PSPM DP024 BY SESSION

PSPM DP024 PAST YEAR QUESTIONS BY SESSION

DF035 SESSION 2015/2016
Answer any six questions.

1. (a) Define
(i) electric field region.
(ii) electric field strength.
[2 marks]

(b) An electron beam enters the uniform electric field between two parallel plates as
shown in FIGURE 1.

FIGURE 1
Copy FIGURE 1 and sketch the path of the electron beam in the region
between the plates and after leaving the plates.

[3 marks]
(c)

FIGURE 2
FIGURE 2 shows two point charges, - q and +q fixed at point L and Q separated by a
distance of 15 cm. Given q = 5μC, calculate
(i) the electric potential at M and P.
(ii) the work done to bring a charge of 1µC from M to P.
(iii) the electric potential energy of the system when the 1 µC charge is

fixed at P.
[10 marks]

2 (a) Define
(i) capacitance.
(ii) one farad.
[2 marks]

(b) Two parallel plate capacitors of capacitance 3 µF and 6 µF are connected in
parallel to a 24 V battery,
(i) Calculate the equivalent capacitance of the circuit and the total energy stored.
(ii) Calculate the charge stored in each capacitor.
(iii) If a dielectric is added to each capacitor, what happens to the amount
of total charge stored? Explain.
[8 marks]

(c) FIGURE 3 shows a circuit of camera flashlight.

FIGURE 3
(i) What is the function of the capacitor in the circuit?
(ii) Calculate the time required to charge the capacitor to 75% of its full

capacity.
(iii) Suggest ONE (1) way to reduce the charging time of the capacitor.

[5 marks]

3 (a) (i) Define drift velocity of free electrons.

(ii) Explain qualitatively the relation between drift velocity and current.

[3 marks]

(b) (i) Define electric current.

(ii) Current of 0.25A flows in a lightbulb for 1 hour. Calculate the number of

electrons that pass through the bulb.

[5 marks]

(c) (i) Define electromotive force,

(ii) Explain why the terminal voltage of a battery reduces after being used

for a certain period.

[3 marks]

(d) (i) A thin film resistor of length 10.0 mm, width 4.0 mm and thickness 9.0
µm is made from carbon. The resistivity of carbon is 3.9 x 10-5 Ωm. Calculate

the resistance.

(ii) What happens to the resistance of the thin film resistor in (i) above if

metallic nichrome is used instead of carbon?

[4 marks]

4 (а) Power rating in a bulb is 150W when it is connected to a 24 V supply.
(i) What is the resistance of the bulb?
(ii) What is the current flow when it delivers only 80 W?
(iii) If two bulbs connected in series or parallel, which combination of bulb
will produce more power/brighter?
[4 marks]

(b) (i) Sketch and label a circuit of potential divider.
(ii) Write the potential difference across one of the resistor. .
(iii) What is the function of potential divider?

[4 marks]
(c)

FIGURE 4
A 6V battery is connected to the circuit shown in FIGURE 4. When switch S is
opened, the current in the battery is 1.0 mA. When the switch is closed in position P
and Q, the current in the battery are 1.2 mA and 2.0 mA respectively. Calculate the
resistance R1 , R2 , and R3.

[7 marks]

5 (a) (i) State the Kirchhoff's laws.

(ii) What are the principles that become the basis for the Kirchhoff's laws?

[4 marks]

(b) For the circuit in FIGURE 5, Ɛ = 12V and R = 3 Ω.

FIGURE 5
Calculate
(i) the total resistance of the circuit.
(ii) the total current in the circuit.
(iii) the current in the 2R resistor.
(iv) the rate of thermal energy dissipated in the 2R resistor.

[4 marks]

(c)

FIGURE 6
For the circuit in FIGURE 6, write the equations according to the Kirchhoff's voltage
law and Kirchhoff's current law

[3 marks]

6 (a) List TWO (2) similarities and TWO (2) differences between electric and magnetic
forces.
[4 marks]

(b) A proton has a velocity of 5.2 x 107 ms-1 in the positive x-direction. It enters a region
of constant magnetic field B perpendicular to its motion. The magnetic field causes it
to move in a circular path in x-y plane with a radius of 1.20 m.
(i) Calculate the magnetic field.
(ii) Sketch a labeled diagram to show clearly the direction of the magnetic field.
[4 marks]

(c)

FIGURE 7
FIGURE 7 shows two long parallel wires separated 15 cm carries current of 8A and
5 A respectively.
(i) Calculate the magnetic field on wire Q.
(ii) Calculate the force per unit length on each wire.
(iii) Sketch a labeled diagram to show clearly the direction of the force and

magnetic field on each wire.
(iv) What is the direction of the force on each wire if both current are in the

opposite direction?
[7 marks]

7 (a) (i) Define one ampere.
(ii) Use the definition above to show that the value of permeability of free
space is 47 x 10-7 H m-1.
[3 marks]

(b)

FIGURE 8

FIGURE 8 shows a square coil of sides 5 cm carrying a current of 1.5A placed in a
uniform magnetic field of flux density of 0.65 T.
(i) Calculate the magnetic force on the side RS and ST.
(ii) Copy FIGURE 8 and mark with arrow the direction of the magnetic

force that acts on each side of the coil.
(iii) What is the resultant force on the coil?
(iv) What will happen to the coil?

[12 marks]

8 (a) State
(i) Faraday's law of electromagnetic induction,
(ii) Lenz's law.
[2 marks]

(b) A 50-turn coil with cross-sectional area of 5.8 x 10m is placed in a uniform magnetic
field of 1.5 T.
(i) Calculate the magnetic flux linkage in the coil when the plane of the coil
makes an angle of 60° to the magnetic field.
(ii) The coil rotates about an axis perpendicular to the uniform magnetic
field at a constant angular velocity of 500 revolutions per second. What
is the maximum induced e.m.f. in the coil?
[6 marks]

(c) A coil of inductance 350 µH carries a current of 1.2 A.
(i) What is the amount of energy in the coil?
(ii) The current in the coil is reduced to zero in 8 ms. What is the induced
emf across the coil?
(iii) List TWO (2) factors that determine the self-inductance of a coil.
[7 marks]

ANSWERS:
DF035 SESSION 2015/2016

1. (c)(i) 1.13x105 V, -4.5x105 V (ii) - 0.337 J (iii) - 0.153 J
2. (b)(i) 9 μF, 1.08 x 10-4 J (ii) 72 μC, 144 μC (c)(ii) 6.65 s
3. (b)(ii) 5.63x1021 electrons (d)(i) 10.83 Ω
4. (a)(i) 3.84 Ω (ii) 4.564 A (c)
5. (b)(i) 6 Ω (ii) 2 A (iii) 1A (iv) 6 W (c) I1 = I2 + I3, 10 = 5I1 + 6I2, 15 = 7I3 - 6I2
6. (b)(i) 0.452 T (c)(i) 1.066x10-5 T (ii) 5.33x10-5 Nm-1
7. (b)(i) 0, 0.05 N (iii) 0
8. (b)(i) 0.376 Wb (ii) 1.18 x103 V (c)(i) 2.52 x10-4 J (iii) 0.053 V

DF045 SESSION 2015/2016

Answer any six questions.

1 (a) (i) What is meant by phase angle of an AC circuit?
(ii) Sketch curves of current and voltage against time on the same graph. Given

that the current leads the voltage by Error! Reference source not
found. rad.

[3 marks]
(b) A sinusoidal 50 Hz AC source is measured to be 120 V by an AC voltmeter.

(i) What is the maximum value of the AC voltage?
(ii) Write the equation of the voltage.

[4 marks]
(c) An RLC series circuit is driven by an AC source given by v = 150 sin (377t). Given

that R = 425 Ω , L = 125 H and C = 350 µF, calculate the
(i) impedance of the circuit.
(ii) maximum current in the circuit.
(iii) phase angle between the current and voltage.
(iv) maximum voltage across the resistor.

[8 marks]

2 (a) An object is placed in front of a spherical mirror. The image formed is virtual,
upright and magnified.
(i) Sketch and label a ray diagram to show the position of the object and
the image.
(ii) State the type of the spherical mirror.
(iii) If the object is located at the center of curvature, state the characteristics of the
image produced.
[5 marks]

(b) A convex mirror has a radius of curvature of 1 m. An object with a height of 2 m is
placed 5 m in front of the mirror. Calculate the
(i) position of the image from the mirror,
(ii) magnification of the image.
(iii) height of the image.
[5 marks]

(c)

FIGURE 1
FIGURE 1 shows a glass rod with a convex surface of radius of curvature 6 cm at
one end. The refractive index of the glass is 1.5. A point object, O is located at 20 cm

from the curved end.
(i) Determine the location of the image.
(ii) If the glass rod is immersed in water with a refractive index of 1.33, determine

the location of the image. State ONE (1) characteristic of the image.
[5 marks]

3 (a) A converging lens with a focal length of 2 cm forms a virtual image of 0.8 cm
tall, 17 cm from the lens.
(i) Determine the position of the object.
(ii) Calculate the size of the object.
(iii) Sketch and label a ray diagram to show the formation of the image.
[5 marks]

(b) Each face of a biconvex lens has a radius of curvature of 15 cm. The index of
refraction of glass lens is 1.50.
(i) Calculate the focal length of the lens in air.
(ii) If the lens is immersed in sea water of refractive index 1.54, calculate
the new focal length and state the type of the lens.
[4 marks]

(c) The objective lens and eyepiece lens of a compound microscope are both converging
lenses and have focal lengths of 10.0 mm and 25.0 mm respectively. The distance
between two lenses is 40.0 mm. The microscope is being used to observe a sample
placed 18.0 mm in front of the objective lens. Calculate the
(i) position of final image.
(ii) overall magnification of the microscope.
[6 marks]

4 (a) State Huygens’ principle.
[2 marks]

(b) Two parallel slits separated by 0.25 mm are illuminated by 546 nm green light. The
interference pattern is observed on a screen 1.2 m away from the slits. Calculate the
(i) position of the second order maximum.
(ii) distance between the first order and the fourth order minima.
[5 marks]

(c) A 500 nm light is incident normally on a diffraction grating. The third-order
maximum of the diffraction pattern is observed at 32º.
(i) Calculate the number of lines per cm of the grating.
(ii) How many bright fringes can be observed?
(iii) What is the effect on the number of bright fringes that can be observed if a
grating with larger number of lines per centimeter is used?
[8 marks]

5 (a)

FIGURE 2
FIGURE 2 shows a thin layer of oil on the surface of water being illuminated by an
incident ray. Given that noil > nwater > nair.
(i) What is the phase change due to the reflections of ray 1 and ray 2?

Justify your answer.
(ii) If θ ≈ 0° and the thickness of oil is t, what is the optical path difference

between reflected rays 1 and 2?
(iii) Why do oil surface appear to have many different colours?

[8 marks]
(b) What will happen to the diffraction pattern of a single slit, if the

(i) slit width is increased?
(ii) wavelength of the light is increased?

[2 marks]
(c)

FIGURE 3
FIGURE 3 shows two glass plates separated at one end by a 0.2 mm diameter wire to
form an air wedge. The plates are 15 cm long and are illuminated from above by a
600 nm light.
(i) How many bright fringes are formed?
(ii) Calculate the separation between two consecutive bright fringes.

[5 marks]

6 (a) State TWO (2) characteristics of electromagnetic radiation energy based on the
(i) classical theory.
(ii) Planck’s quantum theory.
[2 marks]

(b) Sketch a labelled graph to show the variation of photoelectric current with voltage of
the following photoelectric effect experiments:
(i) Two lights of the same frequency but the intensity of the first is twice the
second.

(ii) Two lights of the same intensity but different frequencies.

(iii) Two lights of the same intensity and frequency but using two different
cathode metals.
[6 marks]

(c) A 424 nm light incidences on a metal of a work function of 2.28 eV.
(i) Calculate the stopping potential.
(ii) What is the maximum speed of the emitted electrons?
(iii) Calculate the de Broglie wavelength of the emitted electrons.
[7 marks]

7 (a) (i) State TWO (2) conservation laws of nuclear reaction.
(ii) Explain briefly why energy is released in nuclear fission.

[4 marks]

8 (a) Without using any equation, define
(i) decay constant.
(ii) half-life.

[2 marks]

(c) The activity of a radioisotope sample is 12 mCi. After 5 hours, the activity is 9 mCi.
Given 1 Ci=3.7 x 1010 Bq. Calculate the
(i) decay constant,
(ii) half-life.
(iii) initial number of nuclei in the sample.
(iv) activity of the sample after 30 hours.
[7 marks]

(d) Carbon-14 with a half-life of 5730 years is used to date a bone found at an
archaeological excavation. If the ratio of 14 C to 12 C atoms of the bone is 3.25 x 10-13,
how old is the bone? The ratio of 14 C to 12 C atoms in living matter is 1.3 x 10-12 .
[3 marks]

DF035 SESSION 2016/2017
Answer any six questions.

1 (a)

FIGURE 1.1

FIGURE 1.1 shows three point charges, A, B and C. Each has charge 6 µC and
located 3 cm from the origin, O.
(i) What is meant by the electric field at the origin, O?
(ii) Sketch the electrostatic force on charge B.
(iii) Determine the magnitude and direction of the resultant electric field at the

origin, O.
(iv) Calculate the electric potential at the origin, O.

[11 marks]
(b)

FIGURE 1.2
FIGURE 1.2 shows two parallel charged plates of equal magnitude and opposite
sign. The electric field between the plates is 5 x 104 N C-1.
(i) Sketch the electric field and the equipotential lines between the plates.
(ii) What is work done to displace a +4 µC charge from plate B to plate A?

[4 marks]

2 (a) An air filled parallel plate capacitor of area 0.40 m2 and separation 0.02 m is charged
to a 3000 V potential difference. Then the capacitor is disconnected from the battery.
(i) Calculate the capacitance.
(ii) Calculate the electric field of the capacitor.
(iii) Calculate the charge stored in the capacitor.
(iv) The potential difference between the plates drops to 1000 V when a
dielectric sheet is inserted to fill the space between the plates. Calculate the
dielectric constant.
[9 marks]

(b) A 6V battery is connected in series to a 60 kΩ resistor, and 2 µF and 4 µF capacitors.
(i) Calculate the effective capacitance of the circuit.
(ii) Calculate the time constant of the circuit.
(iii) What is meant by the time constant in the context of charging the current?
[6 marks]

3 (a) Define electric current.
[1 mark]

(b) A bulb drawn 0.4 A current from a 3 V battery in 6.5 minutes. Calculate the
(i) charge that flows in the circuit.
(ii) resistance of the bulb filament.
(iii) energy dissipated in the bulb.
[6 marks]

(c) A heater is made from a wire of length 1.5 m, cross-sectional area 4 x 10-6 m2 and the
temperature coefficient of resistivity 2.0 x 10-3 C-1 . The wire resistivity at 320°C is
6.8 x 10-5 Ω m.
(i) What is meant by the temperature coefficient of resistivity?

(ii) Calculate the resistance of the heater wire at the operating temperature
of 420°C.

(iii) What is the resistance of the heater if the length of the wire is doubled?
(iv) Explain why resistivity varies with temperature.

[8 marks]

4 (a) A 12 V emf battery with an internal resistance of 2.5Ω is connected to a 4Ω
resistor.
(i) What is meant by the electromotive force (emf) of a power source?
(ii) Calculate the voltage across the battery terminal.
(iii) What happens to the terminal voltage of the battery if the internal
resistance increased due to wear and tear? Explain your answer.
[7 marks]

(b)

FIGURE 4

FIGURE 4 shows three resistors connected to a battery.

(i) Calculate the current drawn from the battery.
(ii) Calculate the voltage across the 4Ω resistor.
(iii) What is the current drawn from the battery if one of the 4Ω resistor is

removed?

[8 marks]

5 (a) State Kirchhoff’s Laws. [2 marks]
(b)

FIGURE 5.1
FIGURE 5.1 shows two batteries connected to two resistors. The emf of the battery
E1 is 12V and its internal resistance is negligible. The emf of the battery E2 is 26 V

and its internal resistance is 3 Ω.
(i) Calculate the current entering point B when the switch is opened.
(ii) Calculate the current entering point B when the switch is closed.
(iii) Compare the terminal voltage across battery E2 for both of the above

conditions.
[9 marks]

(c)

FIGURE 5.2
FIGURE 5.2 shows two batteries with emf Ɛ1 and Ɛ2, are connected to a
potentiometer. The length of uniform wire AB is 90 cm and its resistance is 12Ω. The
galvanometer does not show any deflection when AC is 60 cm.
(i) State the function of potentiometer.
(ii) Calculate Ɛ1.

[4 marks]

6 (a) A charge Q is moving in a circle. Does it produce a magnetic field?
Explain your answer.
[3 marks]

(b) Two long, straight parallel wires X and Y are separated by a distance of 20 mm. The
wires carry currents of 3 A in opposite directions.
(i) Sketch the pattern of magnetic field produced by the current-carrying
wires.
(ii) Determine the magnitude of the magnetic field at a point midway
between the wires.
[5 marks]

(c)

FIGURE 6
FIGURE 6 shows two coaxially current loops. Loop 1 has 20 turns with radius 3 cm
and carries a current of 4A in an anti-clockwise direction. Loop 2 has 35 turns with
radius 4 cm and carries current of 5 A in a clockwise direction. Determine the
magnitude and direction of the magnetic field at the center of the two loops.

[5 marks]

(d) A solenoid has 450 turns of length 15 cm carries a current of 3.5 A. Calculate the
magnetic field inside the solenoid.
[2 marks]

7 (a)

FIGURE 7
FIGURE 7 shows a rectangular loop STUV carrying a current of 6 A placed near a
long straight wire carrying a current of 12 A. Determine the force per unit length and
its direction on the straight wire.

[5 marks]
(b) An electron with a velocity of 8 x 10 m enters a uniform magnetic field of 1.2T

perpendicularly.
(i) Calculate the radius of the circular path travelled by the electron in the

magnetic field.
(ii) What happens to the radius of circular path if the electron is replaced

by proton traveling at the same speed? Explain your answer.
[6 marks]

(c) A galvanometer has a 50 turns coil of area 40 cm and a magnetic field of
5 x 10-2 T. The resistance of the coil is 36 Ω. The galvanometer produced a
maximum deflection of 120° when it is connected to a potential difference of 9 V
(i) Calculate the maximum torque of the coil.
(ii) What is the deflection angle of galvanometer if the current through the
galvanometer is 50 mA?
[4 marks]

8 (a)

FIGURE 8.1

FIGURE 8.1 shows two coils P and Q placed near to each other.
(i) What is meant by mutual induction?
(ii) Explain why emf is induced in the coil Q when a sinusoidal voltage is

connected to the coil P, but no emf is induced if coil P is connected to a
battery

(iii) Determine the direction of the induced current in the resistor R when terminal
X is positive and the current increases
[4 marks]

(b)

FIGURE 8.2
FIGURE 8.2 shows a 15 cm metal rod with 1.2 Ω resistance moving at velocity 3.6
ms-1 to the right crossing a uniform magnetic field of 600 mT.
(i) Explain how the motional emf is induced in the rod.
(ii) Calculate the motional induced emf in the metal rod.
(iii) If the rod is connected in series to a 10 Ω resistor, determine the induced

current and its direction.
[9 marks]

(c) A 3.5 mH inductor carries a current of 4 A. Calculate the magnetic energy in the
inductor.
[2 marks]

ANSWER:
DF035 2016/2017

1. (a) (iii) 6 x107 N C-1 (iv) 1.8 x106 V (b)(ii) 2.4 mJ
2. (a) (i) 1.77 x 10-10 F (ii) 1.5 x105 Vm-1 (iii) 5.31 x10-7 C (iv) 3 (b)(i) 1.33μF (ii) 0.08 s
3. (b) (i) 156 C (ii) 7.5 Ω (iii) 468 J (c)(ii) 30.6 Ω (iii) 61.2 Ω
4. (a) (ii) 7.4 V (b)(i) 1.2 A (ii) 2.4 V (b)(iii) 0.86 A
5. (b) (i) 0.82 A (ii) 5 A (c)(ii) 4.5 V
6. (b) (ii) 1.2 x10-4 T (c) 1.07 x10-3 T (d) 1.32 x10-2 T
7. (a) 1.08 x10-4 N m-1 (b)(i) 3.8 x10-5 m (c)(i) 2.5 x 10-3 Nm (ii) 24°
8. (b)(ii) 0.32 V (iii) 0.029 A (c) 28 mJ

DF045 SESSION 2016/2017
Answer any six questions.

1 (a)

FIGURE 1
FIGURE 1 shows graphs of a sinusoidal alternating current (AC) and a sinusoidal
alternating voltage against time across a resistor R.
(i) Calculate the resistance R.
(ii) Express the sinusoidal voltage equation.
(iii) Calculate the phase angle and sketch the phasor diagram of voltage and

current at t = 15 ms.
[7 marks]

(b) A 200 Ω resistor and a 0.4 H inductor are connected to an AC source with an
angular frequency of 250 rad s-1 and a voltage of 30 V. Calculate
(i) the impedance of the circuit.
(ii) the phase angle of the source voltage with respect to the current. Does the
source voltage lag or lead the current?
[8 marks]

2 (a) (i) State two (2) factors that determine the focal length of a lens?
(ii) State the characteristics of the image produced by a convex mirror.
[3 marks]

(b)

FIGURE 2
FIGURE 2 shows two thin lenses with focal lengths 13 cm and 16 cm placed 56
cm apart. An object of 4 mm height is placed at 36 cm in front of the first lens.
Calculate the position and size of the image formed
(i) by the first dens.

(ii) by the second lens.
[7 marks]

(c) An upright image is formed 24 cm from the real object by a spherical mirror. The
image's height is one third of the object's height.
(i) Where the mirror should be placed from the object?
(ii) Sketch a ray diagram to show the formation of the image.
[5 marks]

3 (a) A monochromatic light is illuminated to a diffraction grating which has 5310 lines
per cm. The second-order maximum produced by a diffraction grating is at an
angle of 35°. Calculate the number of maxima that can be seen on the screen.
[6 marks]

(b) Young's double-slit experiment is performed using 589 nm light. The distance
between the slits and the screen is 2 m. The tenth dark fringe is seen 7.26 mm
from the central bright fringe.
(i) Calculate the distance between the two slits.
(ii) Calculate the number of dark fringes that can be seen on the screen.
(iii) What will happen to the interference pattern if the distance between the
slits is decreased?
[7 marks]

(c) A transparent thin film (n = 1.3) is deposited on a glass lens (n = 1.5) to form an
anti-reflective coating. Calculate the minimum thickness of the thin film if the
wavelength of reflected light in air is 500 nm.
[2 marks]

4 (a) State four (4) significant findings from photoelectric experiment.

(b) (i) [4 marks]
Express Einstein’s photoelectric equation with all symbols defined.

(ii) Sketch a graph of stopping potential, Vs versus electron's velocity, v

emitted from the metal surface. Hence, draw a conclusion from the

sketched graph.

[5 marks]

(c) A photon beam of wavelength 437 nm is incident on a metal surface. The

stopping potential of photoelectron is 1.67 V. Calculate

(i) the energy of photon.

(ii) the maximum speed of the ejected electrons.

(iii) the threshold frequency of the metal.

[6 marks]

5 (a) (i) State the wave-particle duality principle of light.
(ii) State the advantages of electron microscope compared to optical
microscope.
(iii) Calculate the momentum of light of wavelength 680 nm.
[6 marks]

(b) (i) With the aid of a diagram, describe Davisson-Germer experiment to
demonstrate the electron diffraction.

(ii) In an electron diffraction experiment, a beam of electrons is directed
towards a crystal of inter atomic spacing of 0.345 nm. If the first order of the

maximum intensity occurs at an angle, θ = 47°, calculate the speed of the
electron.

[9 marks]

6 (a) (i) Define nucleon number of a nucleus.

(b) (ii) A nucleus is given by symbol 207 Pb. What is the number of proton and
(c) 82
7 (a)
(b) neutron in the nucleus?

(iii) Which of the following nuclei are pairs of isotopes?

164C , 173N , 174N , 186O , 187O , 197F , 1214Na , 1224Mg

[6 marks]

(i) What is nucleus binding energy?

(ii) Sketch a graph of binding energy per nucleon versus mass number.

(iii) Explain the processes of nuclear fission and nuclear fusion from the graph as

sketched in question 6(b)(ii).

[5 marks]

Mass of 14 O is 14.008595 u. Calculate the binding energy per nucleon of the
8

nucleus.

[4 marks]

State four (4) conservation laws in a nuclear reaction.

[4 marks]

Bismuth-212 ( 212 Bi) spontaneously undergoes alpha decay to form Thallium-208
83

( 208 Tl). The mass of Bismuth-212, Thallium-208 and alpha are 211.991272u,
81

207.9820047 u and 4.002603 u respectively.

(i) Express the equation of the nuclear reaction.

(ii) Calculate the energy released in the reaction.

[3 marks]

(c) (i) Differentiate between fission and fusion reactions.

(ii) Express fusion reaction of proton-proton cycle that occurs in the sun.

(iii) A fusion reaction is represented by the following equation,

2 H 12H 13H 11H  4.55MeV
1

Calculate the energy released from the fusion of 0.5 kg deuteron.

[8 marks]

8 (a) (i) State the fundamental decay law of radioactive.
(ii) Calculate activity of 2.5 mg Co with half-life 5.62 years.
[4 marks]

(b) State five (5) applications of radioactive tracers in both medicine and industry
areas.
[5 marks]

(c) 199 Pt isotope of 30.8 min half-life is prepared with an initial activity of 7.56 x 1011
78

Bq. Calculate

(i) the mass of 199 Pt in the prepared sample.
78

(ii) the activity of the sample after three half-lives period.

[6 marks]

ANSWER:

DF045 2016/2017

1. (a) (i) 20 Ω (ii) 10 sin (50πt+  ) (b)(i) 224 Ώ (ii) 26.6°
2

2. (b) (i) -0.23 cm (ii) +0.19 cm (c)(i) 18 cm

3. (a) 3, 7 (b)(i) 1.54 x 10-3 m (ii) 5230 (c) 9.615 x 10-8 m

4. (c) (i) 2.84 V (ii) 7.7 x 105 m s-1 (iii) 4.03 x 1014 Hz

5. (a) (iii) 9.75 x10-28 kg m s-1 (ii) 2.89 x 106 m s-1

6. (a) (ii) 82, 125 (c) 6.761 MeV/nucleon

7. (b)(ii) 6.2 MeV (c)(iii) 3.42 x 1026 MeV

8. (a)(ii) 9.78x1010 Bq (c)(i) 6.67x10-7g (ii) 9.45 x 1010 s-1

DF035 SESSION 2017/2018 [1 mark]
Answer any six questions.

1 (a) Define equipotential surface.

(b)

5 μC +

7 cm

2 μC + 15 cm 3 μC

+

FIGURE 1.1
FIGURE 1.1 shows an arrangement of three point charges.
(i) Sketch the two forces that act on the 2 μC charge.
(ii) Determine the magnitude and direction of resultant force on the 2 μC.
(iii) Calculate the total potential energy of the charges.

[12 marks]
(c)

-------

X

Y

+ + + + + ++

FIGURE 1.2
FIGURE 1.2 shows two charged parallel plates. Sketch the path of
(i) a positive charge placed at point Y.
(ii) a positive charge entering horizontally from point X.

[2 marks]

2 (a) A parallel plate capacitor with plate area of 6 cm2 and gap separation of 0.50 mm is

connected to a 9 V battery. After the capacitor is fully charged, the battery is

disconnected.

(i) Calculate the charge on each plate.

(ii) Calculate energy stored in the capacitor.

(iii) What happens to the potential difference if a dielectric is inserted between the

plates? Justify your answer.

[9 marks]
(b) Sketch the arrangement of two capacitors, P and Q with capacitance 12 μF and 6 μF

respectively that can be replaced by an equivalent 4 μF capacitor. Justify your

answer.

[3 marks]
(c) A 12 V battery is connected to a 4 μF capacitor and a 20 Ω resistor. Calculate the

charge in the capacitor at time t = 90 μs.

[3 marks]

3 (a) (i) State Ohm’s law.
(ii) What is the difference between the emf of a battery and the potential
difference across the battery terminals in a circuit?
[3 marks]

(b) A battery has an emf of 16 V with internal resistance of 2 Ω is connected to a heater
with resistance of 4 Ω. Calculate the power dissipated by the heater.
[4 marks]

(c)

FIGURE 3

FIGURE 3 shows a 16 V battery with internal resistance, r connected to a
rechargeable battery with emf, Ɛ and internal resistance 2 Ω, and a lamp with
resistance 4 Ω carrying a current of 2 A. The current through the rechargeable battery
is 5 A. Calculate the
(i) current through the 16 V battery.
(ii) internal resistance, r.
(iii) emf, Ɛ.

[8 marks]
4 (a) State one (1) application of a potentiometer circuit.

[1 mark]
(b)

FIGURE 4.1
FIGURE 4.1 shows a circuit consisting of four resistors and a current of 4 A entering
the circuit. Calculate the
(i) effective resistance.
(ii) current at point P.
(iii) voltage at point P.

[9 marks]

(c)

FIGURE 4.2
An unknown length of platinum wire 0.82 mm in diameter is placed as resistance, Rx
in a Wheatstone bridge as shown in FIGURE 4.2. Resistors R1 and R3 have
resistance of 33Ω and 47 Ω respectively. Balance is achieved when R2 is 3.5 Ω.
Calculate the length of the platinum wire if its resistivity is 1.06 x 10-7 Ω m.

[5 marks]

5 (a) (i) Define current.
(ii) Describe the microscopic model of current.

(b)

FIGURE 5

FIGURE 5 shows a circuit consisting of four identical lamps A, B, C and D and three

switches S1, S2 and S3. One of the lamps is faulty. An ohm-meter is used to detect the

fault by measuring the resistance across terminals P and Q. TABLE 5 shows the

readings of the ohm-meter for different switching positions.

TABLE 5

S1 Switch S3 Ohm-meter readings (Ω)
S2

closed opened opened 12

opened closed opened 18

opened closed closed 18

(i) Determine the resistance of the lamp
(ii) Identify the faulty lamp. Justify your answer.

[5 marks]

(c) A copper wire with length of 130 m has a diamenter of 4 cm. The resistivity and
temperature coefficient of resistivity of the wire is 1.68 x10-8 Ω m and 6.8 x10-3 oC-1
respectively.
(i) If the wire experiences an increase in temperature of 30oC, what is the change
in its resistance?
(ii) Explain why there is an increase in its resistance when the temperature
increases.
[6 marks]

6 (a) Name two (2) sources of magnetic field.
(b)

FIGURE 6

FIGURE 6 shows the path of two charged particles, P and Q moving in a magnetic
field that points out of the page. If both particles have equal mass and magnitude of
charges,
(i) explain why the trajectories of the particles are circular.
(ii) which particle, P or Q has a negative charge? Explain your answer.
(iii) does P has a larger velocity than Q? Explain your answer.

[8 marks]
(c) The plane of two turns coil of area 0.0127 m2 is perpendicular with the magnetic field

of 0.7 T. The current in the coils is 3 A.
(i) Calculate the torque exerted on the coil.
(ii) if the plane make an angle of 300 with the magnetic field, calculate the torque

exerted on the coil?
[5 marks]

7 (a) (i) Define magnetic flux.
(ii) State Faraday’s law.
(iii) What is the meaning of the negative sign in the Faraday’s law?
[3 marks]

(b)

FIGURE 7
FIGURE 7 shows two long parallel current carrying conductor separated by 2 cm.
The net magnetic field at point P is 0.08 mT into the page.
(i) Calculate the magnitude of current in the wire Y.
(ii) Is it possible to produce zero magnetic field at point P? Justify your answer.

[7 marks]
(c) A coil of wire containing 600 circular loops with radius 4.5 cm is placed in a

magnetic field that decreases at the rate of 0.2 T s-1. Calculate the magnitude of the
induced emf if
(i) the plane of the coil is perpendicular to the magnetic field.
(ii) the plane of the coil is parallel to the magnetic field.

[5 marks]

8 (a) Define mutual inductance.
[1 mark]

(b) An inductor coil having 4 turns and 5 mm in diameter carries 6 A current.
(i) Calculate the inductance of the coil
(ii) Calculate the energy stored in the inductor.
(iii) What is the potential difference induced across the inductor if the current
drops to 3 A in 7 μs?
[9 marks]

(c)

FIGURE 8

FIGURE 8 shows a wind gauge that can rotate freely with a square vertical coil with
sides 10 cm attached to a rod. The horizontal component of the Earth’s magnetic field
is 1.5 x 10-5 T
(i) If the angular speed of the wind gauge is 216 rad s-1. the corresponding

induced emf in the coil is 15 mV, how many turns does the coil have?

(ii) Give two (2) suggestions on how you can modify the coil to increase the
induced emf in the coil.
ANSWERS:
DF035 2017/2018 [5 marks]

1. (b) (ii) 18.6 N, 82.60 below negative x-axis. (ii) 2.46 J
2. (a) (i) 9.56 x 10-11 C (ii) 4.3x10-23 J (c) 3.24 x10-3 C
3. (b) 28.52 W (c) (i) 7 A (ii) 3.43 Ω (iii) 2 V
4. (b) (i) 6 Ω (ii) 1.6 A (iii) 8 V (c) 24.9 m
5. (b) (i) 6 Ω (c)(i) 3.5 x 10-4 Ω

6. (c)(i) 0 Nm (ii) 0.0462 Nm

7. (b)(i) 8.4 A (ii) 3.6 A (c)(i) 0.76 V (ii) 0 V
8. (b)(i) 7.89 x 10-5 H (ii) 1.4 x 10-6 J (iii) 0.03 V (c)(i) 463 turns

DF045 SESSION 2017/2018
Answer any six questions

1 (a) Define rms voltage.
[1 mark]

(b) An RLC series circuit has impedance 180 Ω, inductive reactance 110 Ω, and
capacitive reactance 200 Ω. An AC source with rms voltage 30 V and frequency 500
Hz is connected to the circuit.
(i) Calculate the peak voltage of the AC source.
(ii) Calculate the capacitance of the capacitor and inductance of the inductor.
(iii) Calculate the power factor of the circuit.
(iv) Does the source voltage lead of lag the current in the circuit? Justify
your answer.
[14 marks]

2 (a) State the laws of refraction.

[2 marks]

(b) An object is placed 7.5 cm from a concave mirror. The radius of curvature of the
mirror is 10 cm.
(i) Calculate the focal length of the mirror.
(ii) By sketching a ray diagram, determine two (2) characteristics of the image.
[5 marks]

(c) A convex lens has a focal length of 7 cm. An object is placed 3.5 cm to the left of the
lens. A second convex lens having the same focal length as the first one is placed 10
cm to the right of the lens.
(i) Calculate the image distance of the first lens.
(ii) Does the final image diminished, remain unchanged or magnified? Justify
your answer.
[8 marks]

3 (a) (i) Define diffraction.
(ii) Can two different light sources be coherent? Explain your answer.
(iii) Explain with the aid of the diagram, the formation of bright fringes by a
diffraction grating.
[6 marks]

(b) In a Young’s double-slits experiment, a 534 nm light produces the 20th dark fringe at
the same position as the 15th bright fringe produced by another light source. Calculate
the wavelength of the other light source.
[4 marks]

(c) A 473 nm blue light is incident perpendicular to a soap film with a refractive index of
1.34.
(i) Calculate the minimum thickness of the film in order to get bright fringes.
(ii) If the film floats on water with a refractive index of 1.33, will the minimum
thickness of the film decrease, remain unchanged or increase in order to get
bright fringe?
[5 marks]

4 (a) (i) State two (2) differences between the Planck's quantum theory and classical
theory of energy.

(ii) Define threshold frequency.
(iii) What is meant by work function?

[4 marks]

(b) A 473 nm blue light illuminates a metal surface. The stopping potential is 1.25 V
(i) Calculate the maximum speed of the emitted photoelectron.
(ii) Calculate the work function of the metal.
(iii) Sketch a graph of photocurrent against potential difference. Label the stopping
potential.
(iv) Is there any changes in the photocurrent if the intensity of incident light is
increased? Explain your answer.
[11 marks]

5 (a) State wave-particle duality.

[2 marks]

(b) Calculate the mass of a particle travelling at a speed of 1.2 x 106 ms-1 and having a de
Broglie wavelength of 8.8 x 10-14 m.

[3 marks]

(c) Two samples have different sizes 10 nm and 300 nm respectively. What type of
microscope, optical or electron should you use to differentiate between the samples?
Explain your answer.
[5 marks]

(d) High speed beam of electrons are used in a Davisson-Germer experiment.
(i) State the observation of the experiment and explain how it verifies the de
Broglie matter wave.
(ii) If the electron beam is replaced with protons with the same speed what
change will be observed? Explain your answer.
[5 marks]

6 (a) (i) Define isotope.
(ii) Define mass defect and binding energy.

(b) In a 90 Sr nucleus, determine the [3 marks]
38 [4 marks]

(i) proton number.

(ii) nucleon number.

(iii) neutron number.

(c) (i) A U235 nucleus has a mass of 235.04393 u. Calculate the binding energy

92

in MeV per nucleon.

(ii) Sketch a graph of binding energy per nucleon versus nucleon number. Show

on your graph the regions for unstable nuclei. Explain why you choose those

unstable nuclei regions.

[8 marks]

7 (a) (i) State the difference between nuclear fusion and fission processes.
(ii) Describe the process of nuclear fusion in the sun.
[5 marks]

(b) In an induced nuclear reaction, two nuclides are formed as follows,

2 H 174 N X C24He
1 6

The atomic masses:

2 H 2.014102u
1

4 He4.002603u
2

14 N 14.003074u
7

X C12.000000u
6

Is the energy released or absorbed? Justify your answer.

[5 marks]

(c) In a nuclear reaction, U235 absorbs a slow neutron to form 15461Ba , 92 Kr , and three
36
92

neutrons

(i) Write the complete equation for the reaction.

(ii) Is it a chain reaction? Explain your answer.

[5 marks]

8 (a) (i) Define radioactive decay.
(ii) A 23940Th nucleus decays into a daughter nucleus and an α particle as
shown by the following equation

23940ThQP Ra X 
Y

Determine the values of P, Q, X and Y .

(iii) A fossil specimen is believed to be about 18000 years old. How could
this carbon dating be confirmed?
[10 marks]

(b) A radioactive sample initially has 3 x 107 nuclei and half of it decays after 3.16
minutes. Calculate the
(i) initial activity.
(ii) remaining nuclei after 60 minutes.
[5 marks]

ANSWERS:
DF045 2017/2018

1. (b) (i) 42.4 V (ii) 1.59 x 10-6 F (iii) 3.5 x 10-2 H (iv) 0.87
2. (b) (i) 5 cm (c) (i) 7 cm
3. (b) 694 cm (d) (i) 88.2 nm (ii) 176 nm
4. (b) (i) 6.6 x105 m s-1 (ii) 2.2 x 10-19 J
5. (b) 6.3 x 10-27 kg
6. (b) (i) 38 (ii) 90 (iii) 52 (c) (i) 7.4 MeV
7. (b) 13.6 MeV / 2.176 x 10-12 J
8. (a) (ii) P = 230, Q = 88, X = 4, Y = 2 (b) (i) 1.1 x 105 decay per second (ii) 49.24 nuclei

DP024 2019/2020
1.

C1 = 3.00 µF C2 = 6.00 µF

C3 = 1.33 µF

90 V
FIGURE 2

FIGURE 2 shows three capacitors are connected to a battery. Calculate the
(a) effective capacitance.
(b) total charge in the circuit.
(c) charge stored in capacitor C1.
(d) potential difference across capacitor C2.

2. (a) A 6 Ω resistor is placed across the terminal of a 12.0 V battery. Calculate the
(i) current flows through the resistor.
(ii) magnitude of charge pass through the resistor in 2.0 s.
[4 marks]

(b) Two wires are identical in length and resistance. First wire is made of aluminium but
the second wire is made of copper. Calculate the ratio of cross-sectional area of
copper wire to that of aluminium wire.

(Given : Resistivity of copper,ρcu = 1.72 ×10-8 Ω m , Resistivity of aluminium,

ρal = 2.83 ×10-8 Ω m)

[3 marks]

(c)

V
R
mA

90 V
FIGURE 3

FIGURE 3 shows the electric circuit is used to determine the resistance of voltmeter.
When the resistance R is 100 Ω, the reading of milliammeter is 30 mA and the reading of
voltmeter is 2.7 V. Calculate the resistance of the voltmeter.

[4 marks]

3. (a) An object of height 2.0 cm is placed 3.0 cm in front of a concave mirror. If the
height of image is 5.0 cm and virtual image is formed,
(i) sketch and label a ray diagram to show the formation of the image.
(ii) calculate the focal length of the mirror.

[7 marks]

(b) A convex mirror has a focal length of 8.0 cm. If the image is virtual and the
image distance is one third of the object distance, calculate the

(i) object distance.

(ii) magnification of the image.

[4 marks]

(c) The image of 20 cents coin has twice the diameter when a convex lens placed
2.84 cm from it. Calculate the focal length of the lens.

[3 marks]

4. (a) In a Young’s double slit experiment, a yellow monochromatic light of
wavelength 589 nm shines on the double slit. The separation between the slits is

0.059 mm and it is placed 1.50 m from a screen. Calculate the
(i) separation between the zeroth-order maxima and first order maxima.
(ii) separation between the second-order maxima and fourth order maxima on
the screen if blue light of wavelength 412 nm strikes the double slit.
[6 marks]

(b) Two slits with separation of 0.10 mm is illuminated by light 620 nm and the
interference pattern is observed on screen 4.00 m from the slits. Calculate the

(i) distance of third dark fringes from central bright.

(ii) distance between the third dark fringes and fourth bright fringes.

(iii) fringes separation.

[8 marks]

DP024

PHYSICS 2
SEMESTER II
SESSION 2020/2021

Answer all questions.

1. (a) The progressive wave with amplitude 2.0 cm, frequency 10 Hz and wavelength
12.8 cm is moving to the left. Calculate

(i) period.
(ii) progressive wave equation.

[5 marks]

(b) A progressive wave can be represented by the equation
y(x,t) = 20 sin (8πt-6x)

where y and x are in centimeter and t in seconds. Determine

(i) direction of wave propagation
(ii) amplitude
(iii) frequency
(iv) wavelength
(v) wave propagation velocity
(vi) particle vibrational velocity at x = 3 cm and t = 3 s

[11 marks]

2. (a) A copper wire has a diameter of 0.395 mm with resistance is 1.10 Ω.
Given the resistivity of copper is 1.72 x 10-8 Ωm.
(i) Calculate the length of the copper wire.
(ii) If a current of 2 A flows through the wire within 1 minute, calculate
the quantity of charge that pass through the wire during that time.
[4 marks]

(b)

FIGURE 2
Four resistors are connected to a battery as shown in FIGURE 2. Calculate the
(i) effective resistance of the circuit.
(ii) total current in the circuit.
(iii) voltage across resistor Rı.

[8 marks]
3.

FIGURE 3a
(a) FIGURE 3a shows five (5) identical capacitors of 8 uF connected between

point A and B. If the voltage supply across point A and B is 12 V, calculate
the
(i) effective capacitance.
(ii) total charge in the circuit.

. [4 marks]
(b)

FIGURE 3b

FIGURE 3b shows a direct current circuit. When switch Sj is closed, the
capacitor is charging,

(i) calculate the time constant.
(ii) calculate the time taken for the charge to reach 25% of its maximum

value.
(iii) sketch a graph of current against time.

[6 marks]
4. (a)

FIGURE 4a

FIGURE 4a shows the top view of two straight current-carrying conductor.
Sketch the magnetic field lines produced by the two conductors.

[2 marks]

(b) A solenoid has a length of 0.275 m, radius 2.4 cm and 215 number of turns.
A current of 3.2 A flows through the wire of the solenoid. Calculate the
(i) magnetic field at the center of the solenoid.
(ii) maximum magnetic flux produced by the solenoid.

[4 marks]

(c)

FIGURE 4c

FIGURE 4c shows a flexible single loop of radius 15.0 cm situated perpendicularly
in a magnetic field of 0.125 T. The loop is being stretched by grasping point P and Q
until its area is almost zero
(i) If the time taken is 0.3 s, calculate the magnitude of induced emf in the

loop.
(ii) If the loop is replaced with a rigid single loop of a resistance 0.5 Ω,

with the same radius and the magnetic field decreases at the rate of 0.04 T s-1,
calculate the magnitude of the induced emf.
(iii) Refer to (c)(ii), calculate the current in the loop.
(iv) By using Lenz's law, state the direction of induced current in (c)(iii).

[8 marks ]

5. (a) An upright image is formed 20.5 cm from the real object by using the spherical
mirror. The image's height is one fourth of object's height.
(i) Calculate the image distance from the mirror.
(ii) Calculate the radius of curvature of the mirror and state the type of mirror is
used
(iii) Sketch and label a ray diagram to show the formation of the image.

[10 marks]

(b) An object is placed 15 cm in front of a convex lens with focal length 10 cm.
(i) Calculate the image distance and magnification of the image.
(ii) State two (2) characteristics of the image,
[4 marks]

6. (a) In a double-slits experiment, the distance between the two slits is 0.25 mm.
The third bright fringe is 7.45 mm from the central bright. If the distance from
a double-slits to the screen is 2.1 m,
(i) calculate the wavelength of the light.
(ii) calculate the distance of the third dark fringe from the central bright.
(iii) calculate the distance between two consecutive bright fringes.
(iv) state the effect of the fringes separation if the separation distance
between double slit is decreased. Explain your answer.
[10 marks]

(b) A mixture of red light (wavelength = 665 nm) and yellow green light
(wavelength = 565 nm) incident on the double-slits of separation 2 mm. A flat
screen is located 2.25 m away from double slits. Calculate the
(i) distance of third order red fringe from the central bright.
(ii) distance of fourth order yellow green fringe from the central bright.
(iii) separation distance between third order red fringe and fourth order
yellow green fringe.

[4 marks]

ANSWERS:
DF045 2020/2021

1.(a) (i) 0.1 s
(ii) y(x,t) = 2.0 sin (62.83t + 0.491X)
To the right
(b) (i) 20 cm
(ii) 4 Hz
(iii) 1.047 cm
(iv) 0.042 ms -1/4.20 cm s-1
(v) 3331.91 cm s-1 /3.3191 ms-1
(vi) 7.84 m
120 C
2.(a) (i) 4.44 Ω
(ii) 2.70 A
5.40 V
(b) (i) 4μ F
(ii) 48μ C
(iii) 150 s
43.15 s
3.(a) (i) DIY
(ii)

(b) (i)
(ii)
(iii)

4.(a) DIY

(b) (i) 3.14 x10 -3T
(ii) 5.68 x 10 -6 Wb

(c) (i) 0.029 V
(ii) 2.83 x 10 -3 V

(iii) 5.66 x 10-3 A

(iv) Clockwise

5.(a) (i) 4.10 cm

(ii) -10.94 cm Convex mirror

(iii) DIY

(b) (i) -2

(ii) Real,inverted and magnified (RIM)

6.(a) (i) =2.96 x 10 -7m

(ii) 6.22 x 10-3m
(iii) 2.49 x10 -3 m

(iv) increase y inversely d

(b) (i) 2.24 x 10 -3 m

(ii) 2.54 x 10 -3 m
(iii) 3.04 x 10 -4 m

9. (b) 694 cm (d) (i) 88.2 nm (ii) 176 nm

10.(b) (i) 6.6 x105 m s-1 (ii) 2.2 x 10-19 J

11.(b) 6.3 x 10-27 kg

12.(b) (i) 38 (ii) 90 (iii) 52 (c) (i) 7.4 MeV
13.(b) 13.6 MeV / 2.176 x 10-12 J

14.(a) (ii) P = 230, Q = 88, X = 4, Y = 2 (b) (i) 1.1 x 105 decay per second (ii) 49.24 nuclei