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(a) Doping is the introduction of impurity atoms into a semicondoctor (b) Doping increases the conductivity of a semicondoctor by increasing the number of chargers or electron or holes.

The cathode ray tube components are: X = Filament or heater or cathode Y = Anode Z = Plates or deflectors.

(a) Net force is the effective or resultant force resulting from the actions of a system of forces on a body. (b) The principle ofconservation of linear momentum explains that in an isolated or closed system of colliding bodies the total linear momentum in a fixed direction remains constant, e.g. the recoil of gun, colliding trolleys, rocket propulsion, etc. (c) V\(_1^2\) = \(U_1^2 + 2gh_1\) = 0 + 2 x 10 x 2 = 40 \(V_1 = \sqrt{40}\) = 6.325m/s \(v_2^2 = u_2^2 - 2gh_2\) O = \(U^2_2\) - 2 x 10 x 1.8 u = \(\sqrt{36}\) = 6ms\(^{-1}\) Impulse Change in momentun mv\(_1\) - (-mu\(_2\)) = m (v\(_1\) + u\(_2\)) = 0.2(6.325 + 6.000) = 2.46 Ns (d) v = \(\omega \sqrt{r^2 - y^2}\) 2\(\pi\)f\(\sqrt{r^2 - y^2}\) 2 = 2 x 3.14 x 5 x \(\sqrt{r^2 - 0.1^2}\) r = 0.12m (ii) Vmax = \(\omega\)r = 2\(\pi\)fr = 2 x 3.142 x 5 x 0.12 = 3,77 m/s (iii) P.E = \(\frac{1}{2}m \omega^2e^2 = \times \frac{1}{2}m(2 \pi f)^2r^2\) = \(\frac{1}{2} \times 0.02(2 \times 3.142 \times 5)^2 \times (0.12)^2\) = 1.42 x 10\(^{-1}J\)

(a)(i) Thermal equilibrium is a condition in which two bodies in contact have no net flow of heat between them. (ii) Fundamental interval is the difference in temperature between the lower fixed point, i.e. temperature of melting ice at standard atmospheric pressure and that upper fixed point, i.e. temperature of steam at standard atmospheric pressure. (b) Uses of hydraulic press are:- -Compressing metal sheets; -Compressing soft materials into bales; -Compressing paper in printing industries; -Lifting of objects. (c) The material used to reset the steel index in the six's maximum and minimum thermometer is magnet. (d)(i) Heat lost by mixture = Heat gained by water + Heat gained by aluminium. M\(_mC_w\Delta \theta_m\) + C\(_a\Delta\theta_a\) 0.3 x C\(_m\) x (85 - 40) = 0.5 x 4200 (40 - 26) + 90 (40 - 26) 13.5 C\(_m\) = 29400 + 1260 C\(_m\) = \(\frac{30660}{13.5}\) = 2271.1 Jkg\(^{-1}\)K\(^{-1}\) (ii) (\(\alpha\)) The bottle losses heat through conduction and convection. (\(\beta\)) Heat exchanger in: Incubation, refriaeration, air-conditioning, sewage treatment, cooling byradiators, generation of electricity, etc.

(a) Critical angle is defined as the angle of incidence in the denser medium for which the angle of refraction in the less dense medium is 90^\circ. (b) Antinodes are created in a stationary wave when an incident and its reflected waves are superposed and 180^\circ out of phase. (c) n = \(\frac{Sin\frac{(A + Dm)}{2}}{\sin (\frac{A}{2})}\) = \(\frac{Sin\frac{(60 + 46.2)}{2}}{\sin (\frac{60}{2})}\) = \(\frac{sin 53.1}{sin 30}\) = 1.6 (d) No image is obtained on the screen because - Object, screen and mirror are not coaxial; - Object is placed at focal point of mirror; - Object is placed between the focus and the pole; - Screen is located at a distance less than or greater than actual image distance. (e) (i) \(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\) \(\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{30} - \frac{1}{7}\) = \(\frac{5 - 2}{150} = \frac{3}{150}\) U = 75 + 25 = 100cm \(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\) \(\frac{1}{100} + \frac{1}{50} = \frac{1}{50} = \frac{1}{50}\) f = 50cm

a) Dielectric strength is the maximum potential gradient or electric field strength an insulator can withstand without breaking down. It is measured in Vmm\(^{-1}\) or Vm\(^{-1}\). (b)(i) The wave is infra-red wave. (ii) Suitable detector can be -Infra-red camera; -Thermopile; -Bolometer or -Photographic film. (iii) Source of the wave can be - Hot bodies or sun (c) E = \(\frac{F}{q} = \frac{W}{q}\) W =mF = Eq = 1200 x 1.0 x 10\(^{-19}\) = 1200 x 1.0 x 10\(^{-19}\)N (d) X\(_L\) = 1.2\(\pi fL\) = 2 x 3.142 x 50 x 0.50 = 15.7\(\Omega\) X\(_c\) \(\frac{1}{2 \pi fL}\) = \(\frac{1}{2 \times 3.14 \times 50 \times 25 \times 10^{-16}}\) = 127.4 \(\Omega\) (i) Z = \(\sqrt{R^2 + (X_1 - X_c)^2}\) = \(\sqrt{100^2 + (127.4 - 15.7)^2}\) = 149.9\(\Omega\) (ii) I \(\frac{V}{Z} = \frac{220}{149.9}\) = 1.47A

(a)(i) Mass defect is the difference between the mass of a nucleus and the total mass of its nucleons. It expressed in atomic mass unit (a.m.u.). It is also a measure of binding energy. Mass defect = total mass of nucleus – mass of nucleons. (ii) Binding energy is the work done or energy needed to separate the nucleons in a nucleus. It is measured in eV or Joules (J). (b)(i) The effect of decreasing the speed of a photoelectron on: (\(\alpha\)) wavelength --> wavelength increases. (\(\beta\)) energy ---> energy decreases. (ii) \(\lambda = \frac{h}{mv}\) = \(\frac{6.6 \times 10^{-34}}{4.4 \times 10^{-2} \times 10^{-16}}\)m (c) Pairs of isotopes in the figure are; \(^{208}_{82}Pb\) and \(^{212}_{82}Pb\) or \(^{212}_{84}Po\) and \(^{216}_{84}Po\) or \(^{224}_{88}Ra\) and \(^{288}_{88}Ra\) or \(^{288}_{90}Th\) and \(^{232}_{90}Th\) (ii) The series started with isotopes \(^{232}_{90}Th\) (iii) Nuclear equation for; \(\alpha\)Alpha decay \(^{232}_{90}Th\) \(\to\) \(^{228}_{88}Ra\) + \(^{4}_{2}He\) + Energy; \(^{228}_{90}Th\) \(\to\) \(^{22}_{88}Ra\) + \(^{4}_{2}He\) + Energy; \(^{224}_{88}Ra\) \(\to\) \(^{220}_{86}Rn\) + \(^{4}_{2}He\) + Energy; \(^{212}_{84}Po\) \(\to\) \(^{208}_{82}Pb\) + \(^{4}_{2}He\) + Energy; \(^{216}_{84}Po\) \(\to\) \(^{212}_{82}Pb\) + \(^{4}_{2}He\) + Energy; \(^{212}_{84}Rn\) \(\to\) \(^{208}_{82}Po\) + \(^{4}_{2}He\) + Energy; \(^{220}_{84}Rn\) \(\to\) \(^{216}_{84}Po\) + \(^{4}_{2}He\) + Energy; \(^{216}_{84}Rn\) \(\to\) \(^{212}_{82}Pb\) + \(^{4}_{2}He\) + Energy; (\(\beta\)) Beta decay \(^{224}_{88}Ra\) \(\to\) \(^{224}_{89}Ac\) + \(^{o}_{-1}e\) + Energy; \(^{228}_{88}Ac\) \(\to\) \(^{228}_{90}Ac\) + \(^{o}_{-1}e\) + Energy; \(^{212}_{82}Pb\) \(\to\) \(^{212}_{83}Bi\) + \(^{o}_{-1}e\) + Energy; \(^{212}_{83}Ra\) \(\to\) \(^{212}_{84}Ac\) + \(^{o}_{-1}e\) + Energy;

S/N E/v I/A V/V \(\frac{1}{V}\)/V\(^{1}\) l\(^{-1}\)/A\(^{-1}\) 1 1.5 0.30 0.80 1.250 3.333 2 3.0 0.50 0.40 0.717 2.000 3 4.5 0.70 2.00 0.500 1.429 4 6.0 0.90 2.50 0.400 1.111 5 7.5 1.10 3.00 0.333 0.909 Slope = \(\frac{\bigtriangleup {V}^{-1}}{\bigtriangleup {I}^{-1}}\) = \(\frac{V_{2}^{-1} - V_{1}^{-1}}{I_{2}^{-1} - I_{1}^{-1}}\) = \(\frac{3.333 - 0.800}{1.24 - 0.26}\) = \(\frac{2.53}{0.98}\) = 2.6 Intercept C = 0.04 Precaution; - Ensured clean terminals/tight connections - Key removed after taking each reading/key removed - when reading was not being taken. - Avoided parallax error on Voltmeter/Ammeter Noted/corrected zero error on voltmeter/ammeter - Repeated readings (shown on the table) (b) Production of electric current e.g. use of - Cells (accumulators/simple cells) fuel cells (chemical energy) - Generators/dynamos/electromagnetic induction (mechanical) - Solar cells/photocells - Windmills - Tidal waves - Geothemal/thermal - Gas turbines - Hydro power - Nuclear power - Thermocouple/thermopile/themionic (heat energy) - Piezo electric generators - Electrostatic generator (e.g Van de graff generator) ii. \(\frac{1}{Re}\) = \(\frac{1}{R1} + \frac{1}{R2}\) = \(\frac{1}{R} + \frac{1}{R} = \frac{2}{R}\) Re = \(\frac{R}{2}\) RT = \(\frac{R}{2}\) + 2 = 4 \(\frac{R}{2}\) = 4 - 2 = 2 R = 4\(\Omega\)

S/N A/cm B/cm 1.0 10.0 54.00 2.0 15.0 55.00 3.0 20.0 56.00 4.0 25.0 57.00 5.0 30.0 57.00 6.0 35.0 58.00 Slope (s) = \(\frac{\bigtriangleup {B}}{\bigtriangleup {A}}\) = \(\frac{B_{2} - B_{1}}{A_{2} - A_{1}}\) = \(\frac{59 - 53}{30 - 0} = \frac{6}{30}\) = \(\frac{1}{6}\) = 0.2 Intercept C on the vertical axis C = 53 Evaluate (a) \(k_1\) = [\(\frac{1 - 2S}{S}\)]100 = (\(\frac{1 - 2 \times 0.2}{0.2}\)) 100 = (\(\frac{1 - 0.4}{0.2}\))100 \(k_1\) = \(\frac{0.6}{0.2}\) 100 = 300 \(k_2\) = \(\frac{2C}{S}\) - 160 = \(\frac{2 \times 52}{0.2}\) - 160 = \(\frac{106}{0.2}= \frac{1060}{2}\) = 530 - 160 = 370 Precautions; - Avoided draught - Ensured mass did not touch/rest on the table. - Avoided error due to parallax on the metre rule. - Noted zero error on metre rule. - Repeated readings (shown on the table). (b)i. The moment of a force about a point is defined as the product of the force and the perpendicular distance from the point to the line of action of the force. ii. Conditions of rigid bodies in equilibrium; 1. The resultant of the forces in a given direction must be zero/the algebraic sum of resolved components in a given direction must be zero/the vector sum of all the points must = 0 2. The algebraic sum of the moments about any point is zero. 3. The forces must be concurrent or meet at a point.

S/N m/g T/min \(\theta\) = \(\theta_{1} - \theta_{0}\) 1 150.0 2.0 \(\theta\) = 88 - 34 = 56\(^{6}\) 2 200.0 4.0 \(\theta\) = 86 - 34 = 52 3 250.0 6.0 \(\theta\) = 84 - 34 = 50 4 300.0 8.0 \(\theta\) = 80 - 34 = 46 5 350.0 10.0 \(\theta\) = 76 - 34 = 42 Initial temperature of water = 34^\circ Slope s = \(\frac{\bigtriangleup {m}}{\bigtriangleup \theta}\) = \(\frac{m_{2} - m_{1}}{\theta_{2} -\theta_{1}}\) = \(\frac{350 - 50}{62 - 42} = \frac{300}{20}\) S = 150 Evaluate k = \(\frac{50}{S} = \frac{50}{150}\) = 0.333 Precautions; - Avoided splashing of water - Stirred continuously (for even distribution of heat). - Avoided parallax error on the thermometer/measuring cylinder - Repeated readings shown on the table - Ensured the heated mass was gently dropped into the beaker. (b)i. Heat Capacity Is the quantity of heat required to raise the temperature of a substance. ii. Pt = mc\(\theta\) 1200 x t = \(\frac{800}{1000}\) x 4200 (101 x 20) 1200t = 0.8 x 4200 x 81 t = \(\frac{0.8 \times 4200 \times 81}{1200}\) t = \(\frac{272160}{1200}\) t = 2260.8 secs

S/N E/v I/A V/V \(\frac{1}{V}\)/V\(^{1}\) l\(^{-1}\)/A\(^{-1}\) 1 1.5 0.30 0.80 1.250 3.333 2 3.0 0.50 0.40 0.717 2.000 3 4.5 0.70 2.00 0.500 1.429 4 6.0 0.90 2.50 0.400 1.111 5 7.5 1.10 3.00 0.333 0.909 Slope = \(\frac{\bigtriangleup {V}^{-1}}{\bigtriangleup {I}^{-1}}\) = \(\frac{V_{2}^{-1} - V_{1}^{-1}}{I_{2}^{-1} - I_{1}^{-1}}\) = \(\frac{3.333 - 0.800}{1.24 - 0.26}\) = \(\frac{2.53}{0.98}\) = 2.6 Intercept C = 0.04 Precaution; - Ensured clean terminals/tight connections - Key removed after taking each reading/key removed - when reading was not being taken. - Avoided parallax error on Voltmeter/Ammeter Noted/corrected zero error on voltmeter/ammeter - Repeated readings (shown on the table) (b) Production of electric current e.g. use of - Cells (accumulators/simple cells) fuel cells (chemical energy) - Generators/dynamos/electromagnetic induction (mechanical) - Solar cells/photocells - Windmills - Tidal waves - Geothemal/thermal - Gas turbines - Hydro power - Nuclear power - Thermocouple/thermopile/themionic (heat energy) - Piezo electric generators - Electrostatic generator (e.g Van de graff generator) ii. \(\frac{1}{Re}\) = \(\frac{1}{R1} + \frac{1}{R2}\) = \(\frac{1}{R} + \frac{1}{R} = \frac{2}{R}\) Re = \(\frac{R}{2}\) RT = \(\frac{R}{2}\) + 2 = 4 \(\frac{R}{2}\) = 4 - 2 = 2 R = 4\(\Omega\)

Given Data: u = 150 ms\(^{-1.}\), Ø = 30^\circ Time of Flight = \(\frac{2usinØ}{g}\) → \(\frac{2 * 150 * sin30^\circ}{10}\) = 15s t = time taken to reach maximum height = ? t = usin\theta \divg t = [150 \times sin(30)] \div10 t = 7.5secs.

A photoresistor or light dependent resistor is an electronic component that is sensitive to light. When light falls upon it, then the resistance changes. Used where there is a need to sense the presence and absence of light is necessary. These resistors are used as light sensors and the applications of LDR mainly include alarm clocks, street lights, light intensity meters, burglar alarm circuits.

(a) The circuit is half-wave rectifier. (b)

Using the general gas laws: \(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\) P\(_1\) = 800mmHg, V\(_1\) = 76cm\(^3\), T\(_1\) = 273 + 27 = 300k P\(_2\) = 760mmHg, V\(_2\) = ? T\(_2\) = 273 + 0 = 273 (@ STP) \(\frac{800 \times 76}{300} = \frac{760 \times V_2}{273}\) V\(_2 = \frac{800 \times 76 \times 273}{300 \times 760}\) = 72.8cm\(^3\) Therefore, the volume of gas at S.T.P = 72.8 cm\(^3\)