AS PHYSICS. Electricity Homework Questions. moulsham high school

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1 moulsham high school AS PHYSCS Electricity Homework Questions Work with other memebrs of the group to complete at least the first 5 questions using your text books and your knowledge from GCSE. 1.List of data, formulae and relationships moulsham high school 1

2 Data Gravitational constant Acceleration of free fall Gravitational field strength Electronic charge Electronic mass Unified mass unit Planck constant Speed of light in vacuum Molar gas constant Boltzmann constant Avogadro constant Permittivity of free space Permeability of free space G= g= 981. ms g 981. N kg e= m u= h= c= Nm kg C kg ms kg J s R= 831. J K mol k = N ε 0 e a = = = µ = 4π J K 3 1 mol 1 1 Fm 7 NA (close to the Earth) (close to the Earth) Experimental physics Percentage uncertainty = Estimated uncertainty Average value 100% Mechanics Force F p = t For uniformly accelerated motion: v = u + at x = ut + ½ at ² ν² = + ax Work done or energy transferred W = E = p V (Presssure p; Volume V) Power P = Fν moulsham high school

3 Angular speed θ v ω = = t r (Radius of circular path r) Period T 1 π = = f ω (Frequency f) v Radial acceleration a = r = r ω Couple (due to a pair of forces F and F) = F (Perpendicular distance from F to F) Electricity Electric current = naqv (Number of charge carriers per unit volume n) Electric power P = ²R Resistors in series R = R 1 + R + R 3 Resistors in parallel Resistance at temperature θ Capacitance of parallel plates R θ = R ( + αθ) (Temperature coefficient α) = + + R R R R A C = εε 0 1 d 1 3 Capacitors in parallel C = C 1 + C + C 3 Capacitors in series = + + C C C C 1 3 Energy stored W = 1 CV Nuclear physics Mass-energy E = c m Radioactive decay rate dn = λ N (Decay constant λ) dt λ N = N e t 0 moulsham high school 3

4 Half-life T 1 = ln λ Photon model E = hf Energy levels hf = E1 E de Broglie wavelength λ = h p Matter and materials Density ρ = m V Hooke s law F = k x Stress Strain Young modules σ = F A ε = l l E Stress = Strain Work done in stretching W = ½F x (provided Hooke s law holds) Oscillations and waves For a simple pendulum T = π l g For a mass on a spring T = π m k At distance r from a point source of power P, intensity P = 4 πr For Young s slits, of slit seperation s, wavelength λ = xs D (Fringe width x; slits to screen distance D) Refraction sinθ1 sinθ λ1 c1 n = = = λ c n 1 (Refractive index n) moulsham high school 4

5 c sinθ c = 1 c c n1 = c 1 (Critical angle θ c ) Quantum phenomena Maximum energy temperature = hf ϕ (Work function ϕ ) Thermal physics Celcius temperature θ C = T K Xθ X0 Practical Celsius scale θ = X X C Thermal energy transfer Q= mc T (Specific heat capacity c; temperature change T) Change of internal energy U = Q+ W (Work done on body W) Thermal energy transferred on change of state = l m (Specific latent heat or specific enthalpy change l) Rate of thermal energy transfer by conduction = ka T x (Thermal conductivity k; temperature gradient T x ) Kinetic theory pv = 1 Nm( c ) 3 T Average kinetic energy of molecules Mean kinetic energy of molecules = 3kT (Boltzmann constant k) Molar gas constant R= kn A (Avogadro constant N A ) Upthrust U = Weight of displaced fluid Pressure difference in fluid p= ρ g h moulsham high school 5

6 Fields Electric field strength uniform field E = F Q= V d radial field E = kq r (Where for free space or air k = 14πε 0 ) Electric potential radial field V = kq r For an electron in a vacuum tube e V = ( 1mv ) Gravitational field strength radial field g = GM r Gravitational potential radial field V = G M r, numerically Time constant for capacitor charge or discharge = RC Force on a wire Force on a moving charge F = Bil F = BQv Field inside a long solenoid = µ 0 n (Number of turns per metre n) Field near a long straight wire E.m.f. induced in a moving conductor Flux E.m.f. induced in a coil For = sinπft and V = V sin πft : 0 0 = µ 0 πr = Blv Φ = BA rms = Nd Φ dt V = 0 and Vrms = 0 (Number of turns N) Mean power = rms V rms = V 0 0 moulsham high school 6

7 Mathematics sin (90 θ) = cos θ n (x n ) = n ln x n (e kx ) = kx Equation of a straight line y = mx + c Surface area cylinder = πrh + πr² sphere = 4πr² Volume For small angles: cylinder = πr²h sphere = 4 / 3 πr³ sin θ tan θ θ (in radians) cos θ 1. The list gives some quantities and units. Underline those which are base quantities of the nternational (S) System of units. coulomb force length mole newton temperature interval () Define the volt () Use your definition to express the volt in terms of base units Explain the difference between scalar and vector quantities () s potential difference a scalar or vector quantity?... (1) (Total 10 marks) 3. Complete each of the following statements in words: moulsham high school 7

8 The resistance of an ammeter is assumed to be... The resistance of a voltmeter is assumed to be... () Calculate the total resistance of four 5.0 Ω resistors connected in parallel. Total resistance =... () (Total 4 marks) 4. Use the axes below to sketch and label two graphs to show how the current varies with potential difference for (i) a metal wire, and (ii) a semiconductor diode, both at constant temperature. V V Metal wire Semiconductor diode A semiconductor diode carries a current of 0 ma in normal operation. The potential difference across it should be 1.9 V. Complete the diagram below to show how, with the addition of a single component, the semiconducting diode may be powered from a 4.5 V supply. 4.5 V moulsham high school 8

9 Show that the resistance of the additional component is 130 Ω. (Total 6 marks) 5. A student connects the circuit as shown in the diagram. 6.0 V V 400 Ω The reading on the voltmeter is 1.8 V. Calculate the current in the resistor..... Current =... (1) Calculate the resistance of the thermistor Resistance =... () moulsham high school 9

10 The graph shows how the resistance of the thermistor depends on its temperature. Resistance / Ω Temperature / C Determine the temperature of the thermistor. Temperature =... (1) f the e.m.f. of the supply were doubled, would the reading on the voltmeter double? Explain your answer (Total 7 marks) moulsham high school 10

11 6. (a) A student sets up a circuit and accidentally uses two voltmeters V 1 and V instead of an ammeter and a voltmeter. The circuit is shown below. V V 100 Ω V (i) (ii) Circle the voltmeter which should be an ammeter. Both voltmeters have a resistance of 10 MΩ. The student sees that the reading on V is 0 V. Explain why the potential difference across the 100 Ω resistor is effectively zero. (1) () moulsham high school 11

12 (b) The student replaces the 100 Ω resistor with another resistor of resistance R. The reading on V then becomes 3.0 V. (i) Complete the circuit diagram below to show the equivalent resistor network following this change. Label the resistor R. 9.0 V () (ii) Calculate the value of R. R =... (Total 8 marks) 7. The diagram shows two methods of connecting eight heating elements which make up a car rear window heater. The heater is connected to a 1 V car battery. Each element used in circuit P has a resistance of 4 Ω;each used in circuit S has a resistance of 0.50 Ω Circuit P Circuit S + moulsham high school 1

13 (a) Calculate the current drawn from the battery for each circuit. Show your working. Circuit P... Circuit S... (5) (b) Elements 3 and 4 burn out in each circuit and no longer conduct electricity. What are the new values of the currents in each circuit? Circuit P... Circuit S... () (c) What effect would halving the battery voltage have on the power transfer in circuit P? Explain your answer. () (Total 9 marks) Extension questions moulsham high school 13

14 8. Three resistors R 1, R and R 3 are connected in parallel with each other. They could be replaced by a single resistor of resistance R. +V +V 1 3 R 1 R R 3 R 0V 0V Show that the resistance, R, of the equivalent resistor can be calculated from 1 1 = R R R + 1 R3 moulsham high school 14

15 A student has four identical resistors each of resistance 10 Ω. She connects them to form the different networks shown below. Calculate the equivalent total resistance of each network. First network Total resistance =...Ω Second network Total resistance =...Ω Third network Total resistance =...Ω moulsham high school 15

16 She then connects a battery across the second network and adds meters to make the circuit shown below. A current of 50 ma is drawn from the battery. V 50 ma A 10 Ω 10 Ω 10 Ω 10 Ω V 1 Determine the reading on each of the three meters. Reading on ammeter A: Ammeter reading =... ma Reading on voltmeter V 1 : Voltmeter reading =... V Reading on voltmeter V : Voltmeter reading =... V (5) (Total 11 marks) 9. The diagram shows the circuit of a fluorescent light fitting. t consists of a tube, a starter and a ballast resistance of 300 Ω. moulsham high school 16

17 The fluorescent tube is filled with gas. t contains two filaments at A and B of resistance 50 Ω that heat the gas. Ballast 300 Ω 50 Ω A 30 V Starter V starter Tube B 50 Ω When the light is first turned on, the tube does not conduct but the starter does, drawing a current of 0.50 A from the 30 V supply. Calculate the voltages across the ballast resistor and each filament when this current flows Voltage across ballast =... Voltage across each filament =... moulsham high school 17

18 Mark these voltages on the diagram, and hence calculate the voltage across the starter when the starting current is flowing. Mark your answer on the diagram. () The starting current heats the filaments and the gas in the tube but the voltage across the tube is not large enough to make it conduct. However, after a few seconds the starter stops conducting. The voltage across the tube rises and the gas conducts. A current now flows from A to B and the tube lights up. What fundamental change is necessary for a gas, which was an insulator, to be able to conduct? (1) Now that the tube is conducting, the voltage across AB is 110 V. Calculate the power dissipated in the whole circuit Power dissipated =... n a faulty fluorescent lamp the filaments at both ends of the tube glow steadily but the tube does not light up. dentify, with a reason, the faulty component (1) (Total 10 marks) 10. A student wants to determine the e.m.f. ε of a cell and its internal resistance r. He uses the circuit shown and measures the terminal voltage V across the cell and the current in the circuit for each setting of the variable resistor. ε r V A moulsham high school 18

19 He plots the following graph of terminal voltage V against current. V/V /A Show how the relationship V = ε r can be used with his graph to determine the e.m.f. ε of the cell. State its value. E.m.f. =... () Show how the graph can be used to determine the internal resistance r of the cell. Calculate its value. nternal resistance =... The student repeats the experiment using two of these cells in series. On the graph, draw the line that he obtains. () Suggest why the student includes the filament lamp in the circuit. () (Total 9 marks) moulsham high school 19

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