MARKS)
 You are provided with the following:
 A galvanometer
 A dry cell and a cell holder
 A switch
 A wire labelled Y mounted on a piece of wood.
 Eight connecting wires each with a crocodile clip at one end.
 A resistance wire labelled AB mounted on a millimeter scale.
 Six 10 Ohm carbon resistors
 A jockey or crocodile clip
 Micrometer screw gauge (to be shared)
Proceed as follows:
 Set up the circuit as shown in figure 1 below, with X being one of the 10 ohms carbon
Figure 1  Close the switch. Tap the jockey at various points on the wire AB and locate point P at which the galvanometer shows zero deflection, measure and record in table below the length, I where L = PB.
 Repeat the procedure in (b) using X as two 10Ω resistors, three resistors, four resistors, five resistors and six resistors. X is the effective resistance for the parallel combination i.e. X = ^{10}/_{n} where n is the number of resistors in parallel.
 Record your readings in table 1 below. (6 marks)
Table 1
Number of 10Ω carbon resistor One Two Three (4 s.f) Four Five Six (4 s.f) X (Ω) 10 5 3.3333 2.5 2 1.666 L (cm) ± 0.5 59.0 40.7 31.5 25.4 21.4 18.8 1/x (Ω^{1}) 0.1 0.2 0.3 0.4 0.5 0.6 1/L (cm^{1}) 0.01695 0.02457 0.03174 0.03937 0.04673 0.05379  Plot a graph of 1/L (yaxis) against 1/X (5 marks)
follow Ss work
If line is curve or negative gradient don't award for line  Determine the slope m of the graph. (2 marks)
m = Δ1/L = 0.039  0.0245
Δ1/X = 0.4  0.2
= 0.0145 = 0.0725 π/cm
0.2
If line is wrong in (e) deny gradient mark  Given that 1/L = R/KX + 1/K where K = 100cm. Use the graph to determine R. (2 marks)
gradient = R/k
0.0725 = R/100 = 7.25  Ω  Measure the diameter d and the length L of wire Y. (2 marks)
L = ........0.300 ± 0.01.....................m d = ....2.3 x 10^{4}.m 2.1  2.6 x 10^{4}  Determine the crosssectional area A of the wire Y. (1 mark)
A= .........................................m^{2}A = πr^{2}
=22/7 x (2.3 x 10^{4})^{2}
2
= 4.156 x 10^{8} m^{2}  Determine the resistivity p of the wire Y given that its Resistance, R =p^{L}/_{A} (2 marks)
R = PL
A
L = 9.975 x 10^{7}Ωm
7.25 = L x 0.3
4.156 x 10^{8}
QUESTION 2 (20 MARKS)
PART A
You are provided with the following:
 A metre rule
 A stand, boss and clamp
 A piece of string
 A 20g mass
 A 50g mass
 A measuring cylinder containing water
 A concave mirror
 A screen
 A candle
 Pieces of sewing threads
 A mirror holder (Lens holder)
 Using a string, suspend the metro rule on the stand so that it balances horizontally at its center of gravity. Record the centimetre mark at which the metre rule balances.
Centimetre mark ..50.0.. cm (1 mark) 57  53.0 cm 1dp  With the motre rule balanced at its centre of gravity, suspend a 20 g mass at a distance of 30cm from the centre of gravity. Suspend the 50g mass on the other side of the centre of gravity and adjust its position until the rule is balanced. See figure 3.
Record the distance d of the 50 g mass from the centre of gravity,
d= ......15.0.......cm ± 1 cm 1 dp
d= ....0.150......m 3 dp (1mk) 
 Record the volume of the water in the measuring cylinder provided.
V= ...17 cm^{3}
15  20cm^{3 } Accept ml  Immerse the 20g mass fully into the water and adjust the position of the 50 g mass so that the rule balances horizontally. Record the volume V1 of the water plus 20 g mass and the distance di of the 50 g mass from the centre of gravity.
V_{1} =....20cm^{3}..... (1mk) 17.5  22.5cm^{3}
d_{1} = ...13.0......cm (1mk) 11.0  15.0 cm 
 Determine the volume of the water displaced (1mk)
20  17 = 3cm^{3} volume = V_{1}  V  Determine the weight of the water displaced. (density of water 1g/cm^{3})
convenience of volume to mass ie m = ve
must be shown
convert mass to newtons (kg to N)
 Determine the volume of the water displaced (1mk)
 Record the volume of the water in the measuring cylinder provided.

 Use the Principle of moments to determine the apparent weight of the 20 g mass when fully immersed in water. (g = 10N/kg) (2mks)
principle of moments substituted
answer
4 s.f or exact  Calculate the weight of the 20 g mass in air. (g = 10N/kg) (1mk)
20/1000 x 10 = 0.2N
No units
1/2 mk
Ans from correct working  Determine the apparent loss in weight of the 20 g mass. (1mk)
wt in air  wt in water or wt of H_{2}0) displaced
Ans from correct working
No units 1/2 mk
PART B
 Use the Principle of moments to determine the apparent weight of the 20 g mass when fully immersed in water. (g = 10N/kg) (2mks)
 Light the candle and place it at distance u=20 cm in front of the concave mirror. Adjust the position of the screen until a sharp image of the candle flame is obtained. See Figure below.
 Read and record the distance v between the screen and the mirror.
v = ..18.0  22.0 cm.. (1mk)  Determine:
 The magnification m of the mirror (1mk)
m = v/u  The value fi given that F1 = ^{mu}/_{m + 1}substitution
answer
 The magnification m of the mirror (1mk)
 Read and record the distance v between the screen and the mirror.
 Repeat part e) for distance u¡ 18cm
 Read and record the distance vi between the screen and the mirror.
v_{1} = ...20.5  24.5... (1mk)  determine the magnification my of the mirror (1mk)
answer from correct working  Hence determine f_{2}Answer from correct working no units
1/2 mks
 Read and record the distance vi between the screen and the mirror.
 Determine the average value of f. (1mk)
answer from correct working
no units
1/2 mk
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