1 PSPM SP025PAST YEAR QUESTIONS BY SESSION SF026 SESSION 2013/2014 Answer any six questions. 1 (a) (i) Name a quantity that indicates how fast a capacitor is charging and discharging. State your reasoning. (ii) Explain why inserting a dielectric between the plates of a capacitor increases its capacitance. [5 marks] (b) FIGURE 1 FIGURE 1 shows an arrangement of capacitors. If the equivalent capacitance is 0.5 μF, calculate the value of capacitor C. [3 marks] (c) FIGURE 2 shows a charge Q at the vertex of an equilateral triangle with sides 1 mm. If 138 J of work is done in bringing a −4.8 μC point charge from infinity to position M, (i) determine the magnitude and type of the charge Q. (ii) calculate the electric field at position N. [7 marks] 2 (a) (i) * State ONE application of a Wheatstone bridge. Explain the principle used in such application. FIGURE 2 Q M N 0.2 μF 0.8 μF C 0.6 μF
2 (ii) State TWO laws to be used in determining the currents in the circuit as shown in FIGURE 3. [5 marks] (b) A toaster has a heating element made of nichrome wire and connected to a 220 V source. The wire is initially at 20°C with current 1.8 A. When the toaster reaches its final operating temperature, the current is 1.53 A. Calculate the (i) power delivered to the toaster at its operating temperature. (ii) final temperature of the heating element if the temperature coefficient of resistivity for nichrome wire is 4×10−4 °C−1 . [4 marks] (c) The emf of a battery with internal resistance is 12 V. When an unknown resistor R is connected to the battery, the current is 0.8 A. If another resistor R is added in series, the current is 0.6 A. Calculate the (i) value of the resistor R. (ii) internal resistance of the battery. (iii) terminal voltage of the battery. [6 marks] 3 (a) (i) In what condition would a charged particle experience a magnetic force? (ii) Two charged particles moving in the same direction are projected perpendicularly into a uniform magnetic field. If the particles are deflected in opposite directions, what can you say about them? Explain your answer. [4 marks] (b) A circular loop L1 of radius 5 cm carries a 15 A current. (i) Calculate the magnetic field at its center. (ii) FIGURE 4 Another loop L2 of radius 1.5 cm, having 50 turns and carrying a 2 A current is placed at the center oh loop L1 as shown in FIGURE 4. What will be the FIGURE 3 L1 L2
3 resultant magnetic field at their common center if the two currents flow in the same direction? (iii) If loop L1 in FIGURE 4 is fixed but loop L2 is free to turn about its central axis, what will be the torque on loop L2 when its plane is parallel to loop L1? [6 marks] (c) A 2 A current flows towards left in a wire having a mass per unit length of 0.5 g cm−1 . If the wire is placed horizontally on the table, what are the magnitude and direction of the minimum magnetic field needed to float the wire? [5 marks] 4 (a) FIGURE 5 shows a bar moving on rails to the right with a velocity v in a uniform magnetic field directed out of the page. A resistor R connects the rails. (i) What is the direction of induced current in resistor R? Explain your answer. (ii) State TWO ways to increase the induced current with R fixed. [5 marks] (b) A rectangular coil of 60 turns, dimensions 0.1 m×0.1 m and total resistance 10 Ω, rotates with angular speed 30 rad s−1about the y-axis in a 1.5 T magnetic field directed along the x-axis. Calculate the (i) maximum induced emf in the coil. (ii) maximum rate of change of magnetic flux through the coil. [6 marks] (c) Two coaxial solenoids, P and Q have 400 and 700 turns respectively. A current of 3.5 A in coil P produce an average flux of 300 μWb through each turn of P and average flux of 90 μWb through each turn of Q. Calculate the (i) Inductance of solenoid P. (ii) Mutual inductance. [4 marks] 5 (a) A voltmeter shows a reading of 220 V for a 50 Hz AC voltage. (i) Calculate the maximum value of the AC voltage. (ii) Write the equation for the AC voltage. [4 marks] (b) A 0.9 kΩ resistor, 0.25 μC capacitor and 2.5 H inductor are connected in series across a 240 Hz AC source with 140 V peak voltage. (i) Calculate the impedance. (ii) Calculate the maximum current. (iii) Calculate the phase angle between the current and voltage. R v FIGURE 5
4 (iv) Which quantity lags: current or voltage? Explain your answer. (v) How to achive resonance in the circuit? [11 marks] 6 (a) State THREE conditions for interference to occur in a Young’s double-slit experiment. [3 marks] (b) * Two thin parallel glass in-contact are illuminated normally with a 580 nm light. As the plates are slowly moves apart, dark surface is observed followed by bright surface. (i) Explain the formation of the dark and bright surfaces. (ii) Calculate the plate separation at the first dark surface. [5 marks] (c) A 632.8 nm light is incident normally on a diffraction grating with 6000 lines per cm. Only the zeroth, first and second order bright fringes are observed. Explain mathematically why the third order is not observed. [2 marks] (d) A lens is made of glass with refractive index 1.6 and radii of curvatures, r1= 6 cm and r2 = 4 cm. An object is located 30 cm from the lens. (i) Calculate the focal length of the lens. (ii) By sketching a ray diagram, determine TWO characteristics of the image. [5 marks] 7 (a) (i) State TWO characteristics of light in the classical theory that fails to justify the photoelectric effect. (ii) State the significance of the photoelectric effect experiment. [3 marks] (b) When a 546 nm light is used in a photoelectric experiment, the stopping potential is 0.38 V. (i) Calculate the work function of the metal. (ii) Calculate the threshold wavelength. (iii) Calculate the minimum de Broglie wavelength of the electron. (iv) Will electron be emitted if the target material is replaced with silver with work function 4.73 eV? Justify your answer. [9 marks] (d) State ONE advantage of electron microscope compared to optical microscope. What makes it better? [3 marks] 8 (a) (i) * Describe the process of nuclear fusion in the sun. (ii) Sketch a graph of binding energy per nucleon against nucleon number. Label on the graph regions for nuclear fission and fusion. Explain the occurrence of such nuclear reactions in the particular regions. [6 marks] (b) Gold, 197 79 Au is irradiated by a flux of slow neutrons and electrons are emitted. Given the mass of 197 79 Au = 196.966552 u and 198 80Hg = 197.966752 u.
5 (i) Write the nuclear reaction equations. (ii) Calculate the maximum energy (in MeV) of the emitted electron. [3 marks] (c) A prepared sample of radioactive isotope has an activity of 10.0 mCi. After 4 hours, the activity is 8.0 mCi. Calculate the (i) half-life of the isotope. (ii) number of the isotope in the prepared sample. (iii) sample activity 30 hours after it is prepared. (Given 1 Ci = 3.7×1010 decay per second) [6 marks] ANSWERS: SF026 SESSION 2013/2014 1. (b) 0.4 F (c) (i) -3.19 x10-6 C (ii) 6.28 x 1010 N C-1 2. (b) (i) 337 W (ii) 461C (c) (i) 5 (ii) 10 (iii) 6 V 3. (b) (i) 1.88 x 10-4 T (ii) 4.38 x 10-3 T (iii) 0 N m (c) 0.245 T (out of page) 4. (a) (i) upwards (b) (i) 27 V (ii) 0.45 Wb s−1 (c) (i) 0.0343 H (ii) 0.018 H 5. (a) (i) 311 V (b) (i) 1434 (ii) 0.0976 A (iii) 51.1 (iv) current 6. (b) (ii) 2.90 x 10-7 m (d) (i) −20 cm (ii) virtual, upright, diminished 7. (b) (i) 3.03 x 10-19 J(ii) 6.55 x10-7 m (iii) 1.99 x 10-9 m (iv) No 8. (b) (ii) 7.38 MeV (c) (i) 4.48 x104 s (ii) 2.39 x1013 nuclei (iii) 6.94 x107 decays per second
6 SF026 SESSION 2014/2015 Answer any six questions. 1 (a) (i) What is meant by electric field strength at a point in an electric field? (ii) Define time constant in a capacitive circuit during discharging. [2 marks] (b) FIGURE 1 shows a charged ball floating vertically above another charged ball at an equilibrium distance d apart in a test tube. (i) Sketch the forces acting on the floating ball. (ii) What is the type of charge on the balls? (iii) If the charge on each ball is tripled, determine the new equilibrium distance between the balls in terms of d. [5 marks] (c) FIGURE 2 shows two parallel plate capacitors C1 and C2 connected in series and fully charged by a 6 V battery. The capacitors have the same plate area and are filled with similar dielectric material. The distance of separation of the plates for C1 and C2 are 2 mm and 4 mm respectively. (i) Sketch and label the electric field lines and equipotential surfaces between the plates of capacitor. (ii) Calculate the potential difference across capacitor C2. (iii) Calculate the electric field strength in the region between the plates of capacitor C1. [8 marks] d FIGURE 1 C1 C2 FIGURE 2 6 V
7 2 (a) FIGURE 3 shows some of the free electron inside a section of a cylindrical copper wire. The wire is connected to an emf source, and the direction of the electric field, E is as indicated in figure. (i) Sketch a diagram to show the motion of one free electron, the directions of drift velocity and the current. (ii) If the current in the wire is 50 mA, calculate the number of electrons passing a point in 10 s. [5 marks] (b) A battery has an emf of 9 V. The terminal voltage is 8 V when the battery is connected across a resistor of 5 . Calculate the (i) current through the resistor. (ii) power dissipated by the resistor. (iii) internal resistance of the battery. [3 marks] By referring to FIGURE 4, determine (i) I1, I2 and I3. (ii) the potential difference across the 18 resistor. [7 marks] 3 (a) Sketch the magnetic field lines for a current-carrying (i) straight wire. (ii) solenoid. [2 marks] (b) A two turns circular coil was made from a 3 m long wire. Calculate the magnetic field strength at the center of the coil if it carries 0.5 A current. [3 marks] E FIGURE 3 25 16 18 18 V 12 V I1 I2 I3 FIGURE 4
8 (c) FIGURE 5 shows two wires separated by 12 cm carrying currents of 3.5 A in opposite directions. (i) Determine the direction and magnitude of the net magnetic field at a point midway between the wires. (ii) Calculate the magnitude of the net force per unit length experienced by the wires. [6 marks] (d) FIGURE 6 shows an electron travelling in a region of uniform electric and magnetic fields which are perpendicular to one another. The strength of electric field and magnetic field are 3.9 104 V m1 and 6.5 102 T respectively. (i) Calculate the velocity of electron. (ii) Calculate the kinetic energy of electron. (iii) If the electric field is removed, determine the magnitude and direction of the magnetic force on the electron. [4 marks] 4 (a) (i) Define magnetic flux. (ii) A 0.2 T magnetic field is directed parallel to the plane of a circular loop of radius 0.2 m. Calculate the magnetic flux through the loop. [3 marks] (b) (i) A coil of 100 turns and area 0.5 cm2 is placed in changing magnetic field. The rate of change of magnetic field is 1.08 T s-1 . Calculate the induced emf in the coil. (ii) A coil of N turns with an area 6.8 10-2 m2 is rotating at frequency 90 Hz in a uniform magnetic field 0.28 T. If the maximum induced emf in the coil is 128.5 V, calculate the value of N. [5 marks] 3.5 A 3.5 A 12 cm FIGURE 5 FIGURE 6
9 (c) A solenoid of radius 5 cm has 200 turns and length of 15 cm. Calculate the (i) inductance. (ii) rate at which current must change for it to produce an induced emf of 50 mV. [4 marks] (d) Two coaxial coils are wound around the same cylindrical core. The primary coil has 350 turns and the secondary coil has 200 turns. When the current in the primary coil is 6.5 A, the average flux through each turn of the secondary coil is 0.018 Wb. Calculate the (i) mutual inductance of the pair of coils. (ii) average flux through each turn of the primary coil when the current in the secondary coil is 1.5 A. [3 marks] 5 (a) An RL series circuit with a 0.056 H inductor and 250 resistor is connected with a source of peak voltage 240 V at the frequency 200 Hz. Calculate the (i) inductive reactance of the circuit. (ii) impedance of the circuit. (iii) power factor for this circuit. (iv) rms voltage of the source. (v) average power delivered by the source. [6 marks] (b) An RLC circuit consists of a 40 resistor, a 22 mH inductor and a 400 nF capacitor connected in series to the AC source which has a peak voltage of 100 mV and a frequency of 1.6 kHz. (i) Calculate the capacitive reactance. (ii) Calculate the rms current. (iii) Determine the phase angle. (iv) Sketch the phasor diagram to represent the voltages across the components and the source. [9 marks] 6 (a) (i) Write the lens maker equation and explain the sign convention used for the radii of curvatures. (ii) FIGURE 7 shows a converging lens made of material with refractive index 2.26. One of the surface of the lens is plane and the other has a radius of curvature of 14.5 cm. Determine the focal length of the lens. [4 marks] FIGURE 7
10 (b) A diverging lens has a focal length f. An object is placed at position 2f from the lens. Sketch a labelled ray diagram to determine the characteristics of the image. [5 marks] A double–slit patent is viewed on a screen 1 m from the slits. If the third order minimum are 20 cm apart, determine the (i) ratio of wavelength to separation between the slits. (ii) distance between the first order minimum and third order maximum on the screen. [6 marks] 7 (a) Calculate the number of photon per second in a red laser beam with wavelength 700nm and 1 mW power. [3 marks] (b) State TWO (2) features of the photoelectron which cannot be explained using the classical theory in a photoelectric experiment. [2 marks] (c) When light of wavelength 400 nm falls on a lithium surface in a photoelectric experiment, electrons having a maximum kinetic energy of 0.8 eV are emitted. Calculate the (i) energy of the incident photons (in eV). (ii) maximum speed of the electrons. (iii) stopping potential of the surface. (iv) work function of lithium (in eV). (v) threshold frequency of lithium. [7 marks] (d) (i) State the de Broglie relation for momentum of a particle with its associated wavelength. (ii) An athlete of mass 65 kg takes 12 s to finish a 100m race in a spot event. Calculate the de Broglie wavelength of the athlete. [3 marks] 8 (a) Iodine-131 is among the radioactive isotopes leaked from the crippled Fukushima Daiichi Nuclear Power Plant after 2011 Tohoku earthquake and tsunami in Japan. The half-life of the iodine-131 nuclei, calculate the (i) decay constant. (ii) initial activity. (iii) activity after 20 days. [5 marks] (b) * A nuclear reaction is represented by the following equation 21 4 24 1 10 2 12 0 Ne He Mg n Given the following information: 21 10 4 2 24 12 20.993849 4.002603 23.985042 Ne u He u Mg u
11 (i) Explain whether the reaction is a fusion or fission reaction. (ii) Calculate the mass defect. (iii) Calculate the energy released in the reaction. [5 marks] (c) * The energy radiated by the Sun is from the fusion reaction of deuterium atoms. (i) Explain why the fusion of deuterium atom happens in the Sun but not on the Earth. (ii) Write an equation to represent the fusion of deuterium atom. [5 marks] ANSWERS: SF026 SESSION 2014/2015 1. (b) (iii) 3d (c) (ii) 4V (iii) 1000 V m−1 2. (a) (ii) 3.12 x 1018 electron (b) (i) 1.6 A (ii) 12.8 W (iii) 0.625 (c) (i) 0.146 A, 0.521 A, 0.667 A (ii) 12 V 3. (b) 2.63 x10-6 T (c) (i) 2.35 x10-5 T(into the page) (ii) 5 1 2 04 10 N m . (d) (i) 6.00x105 m s-1 (ii) 1.64 x10-19 J (iii) 6.24 x 10-15 N (to the left) 4. (a) (ii) 0 Wb (b) (i) -5.4x 10-3 V (ii) 12 turns (c) (i) 2.63 x10-3 H (ii) −19.0 A s−1 (d) (i) 0.554 H (ii) 0.00237 Wb 5. (a) (i) 70.4 (ii) 260 (iii) 0.962 (iv) 170 V (v) 107 W (b) (i) 249 (ii) 1.45 x10-3 A (iii) 35 6. (a) (ii) 11.5 cm (b) virtual, upright, diminished (c) (i) 0.0286 (ii) 0.0429 m 7. (a) 3.52 x1015 photons per second (c) (i) 3.11 eV (ii) 5.30 x 105 m s-1 (iii) 0.8 V (iv) 2.31 eV (v) 5.58 x1014 Hz (d) (ii) 1.22 x 10-36 m 8. (a) (i) 1.00 x 10-6 s -1 (ii) 3.00 x1010 Bq (iii) 5.33 x 109 Bq (b) (i) fission (ii) 2.75 x 10-3 u (iii) 2.56 MeV
12 SF026 SESSION 2015/2016 Answer any six questions. 1 (a) Define (i) electric field. (ii) electric potential. [2 marks] (b) FIGURE 1 shows two charges +50 C and −20 C separated by 0.8 m. Determine the (i) electric field at point A due to the negative charge. (ii) electric potential at point A. (iii) external work required to bring a +2 C charge from infinity to point A. [8 marks] (c) A parallel plate capacitor of 47 F is charged by a 12 V battery. The battery is disconnected after the capacitor is fully charged. (i) Calculate the charge on the plate. (ii) What will happen to the potential difference between the plates if the distance between plates is doubled? Justify your answer. [5 marks] 2 (a) FIGURE 2 shows a tungsten wire connected to a battery with internal resistance r. At room temperature of 23C, the readings of voltmeter and ammeter are 8.74 V and 437 FIGURE 1 FIGURE 2
13 mA respectively. After the tungsten is heated to 190C, the voltmeter reading is 8.85 V and the ammeter reading is 253 mA. Calculate the (i) emf and internal resistance of the battery. (ii) temperature coefficient of resistivity of tungsten wire. [8 marks] (b) FIGURE 3 shows four identical bulbs connected to a 6 V battery and a switch. When the switch is off, the ammeter reading is 0.5 A. (i) Calculate the resistance of the bulb. (ii) What happen to the reading of the ammeter when the switch is on? Explain your answer. [7 marks] 3 (a) A negative particle is moving at velocity v enters a region of uniform magnetic field B which is perpendicular to the particle’s velocity. What happens to the velocity and kinetic energy of the particle? Explain your answer. [4 marks] (b) FIGURE 4 shows a rectangular current-carrying wire loop which is free to rotate about a vertical axis in a uniform magnetic field of 1.42 T. The current in the loop is 250 mA. FIGURE 3 FIGURE 4
14 (i) Determine the magnetic force exerted on a-b. (ii) The rectangular wire is rotated by 90 about the axis shown in FIGURE 4. At this position, what is the magnetic force on a-b? Explain your answer. [5 marks] (c) Two long straight parallel wires are placed 0.2 m apart. Each wire carries a current of 1.5 A in the same direction. (i) Calculate the magnitude of the force per unit length on the wires. (ii) What is magnetic field at a point midway between the wires? Justify your answer. (iii) What happen to the force on the wire if each wire carries the same current but in opposite direction? [6 marks] 4 (a) A bar magnet is hanging by a string as shown in FIGURE 5. When the magnet is swung towards the coil, the galvanometer needle deflects to the right. (i) Why the galvanometer needle deflects? (ii) What happen to the galvanometer when the magnet moves away from the coil? State the law to explain this phenomenon. (iii) If the magnet is static but the coil is brought towards the magnet, what will happen to the galvanometer? [5 marks] (b) A rectangular coil of 250 turns and size 20 cm 30 cm rotates at a constant angular velocity of 500 rpm in a uniform magnetic field of 40 mT. (i) Calculate the maximum magnetic flux through the coil. (ii) Calculate the voltage produced by the coil when coil makes an angle 30 with the magnetic field. (iii) What is the maximum voltage produced by the coil? [5 marks] The current flowing through a solenoid changes from 1.75 A to 3.00 A within 1.25 ms. The back emf induced across the solenoid due to this change is 6 V. (i) Calculate the self-inductance of solenoid. FIGURE 5
15 (ii) If the length of the solenoid is 25 cm and the cross-sectional area is 40 cm2 , calculate the number of turns of the solenoid. [5 marks] 5 (a) FIGURE 6 shows a graph of alternating current through a 220 resistor. (i) Calculate the rms current through the resistor. (ii) Calculate the peak voltage across the resistor. (iii) State the equation of voltage across the resistor. (iv) Calculate the average power dissipated by the resistor. [7 marks] (b) A sinusoidal voltage V(t) = 20 sin (50t) is applied to a series RLC circuit with R = 670 , L = 250 mH and C = 47 F. (i) Calculate the impedance of the circuit. (ii) Calculate the phase angle of the circuit. (iii) The frequency of AC source is adjusted until it draws maximum current. Calculate the frequency of AC source at this instant. (iv) When the frequency of AC source is adjusted, does it change the power dissipated by the circuit? [8 marks] 6 (a) An image of 15 cm height is formed 24 cm behind the convex lens as shown in FIGURE 7. The origin of the image is from an object of 5 cm height located in front of a convex lens. Calculate the (i) object distance. FIGURE 6 FIGURE 7
16 (ii) focal length of the lens. [4 marks] (b) An object placed 10 cm in front of curved mirror produced an image 5 cm behind the mirror. Calculate the focal length of the mirror and state the type of the mirror. [3 marks] (c) White light is incident on a soap film of refractive index 1.33 in air. The reflected light looks bluish because the red light of wavelength 670 nm is absent in the reflection. (i) Does the light change phase when it reflects at air-film interface? Explain your answer. (ii) Does the light change phase when it travels in film and reflects at film-air interface? (iii) What happen to the wavelength and frequency of light when it travels from air to the film? (iv) Determine the minimum thickness of the soap film. [8 marks] 7 (a) FIGURE 8 shows a photocell connected to a battery, ammeter, voltmeter and rheostat. The photocell is exposed to a monochromatic light of wavelength 275 nm. Initially, the reading of voltmeter is zero and the reading of ammeter is 5 nA. The rheostat is adjusted until the ammeter reading reaches zero and the voltmeter reading is 0.3 V. (i) Sketch a graph of current flow in the circuit against the voltage across the photocell. (ii) Calculate the work function of the photocell in eV. (iii) Calculate the threshold frequency of the photocell. (iv) The photocell is then exposed to monochromatic light of wavelength 320 nm. What is the ammeter reading? Explain your answer. [10 marks] FIGURE 8
17 (b) In Davisson-Germer experiment, an electron is accelerated from rest through a potential difference of 2500 V and the diffraction pattern is observed on the tube screen. (i) Calculate the de Broglie wavelength of electron. (ii) Calculate the momentum of electron. (iii) If the potential difference is increased up to 3000 V, what happen to the diffraction pattern? Explain your answer. [5 marks] 8 (a) (i) Define binding energy. (ii) Calculate the energy needed to remove a neutron from C 13 6 . Given: mass of C 12 6 = 12.000 000 u and C 13 6 = 12.003355 u. [5 marks] (b) (i) * State two (2) differences between fusion and fission reactions. (ii) * Explain the proton-proton cycle that sustains the energy released by the sun. (iii) * The nuclear reaction is represented by the following fission reaction: U n Kr Ba 3 n 1 0 144 56 89 36 1 0 235 92 Total mass before the reaction is 236.0526 u. Total mass after the reaction is 235.8373 u. Calculate the energy released in MeV. [6 marks] (c) The activity of a radioactive source decreases by 5% in 28 hours. Calculate the halflife of the source. [4 marks] ANSWERS: SF026 SESSION 2015/2016 1. (b) (i) 7.2 X 105 NC-1 (upwards) (ii) 1.17 X105 V (iii) 0.234 J (c) (i) 5.64 X 10-4 C 2. (a) (i) 9 V, 0.6 (ii) 0.0045 K-1 (b) (i) 8 3. (b) (i) 0.071 N (downward) (ii) 0 N (c) (i) 2.25 x 10-6 Nm-1 (ii) 0 T 4. (b) (i) 0.0024 Wb (ii) 27.2 V (iii) 31.42 V (c) (i) −0.006 H (ii) 546 turns 5. (a) (i) 42 mA (ii) 13.2 V (iv) 0.4 W (b) (i) 677 (ii) 8.17 (iii) 46.4 Hz 6. (a) (i) 8 cm (ii) 6 cm (b) −10 cm (convex/diverging) (c) (iv) 252 nm 7. (a) (ii) 4.22 eV (iii) 1.02 x 1015 Hz (iv) 0 A (b) (i) 2.46 x 10-11 m (ii) 2.7 x 10-23 kg m s-1 8. (a) (ii) 4.95 MeV (b) (iii) 201 MeV (c) 378.4 hours
18 SF026 SESSION 2016/2017 Answer any six questions. 1. (a) (i) The strength of a uniform electric field is 200 V m. What is meant by the statement? (ii) Sketch a diagram to show the equipotential lines and electric field lines of an isolated positive charge. [3 marks] (b) FIGURE 1.1 shows three point charges placed at each vertices of a right angle triangle. Calculate the (i) electric potential at point P. (ii) electric potential energy of the system. [6 marks] (c) FIGURE 1.2 shows two fully discharged capacitors, 25 F and 50 uF are connected in series with a 15 kΩ resistor. The capacitors are charged when switch S is closed at X. (i) What is the time constant of the charging circuit? (ii) Switch S is closed at Y after the capacitors are fully charged. What is the initial current in the circuit? [6 marks] 2 (a) State Ohm’s law. [2 marks]
19 (b) (i) You are given several 1 kΩ resistors. How do you connect the resistors to a circuit that requires a 500 Ω resistance? Show your suggestion. (ii) FIGURE 2.1 shows a circuit consisting of two batteries, two resistors and an ammeter. If the ammeter has internal resistance of 5.0 Ω, what is the reading shown by the ammeter? [7 marks] (c) FIGURE 2.2 shows a potentiometer circuit consists of a uniform wire XY of length 100 cm and its resistance 5.0Ω. The emf of cell A and B is 4.0 V and 3.0 V, respectively. The internal resistance of both cells are negligible. (i) What is the length of XP when the galvanometer reading is zero? (ii) If a 1.0Ω resistor is connected in series with cell A, what is the new balanced length XP'? [6 marks] 3 (a)
20 Two protons P and Q move with the same speed vp= vQ a uniform magnetic field B. At a certain moment, the directions of their velocities are as shown in FIGURE 3.1. Describe the subsequent motion of each proton. Justify your answer. [4 marks] (b) A beam of hydrogen ions contains isotopes H 1 1 and H 2 1 . The beam enters a velocity selector which consists of a 0.20 T magnetic field and a 2.5 x 10Vm-1 electric field. Ions that emerge from the velocity selector enter a region of a 0.30 T uniform magnetic fields. After leaving the velocity selector, calculate the (i) velocity of the ions. (ii) radius of the semi circular path of each ion. Given the mass of H 1 1 and H 2 1 are 1.67 x 10 kg and 3.34 x 10 kg respectively. [5 marks] (c) FIGURE 3.2 A rectangular loop ABCD with dimensions of 8.0 cm x 3.0 cm is carrying a current of 1.5 A, The loop lies horizontally on a table beside a long wire carrying a current of 22 A as shown in FIGURE 3.2. Due to the current in the wire, determine the magnitude and direction of (i) magnetic flux densities on the loop segments AD and BC. (ii) magnetic forces on the loop segments AD and BC. [6 marks] 4 (a) State (i) Faraday's law of electromagnetic induction. (ii) Lenz’s law. [2 marks] (b) A coil of 60 turns and cross-sectional area 4.65 x 10 m is placed in a uniform magnetic field of 0.80 T. The plane of the coil is perpendicular to the field. (i) Calculate the total magnetic flux through the coil. (ii) Calculate the average induced emf generated in the coil if the magnetic field is reduced to zero in 0.50s. (iii) Sketch a diagram to show the direction of the induced current in the coil with respect to the direction of the magnetic field based on the condition in. Explain. [6 marks] (c) A 6.0 mH inductor and a switch are connected in series to a 15 V battery. The total resistance of the circuit is 8.0 Ω. When the switch is closed, calculate the (i) Initial rate of current change.
21 (ii) Final value of the current. (iii) Final energy stored in the inductor. [7 marks] 5 (a) Define alternating current (AC). [1 mark] (b) A 3.0 kgΩ resistor and an inductor are connected in series with a 12 V AC supply. The inductor’s reactance is 4.7 kΩ. (i) Calculate the impedance of the circuit. (ii) Find the rms current in the circuit. (iii) Sketch a phasor diagram to show the voltages across the resistor VR and the inductor VL, and the supply voltage V. [6 marks] (c) An electric motor is connected to a 230 V, 50 Hz AC supply. The motor has a resistance of 15 Ω and an inductive reactance of 27 Ω. Calculate the (i) power factor of the system. (ii) average power. (iii) the value of capacitor to be added in series with the motor so that the power factor is 1. [8 marks] 6 (a) (i) State the laws of reflection. (ii) Explain the meaning of interference. (iii) When do two waves are said to be coherent? [4 marks] (b) An object is 20 cm from a convex lens of focal length 12 cm. Calculate the image distance and magnification of the image formed by the lens. [3 marks] (c) A beam consists of two monochromatic lights 400 nm and 600 nm, is incident normally on a diffraction grating which has 540 lines mm. Calculate the (i) angular separation between the first-order diffraction of the lights. (ii) highest order of diffraction that can be observed with the 600 nm light. [8 marks] 7 (a) The energy of a photon and the kinetic energy of an electron is the same in vacuum, that is 6.0 eV. (i) What is the velocity and the wavelength of the photon? (ii) Obtain the wavelength associated with the electron. [8 marks] (b) Light of wavelength 500 nm is used in a photoelectric experiment with caesium photocell. The work function of caesium is 2.14 eV. Calculate the (i) threshold frequency of caesium. (ii) maximum kinetic energy of the photoelectrons in Joule. (iii) stopping potential. [7 marks] 8 (a) (i) * Define isotopes. (ii) Name the constituents and their numbers in C 14 6 .
22 [4 marks] (b) * A foil of beryllium-9 ( Be 9 4 ) is irradiated with alpha particles. The process produces carbon-12 and emits an intense radiation. Atomic masses of He 4 2 , Be 9 4 and C 12 6 are 4.00260 u, 9.01212 u and 12.00000 u, respectively. (i) Write the equation for the reaction and state the type of the radiation. (ii) Calculate the mass difference of the reaction in atomic mass unit. (iii) Find the energy equivalent of the lost mass in MeV. [6 marks] (c) 8 days after its preparation, the activity of a sample of radioisotope was 540 decays per second. The activity further reduced to 200 decays per second after 14 days from the date of preparation. Calculate the (i) decay constant. (ii) half-life of the radioisotope. [5 marks] ANSWERS: SF026 SESSION 2016/2017 1. (b)(i) 3.9 x 108 V (ii) -1.40 x 106 J (c)(i) 0.25 s (ii) 5.33 x 10-4 A 2. (b)(i) 500 Ω (ii) 0.16 A (c)(i) 75 cm (ii) 90 cm 3. (b)(i) 1.25x106 m s-1 (ii) 0.043 m 0.086 m (c)(i) 8.8x10-4 T into the page, 5.2x10-5 into the page (ii) 3.96 x10-5 N to the left, 2.33 x 10-6 to the right 4. (b)(i) 0.022 Wb (ii) 0.044 V (c)(i) 2.5x103 A s-1 (ii) 1.875 A (iii) 1.055 x 10-2 J 5. (b)(i) 5.58 kΩ (ii) 2.15 mA (c)(i) 0.486 (ii) 832 W (iii) 1.18 x10-4 F 6. (b) 30 cm, -1.5 (c)(i) 6.43° (ii) 3 7. (a)(i) 3x108 m s-1 , 207 nm (ii) 5.01x10-10 m (b)(i) 5.16 x 1014 Hz (ii) 5.54x10-20 J (iii) 0.35 V 8. (b)(ii) 6.055x10-3 u (iii) 5.64 MeV (c)(i) 0.166 day-1 (ii) 4.18 days
23 SF026 SESSION 2017/2018 Answer any six questions. 1 (a) Define (i) Coulomb’s law. (ii) capacitance. [2 marks] (b) FIGURE 1.1 FIGURE 1.1 FIGURE 1.1 shows charges, Q1 = +5μC, Q2 = -4μC and Q3 = +4μC in x-y plane. Determine the magnitude and direction of the net electric force on Q3. [7 marks] (c) FIGURE 1.2 An electron enters a region of uniform electric field E as in FIGURE 1.2. If the magnitude of electric field is 200 N C-1 , calculate the acceleration of the electron. [3 marks] (d) FIGURE 1.3 FIGURE 1.3 shows a circuit consists of four capacitors. Calculate the equivalent capacitance between terminals a and b.
24 [3 marks] 2 (a) Explain the effect of temperature on the electrical resistance of metals. [2 marks] (b) The resistivity of a copper wire is 1.72 x 10-8 Ω m. An electric current of 2.07 A flows in the wire. If the wire has cross-sectional area of 8.0 x 10-7 m2 and length of 50 m, calculate the (i) resistance of the wire. (ii) potential difference across the wire. (iii) energy dissipated in 1 minute. [7 marks] (c) FIGURE 2 Determine I1, I2 and I3 in FIGURE 2. [6 marks] 3 (a) (i) Define magnetic field. (iii) Sketch the magnetic field lines surrounding a current carrying loop. [3 marks] (b) FIGURE 3.1 FIGURE 3.1 shows a positively charged ion passes the velocity selector, where a magnetic field of 100 mT is perpendicular to an electric field of 1.0 kV m-1 . A magnetic field of equal magnitude is used to deflect the ion in a circular path with a radius of 15 mm in the deflection chamber. Calculate the
25 (i) velocity of the ion. (ii) mass of the ion. [4 marks] (c) FIGURE 3.2 FIGURE 3.2 FIGURE 3.2 shows two long straight parallel wires that are 1.0 m apart and carry currents I1 = 6.0 A and I2. (i) Calculate the magnitude and direction of I2 for the net magnetic field at P to be zero. (ii) Based on anwer in 3(c)(i), calculate the magnitude and direction of the net magnetic field at Q. [8 marks] 4 (a) State Faraday’s law. [1 mark] (b) FIGURE 4.1 A long straight wire carrying current, I is placed near a coil as in FIGURE 4.1. (i) If I is decreasing in magnitude, determine the direction of the induced current and the direction of the induced magnetic field in the coil. (ii) If I is constant in magnitude, give two (2) ways to induce current in the coil. [4 marks]
26 (c) FIGURE 4.2 FIGURE 4.2 shows a conductor of length L = 0.065 m moves perpendicularly in a uniform magnetic field of 1.20 T. The emf induced in the conductor is 0.32 V. (i) Calculate the speed of the conductor. (ii) If the total circuit resistance is 0.8 Ω, determine the magnitude and direction of the induced current. [5 marks] (d) A solenoid of inductance 7.3 mH has 450 turns and length 24 cm. Determine the (i) cross-sectional area of the solenoid. (ii) induced emf in the solenoid if its current drops from 3.2 A to zero in 55 ms. [5 marks] 5 (a) (i) Give two (2) characteristics of a series RLC alternating current circuit at resonance. (ii) If the frequency in an AC circuit is increasing, what happens to the resistance, capacitive reactance and inductive reactance? [5 marks] (b) An RLC circuit with resistance 160 Ω, capacitance 15 μF, inductance 230 mH, frequency 60 Hz and peak voltage 36 V. Calculate the (i) impedance. (ii) phase angle between the current and the voltage. (iii) rms current. (iv) average power dissipated in the resistor. [10 marks] 6 (a) State Huygens’s principle. [1 mark] (b) An object is placed in front of a concave mirror with 25 cm radius of curvature. A real image twice the size of the object is formed. (i) Sketch a ray diagram to illustrate the formation of the image. (ii) Determine the object distance from the mirror. [7 marks] (c) FIGURE 6
27 FIGURE 6 shows a flint glass lens of refractive index 1.61 is coated with a thin layer film of magnetism fluoride of refractive index 1.38. A ray of light of wavelength 565 nm is incident at right angles to the film. (i) Sketch the light rays that interfere after being reflected from both surfaces of the film. Label the reflected ray(s) that undergo phase change. (ii) What minimum thickness should the magnesium fluoride film have if the reflection of the 565 nm light is to appear dark? (iii) If a lens is used to suppress the reflection of light at high frequencies. What should be done to the thickness of the film? Explain your answer. [7 marks] 7 (a) State (i) The Planck’s hypothesis of light. (ii) The duality of light. [2 marks] (b) One of the advantages of an electron microscopes is that we can see much finer details than an optical microscopes. Explain how this is possible. [2 marks] (c) When a monochromatic light of frequency 7.90 x 1014 Hz incidents upon a metal surface, the stopping potential needed to terminate the emission of photoelectrons is 0.2 V. Calculate the (i) work function of the metal. (ii) threshold frequency of the metal. [7 marks] (e) The power of He-Ne laser is 7.5 mW and produces light of wavelength 633 nm. How many photons are emitted by the laser for 5 minutes? [4 marks] 8 (a) Sketch the graph of binding energy per nucleon against nucleon number. Label the regions for possible nuclear fission and fusion on the graph. [2 marks] (b) A sample of radioactive nuclide Pt 199 has an initial activity of 7.56 x 1011 Bq. (i) After 92.4 minutes, the activity has decreased to 9.45 x 1010 Bq. Calculate the half-life of the nuclide. (ii) How many radioactive nuclei were initially present in the sample? (1 Bq = 1 decay per second) [6 marks] (c) (i) * Describe the operating principle of a nuclear fission reactor. (ii) * In a nuclear reaction, when a nuclide Li 7 3 is bombarded by a proton, two alpha particles He 4 2 are produced. The reaction is given by H Li He He 4 2 4 2 7 3 1 1 Given the mass of H 1 1 is 1.007825 u, the mass of Li 7 3 is 7.016004 u and the mass of He 4 2 is 4.002603 u. Calculate the energy released in MeV.
28 ANSWERS: SF026 SESSION 2017/2018 1. (b) 1.38 N, 32.880 (c) 3.52 x 1013 m s-2 (d) 8.23 μF 2. (b)(i) 1.075Ω (ii) 2.23 V (iii) 276 J (c)(i) I1 = -2 A, I2 = 4 A, I3 = -6A 3. (b)(i) 1x104 m s-1 (ii) 2.4x10-26 kg (c)(i) 2A, out of the page (ii) 2.13 x 10-6 T, to the right (upward) 4. (c)(i) 4.10 m s-1 (ii) 0.4 A (d)(i) 6.88 x 10-3 m2 (ii) 0.42 V 5. (b)(i) 183.62 Ω (ii) 29.380 (iii) 0.138 A (iv) 3.06 W 6. (b)(ii) 18.75 cm (c)(ii) 1.02 x10-7 m 7. (c)(i) 4.92 x 10-19 J (ii) 7.42 x 1014 Hz (d) 7.16 x 1018 8. (b)(i) 1848 s (ii) 2.016 x1015 (c)(ii) 17.35 MeV
29 SP025 SESSION 2018/2019 1 FIGURE 1 FIGURE 1 shows two charges, Q1 = +8 µC and Q2 = -6 µC placed 4 m apart. (a) Calculate the electric potential at points A and B. [4 marks] (b) Calculate electric potential difference between points A and B. [1 mark] (c) Determine the electric field at point A. [8 marks] 2 FIGURE 2 FIGURE 2 shows three capacitors C1, C2 and C3, each 12 µF connected between points A and B. (a) Calculate the effective capacitance. [3 marks] (b) If the potential difference across AB is 9 V, calculate the stored energy. [1 mark] 3 (a) Calculate the number of electrons that flow in a wire if it carries a current of 2 A for 5 s. [3 marks] (b) A 2.5 kW heater is connected to a 220 V power supply. (i) Calculate the current and resistance in the heater. (ii)The coil of heater is made from a wire of cross-sectional area 2x10-7 m2 and resistivity 1.1x10-6 Ω m. Calculate the length of the wire. (iii) The voltage of the power supply is then changed to 110 V. Calculate the new power output of the heater. [7 marks]
30 (c) FIGURE 3 FIGURE 3 shows a circuit with a battery having an emf of 12 V and an internal resistance of 0.2 Ω connected in series to two resistors, 3.3 Ω and 2.0 Ω. (i) Calculate the current in the circuit. (ii)Calculate the terminal voltage across the battery. [5 marks] 4 (a) FIGURE 4.1 FIGURE 4.1 shows the Earth’s magnetic field of 1.8x10 -4 T normal to an aluminium frame of dimensions 60 cm x 85 cm. (i) Calculate the magnetic flux through the frame. (ii)The frame is flipped so that it is parallel to the Earth’s magnetic field in 0.2 s. Calculate the induced emf. [6 marks] (b) FIGURE 4.2
31 FIGURE 4.2 shows 0.6 m long metal bar being pulled to the right at a steady speed of 5.7 m s-1 perpendicular to a uniform 0.7 T magnetic field. The metal rails are connected to a 5 Ω resistor. (i) Calculate the magnitude of the emf induced in the circuit. (ii)Calculate the current through the resistor and its direction in the metal bar. [4 marks] (c) A solenoid of length 8x10-2 m and cross-sectional area 5x10-5 m-2 contains 6500 turns per meter length. Calculate the self-inductance of the solenoid. [3 marks] 5 (a) FIGURE 5 FIGURE 5 shows an AC source with a voltage of V = 200 sin ωt connected to a 100 Ω resistor. Calculate the (i) rms voltage. (ii) rms current in the resistor. (iii) average power delivered to the circuit. [5 marks] (b) A series RLC circuit consisting of 35 mH inductor, 45 µF capacitor and 85 Ω resistor is connected to an AC generator of 150 V, 60 Hz. Calculate the (i) capacitive reactance. (ii)inductive reactance. (iii) impedance. (iv) phase angle. [8 marks] 6. (a) An external side mirror of a car is convex with a radius of curvature 18 m. Determine the location of the image for an object 10 m from the mirror. [3 marks]
32 (b) FIGURE 6 FIGURE 6 shows an object embedded in a solid glass with a hemispherical end of radius 30 cm and refractive index 1.50. The object is 40 cm inside the glass. Calculate the image distance. Refractive index of air is 1. [2 marks] (c) A 2 cm height object is placed 7 cm from a concave mirror whose radius of curvature is 12 cm. Determine the (i) image distance. (ii)image height. (iii) two (2) characteristics of the image. [7 marks] 7 (a) Orange light of wavelength 600 nm is incident normal to a diffraction grating having 3500 lines per cm. (i) Calculate the slit separation. (ii) Determine the maximum number of bright fringes that can be observed. (iii) How can the number of bright fringes be increased? [5 marks] (b) FIGURE 7 FIGURE 7 shows two paths of coherent lights from point A and B that produce an interference pattern at point C. Determine whether it is a constructive or destructive interference if AC and BC are 2.2λ and 5.7λ respectively. [3 marks] (c) Calculate the thickness of a soap film so that a 600 nm light incident to the film would produce constructive interference. Index of refraction of soap film is 1.33. [4 marks]
33 8 In a photoelectric effect experiment, light of frequency 1.15x1015 Hz strikes a metal surface and electrons are emitted immediately. The work function of the metal is 2.3 Ev. Calculate the (a) threshold frequency of the metal. [2 marks] (b) maximum kinetic energy of the photoelectrons. [2 marks] (c) stopping potential of the photoelectrons. [2 marks] 9 (a) Calculate the speed of a neutron with de Broglie wavelength 9x10-11 m. [2 marks] (b) Calculate the wavelength of an electron that has been accelerated across a potential difference of 100 V. [2 marks] 10 (a) * A nuclear reaction can be written as: N H C He 4 2 12 6 2 1 14 7 Calculate the energy released (MeV) in the reaction. Given [4 marks] (b) A 2 g sample of radioactive iodine I 131 53 has a half-life of 8 days. (i) Calculate the decay constant. (ii) Calculate the initial number of atoms in the 2 g sample. (iii) Calculate the activity of the sample after 2 days. [4 marks] ANSWERS: SP025 SESSION 2018/2019 1. (a) 1.32 X 10 4 V, -1.09 X 10 4 V (b) -2.41 X 10 4 V (c) 6.92 X 10 3 NC-1 , -75.5 OC 2. (a) 8μF (b) 3.24 X 10 -4 J 3. (a) 6.25 X 10 19 (b)(i) 11.4 A, 19.4 Ω (ii) 3.5 m (iii) 624/627 W (c)(i) 2.2 A (ii) 11.6 V 4. (a)(i) 9.18 X 10 -5 Wb (ii) 4.59 X 10 -4 V (b)(i) 2.4 V (ii) 0.48 A (downward/clockwise) (c) 2.12 x 10 -4 H
34 5. (a)(i) 141 V (ii) 1.4 A (iii) 196 W (b)(i) 59 Ω (ii)13 Ω (iii) 97 Ω (iv) -28.4 o 6. (a) -4.7 m (b) -0.48 m (c)(i) 42 cm (ii) 12 cm (iii) bigger, inverted, real 7. (a)(i) 2.86 x 10 -6 m (ii) 9 (iii) decrease wavelength/number of lines per cm (b) destructive (c) 113 nm 8. (a) 5.55 x 10 14 Hz (b) 3.9 x 10 -19 J (c) 2.44 V 9. (a) 4.4 x 10 3 ms-1 (b) 1.2 x 10 -10 m 10. (b)(i) 8.66 x 10 -2 days -1 (ii) 9.19 x 10 21 atoms (iii) 7.75 x 10 15 decay/sec
35 SP025 SESSION 2019/2020 1 (a) FIGURE 1 (i) The electric field at a point 10 cm away from a charge P as in FIGURE 1 is Determine the charge of P. (ii) With reference to FIGURE 1, a charge Q is placed 10 cm away from charge P. When charge Q is moved horizontally to the right to a position 5 cm from its initial position, there is a 0.54 J change in its electric potential energy of the system. What is the charge of Q? (iii) Sketch the electric force vectors on charge P and Q. (iv) If charge Q is again moved horizontally to the right to a new position, and the electric force on it is – 4.05 N, how far apart is charge Q from charge P? [10 marks] (b) Two oppositely charged parallel plates are held 2 mm apart. A of work is needed to move a 2 µC point charge from one plate to the other. Calculate the electric field between the plates. [3 marks] 2 FIGURE 2 (a) The graph in FIGURE 2(a) shows how the charge, Q on a capacitor P changes with time, t when it is charged through a 20 Ω resistor. Determine the capacitance of capacitor P. (b) Capacitance P is then arranged as shown in FIGURE 2(b). Determine the effective capacitance. [4 marks]
36 3 (a) FIGURE 3.1 For the circuit in FIGURE 3.1, determine the (i) current I1, I2 and I3. (ii)number of electrons passing through the 9 Ω resistor in 2 s. (iii) power dissipated by the 5 Ω resistor. (iv) change in the resistance of the 2 Ω resistor when there is a 30 ℃ rise in its temperature. The temperature coefficient of resistivity of the resistor is [10 marks] (d) FIGURE 3.2 FIGURE 3.2 shows a potential divider circuit. (i) Calculate the output voltage. (ii)If a voltmeter of resistance 3000 Ω is connected across the output, determine the reading of the voltmeter. [5 marks] 4 (a) FIGURE 4.1
37 FIGURE 4.1 shows a rectangular wire loop 0.3 m x 0.2 m moving horizontally to the right at 12 m s-1 in a uniform magnetic field of 0.8 T. The induced current in the wire is 3 A. (i) Determine the resistance of the wire loop. (ii)Determine the direction of the induced current. Explain how you determine the direction of the induced current. [4 marks] (b) FIGURE 4.2 A 6 cm long solenoid with 400 turns and cross-sectional area experience a changing current as shown in graph in FIGURE 4.2. Determine the (i) Induced emf. (ii)Magnetic flux through each turn and the stored energy at the instant when the current is 3 A. [9 marks] 5 FIGURE 5 FIGURE 5 shows a phasor diagram of an RL series circuit connected to an AC source with rms voltage across the inductor of 62.8 V at 50 Hz, 0.8 H inductor and an unknown resistor. (a) Determine the (i) resistance of the resistor. (ii) peak voltage of the AC source. (iii) average power. [9 marks]
38 (b) If the resistor is removed from the circuit, draw the variation of current, I and voltage, V against time, t on the same labelled graph. [4 marks] 6. (a) An object is placed 15 cm in front of a mirror. The image formed by the mirror is upright and magnified 2 times. (i) Is the mirror convex or concave? Explain your answer. (ii) What is another characteristic of the image? Explain your answer. (iii) Determine the radius of curvature of the mirror. [7 marks] (b) FIGURE 6.1 FIGURE 6.1 shows a lens with radii of curvature of 15 cm and 50 cm, made of glass with refractive index 1.55. Determine the focal length and type of lens. [2 marks] (c) FIGURE 6.2 FIGURE 6.2 shows and object and a glass rod immersed in a liquid. The rod has a refractive index of 1.7 and radius of curvature 8.0 cm. If the object distance is 15 cm and the virtual image distance is 13 cm, determine the refractive index of the liquid. [3 marks] 7 (a) In a double slit experiment, the incident wavelength is 660 nm, the slit separation is 0.25 mm, and the screen is placed 90 cm away from the slits. (i) Calculate the distance from the second to the thrid destructive inteference fringe. (ii) The double-slits is now replaced with a diffraction grating. If the maximum number of bright fringes is 15, calculate the slit separation of the grating. [9 marks]
39 (b) A soap film with refractive index 1.3 and minimum thickness 0.177 µm appears reddish under white light. Calculate the wavelength of light that is missing from the reflection. [3 marks] 8 FIGURE 8 FIGURE 8 shows a graph of photoelectron maximum kinetic energy, Kmax against frequency of light, f from a photoelectric effect experiment. Calculate the (a) maximum speed of the photoelectron. (b) stopping potential. (c) threshold frequency. [6 marks] 9 A beam of electrons is accelerated through a potential difference of 4500 V in a Davisson and Germer experiment. (a) Calculate the de Broglie wavelength of the electrons. [2 marks] (b) Will the diffraction pattern become larger, remain unchanged or narrower when proton is used instead of electrons? Justify your answer. [2 marks] 10 (a) Calculate the binding energy per nucleon of a sodium nucleus in MeV nucleon-1 . The atomic mass of sodium is 22.989769 u. [4 marks] (b) Calculate the activity of a 5 µg which has a half-life of 14.9 hours. Note: PSPM 2 in this session was cancelled due to the outbreak of Covid-19.
40 SP025 SESSION 2020/2021 1 (a) FIGURE 1 FIGURE 1 shows three fixed point charges, Q1 = +12 nC, Q2 = +3 nC and Q3 = -4 nC. (i) Sketch the electric force diagram on the charge Q3. (ii) Calculate the total electric potential energy of the system. [4 marks] (b) A small ball with mass 25 g has a total charge of +20 μC is placed between two parallel charged plates. (i) In static equilibrium, determine the magnitude of the electric field in the plates. (ii) Calculate the acceleration of the ball if moves horizontally parallel with electric field. [6 marks] 2 An uncharged capacitor of 58 μF is connected in series with a resistor of 100 k. Then the capacitor starts charging through the resistor. Calculate the time required for the capacitor to reach 30% of its maximum charge. [3 marks] 3 (a) FIGURE 2 FIGURE 2 shows R1= 10 , R2 = 12 and R3 = 5 are connected to a 15 V power supply. Calculate the
41 (i) effective resistance. (ii) potential difference across R3. [7 marks] (b) FIGURE 3 FIGURE 3 shows a circuit consisting of two batteries and two resistors. Calculate the value of I3 and R3. [5 marks] 4 (a) A 14 turns circular coil is placed on a paper which lies in 1.2 T magnetic field pointing inwards to the paper. The coil's diameter changes from 22.5 cm to 7.2 cm in 1.8 s. (i) Determine the direction of the induced current. (ii) Calculate the magnitude of the emf induced in the circuit. (iii) Calculate the induced current if the circular coil resistance is 7.5 . [6 marks] (b) A circular coil of N turns with current 9.4 mA has an inductance 15 mH. Calculate the (i) magnetic flux linkage through the coil. (ii) radius of the coil if N= 420 turns. [4 marks] 5 (a) A series RLC circuit attached to a power supply of peak voltage 140 V with a power factor of 0.76. Given I=4.5 sin 20πt where I in A and t in s.. (i) Calculate the rms current in the circuit. (ii) Calculate the value of resistance. (iii) Determine the impedance. [6 marks] (b) An inductor is connected in series to an AC voltage supply of 30 V and frequency 60 Hz. Inductive reactance of the inductor is 98 . Calculate the (i) inductance. (ii) peak current. [4 marks]
42 6 (a) An orange is placed 25.2 cm in front of a diverging lens with a focal length of 18.0 cm. (i) Sketch the ray diagram to show the formation of the image. (ii) Determine the image distance. (iii) Determine the magnification. (iv) Determine two (2) characteristics of the image. [7 marks] (b) The convex meniscus lens has a 17 cm radius for the convex surface and 25 cm for the concave surface. The lens is made of glass with a refractive index, n= 1.52 in air. Refractive index of air is 1.0. Determine the focal length of the lens. [3 marks] 7 (a) Two narrow slits separated by 2.4 mm are illuminated by a light with λ = 512 nm. The screen is placed 6.5 m from the slits. Determine the (i) distance between adjacent bright fringes on a screen. (ii) distance of the fifth dark fringe from the central bright fringe. [5 marks] (b) A monochromatic light of wavelength 620 nm is incident on a single slit and forms a diffraction pattern on a screen 1.2 m away. The distance of seventh dark fringe from the central maximum is 18.0 mm. Determine the (i) size of the single slit. (ii) distance of the second bright fringe from the central maximum. [5 marks] 8 A photoelectric effect experiment was conducted using a metal of work function 1.5 eV and the stopping potential of 2.0 V. Calculate the (a) threshold wavelength. (b) maximum velocity of the photoelectrons. (c) wavelength of photons. [5 marks] 9 A particle is moving three times faster than proton. The ratio of the de Broglie's wavelength of the particle to the proton is 1.716 104 . Calculate the mass of particle. [3 marks] 10 (a) Calculate the binding energy per nucleon for Thallium, in MeV per nucleon. Given atomic mass Tl= 204.974401 u. [4 marks] (b) Radioactive nuclei has a half-life of 0.99 s. Determine the time taken for 25% of the nuclei to decay away. [3 marks]
43 ANSWERS: SP025 SESSION 2020/2021 1. (a)(ii) -4.48 10-6 J (b)(i) 1.23 104 V m-1 (ii) 9.81 m s-2 /13.88 m s-2 2. (a) 2.07 s 3. (a)(i) 13.53 (ii) 3.91 V (b) 6 A, 3 Ω 4. (a)(i) Clockwise direction (ii) 0.333 V (iii) 0.044 A (b)(i) 1.41 10-4 Wb (ii) 43.08 10-3 m 5. (a)(i) 3.18 A (ii) 23.66 (iii) 31.13 (b)(i) 0.26 H (ii) 0.433 A 6. (a)(ii) -10.5 cm (iii) 0.42 (iv)Virtual,upright,diminished (b) 102.2 cm 7. (a)(i) 1.39 10-3 m (ii) 6.24 10-3 m (b)(i) 2.89 10-4 m (ii) 6.44 10-3 m 8. (a) 8.29 10-7 m (b) 8.38 105 m s-1 (c) 3.55 10-7 m 9. 3.25 10-32 kg 10. (a) 7.88 MeV/nucleon (b) 0.41 s