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Electric field & capacitor

Date:

Time: Total marks available: Total marks achieved: ______

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Questions

Q1.The unit for capacitance is the farad. The farad can also be written as

A A s V–1

B A s–1V–1

C A–1 s–1V

D A–1 s V

(Total for question = 1 mark)

Q2.A capacitor can be charged and discharged using the following circuit. It can be assumed that the ammeter has zero resistance.

(a) Initially the switch makes contact at X. Calculate the charge stored by the capacitor when it is fully charged.

(2) .............................................................................................................................................

............................................................................................................................................. (b) The switch is moved to make contact at Y so that the fully charged capacitor is discharged through the 220 Ω resistor.

Calculate the charge remaining on the capacitor after it has been discharging for 1.0 ms and comment on your answer.

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Comment

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(c) The capacitor is charged and discharged 500 times per second.

Calculate the average current through the ammeter.(2)

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(Total for question = 8 marks) Q3.Between 1909 and 1911 Rutherford's alpha particle scattering experiment provided evidence for the nuclear model of the atom. Alpha particles were fired at a thin gold foil and their paths observed.

(a) Describe the observations from the alpha particle scattering experiment.

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(b) An alpha particle approaches a gold nucleus. It reaches a distance of 4.5 × 10–14m from the gold nucleus. Calculate the force between the alpha particle and the gold nucleus.

proton number for gold = 79(3)

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(Total for question = 6 marks)

Q4.A teacher states 'the repulsive force between 1 C of charge on the ground and 1 C of charge on a 1000 kg mass is large enough to support the mass when it is 1 km above the ground'. of 29

Determine whether the teacher is correct.

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(Total for question = 4 marks) Q5.A timer circuit includes a capacitor and a variable resistor in series.

(a) The graph shows how the current in the timer circuit varies with time when the capacitor discharges through the variable resistor. The resistance of the variable resistor is 8.2 kΩ.

(i) Show that the capacitance of the capacitor is about 0.02 F.(3)

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(ii) Calculate the initial charge on the capacitor.(3)

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(iii) Calculate the energy initially stored in the capacitor.(2)

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(b) In another timer circuit the capacitance of the capacitor is 470 μF. The circuit switches off when the potential difference falls to 15% of its initial value. The variable resistor is adjusted so that the timer circuit switches off after 3.5 minutes.

Calculate the resistance of the variable resistor.(3)

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(Total for question = 11 marks) Q6.Two parallel plates have a potential difference of 12 V across them and are separated by a distance of 5.0 × 10–4m.

What is the magnitude of the electric field strength halfway between the plates?

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A 6000 Vm–1

B 12 000 Vm–1

C 24 000 Vm–1

D 48 000 Vm–1

(Total for question = 1 mark)Q7.The diagram shows two horizontal parallel plates separated by a distance d. There is a potential difference V across the plates. An oil drop with charge Q is held stationary between the plates.

Which of the following gives the mass m of the oil drop?

(Total for question = 1 mark) Q8.Some lights are designed to dim gradually after being switched off. This can be done using a capacitor in a timer circuit.

The circuit diagram shows how a potential difference (p.d.) can be supplied across a resistor for a limited time.

*(a) When the switch is at position A, the capacitor charges. of 29

(i) In terms of the movement of electrons, explain what happens to the capacitor as it becomes fully charged.

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(ii) Calculate the energy stored in the charged capacitor.(2)

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*(b) The switch is moved to position B and the capacitor discharges through the resistor.

(i) Describe what happens to the current through the resistor.(2)

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(ii) For the circuit shown, the p.d. across the capacitor falls to 10% of the supply p.d. after 25 s.Calculate the resistance of the resistor in the circuit.

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(Total for question = 9 marks)Q9.Two charged spheres of equal mass are suspended with insulating threads of equal length. One sphere has a charge of +Q and the other has a charge of +10Q.

Which of the following shows the arrangement of these spheres when they are in equilibrium?

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A B C D

(Total for question = 1 mark) Q10.Regenerative braking is used in electric cars. When the driver applies the brakes the motor acts as an electric generator, making use of the rotation of the wheels as they slow down. This enables the battery to be charged whilst the car is braking.

The diagram shows a coil in a magnetic field which when rotating can be used as an electric generator.

*(a) The coil rotates.

Explain how this produces a current in the coil.(3)

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*(b) State why the current produced in the coil cannot be used directly to charge a battery.

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*(c) When regenerative braking is being used, explain how the magnitude of the generated e.m.f. changes as the driver brakes steadily.

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(Total for question = 7 marks)Q11.The photograph shows a digital coulombmeter which measures electric charge.

The charge the coulombmeter is measuring is stored on a capacitor inside the meter. A voltmeter inside the coulombmeter measures the potential difference across the capacitor. This value is converted so that the display shows the charge in nanocoulomb.

(a) State why the voltmeter must have a very high resistance.

(1)

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(b) A coulombmeter is charged. A resistor with resistance 4.6 MΩ is placed across the terminals and the capacitor discharges through the resistor. The charge shown on the display is recorded and a graph of charge against time is produced.

(i) Use the graph to determine the capacitance of the capacitor in the coulombmeter.(3)

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(ii) Calculate the energy initially stored by the capacitor.(2)

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(c) The notes with the coulombmeter state:

Explain why the charge will be transferred to the capacitor with a much higher capacitance.(2)

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(d) The data for the graph was obtained by using a video camera to record the coulombmeter display and replaying this frame by frame.

State an advantage of using this method.(1)

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Q12.Answer the question with a cross in the box you think is correct ( ). If you change your mind about an answer, put a line through the box ( ) and then mark your new answer with a cross ( ).

Two conducting plates are 5 cm apart. The potential difference between the plates is 10 V as shown.

Which diagram correctly shows the electric field between the plates?

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(Total for question = 1 mark) Q13.A potential difference of 0.2 V is applied across parallel plates with a separation of 4 cm.

What is the electric field strength halfway between the plates?

(1)

A 0.05 V m−1

B 0.1 V m−1

C 5 V m−1

D 10 V m−1

(Total for question = 1 mark) Q14.The diagram shows the parts of an electron deflection tube.

(a) The electron gun consists of a hot metal filament and a positively charged anode.

Explain how this produces a beam of electrons.(2)

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(b) The potential difference between the hot metal filament and the anode is 2.1 kV.

Calculate the velocity of the electrons as they leave the electron gun.(3)

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(c) The electron beam passes between plates across which a potential difference has been applied. The electron beam is deflected, as shown in the photograph.

On the diagram below, sketch the electric field between the plates.(2)

(d) A potential difference of 550 V is applied across the plates of another deflection tube. The vertical separation of the plates is 5.0 cm.

(i) Show that the electrostatic force on an electron between the plates is about 2 × 10−15 N.(3)

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(ii) The electrons in the beam enter the region between the plates with a horizontal velocity of 2.2 × 107 m s−1.

Determine the vertical deflection of the beam after travelling 10 cm horizontally between the plates.(4)

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(Total for question = 14 marks) Q15.A 500 μF capacitor is charged to a potential difference V1 . A second capacitor of capacitance 50 μF is charged to a potential difference V2 so that the two capacitors store the same amount of energy.

The value of is

A 100

B 10

C 0.1

D 0.01

(Total for question = 1 mark) Q16.Two capacitors of capacitance 1000 μF and 10 μF are charged so that they store the same amount of energy. The potential difference (p.d.) across the 1000 μF capacitor is V1 and the p.d. across the 10 μF capacitor is V2.

The value of is

A 1 × 10−4

B 1 × 10−2

C 1 × 102

D 1 × 104

(Total for question = 1 mark) Q17.A capacitor of capacitance C stores a charge Q when the potential difference across it is V.

Which of the following expressions is the energy stored on the capacitor?

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A potential difference V is applied across two identical capacitors of capacitance C connected in parallel.

Which of the following expressions gives the total energy stored on the capacitors?

(Total for question = 1 mark) Q19.In a large-angle alpha particle scattering experiment, alpha particles were directed at thin gold foil and their paths observed. Most of the alpha particles passed straight through the foil or were deflected through a small angle. A very small number were deflected through an angle greater than 90°.

(a) State what can be deduced about the atom given that most alpha particles passed straight through the foil.

(1) .............................................................................................................................................

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(b) The point below represents a gold nucleus.Add lines to show the electric field due to the gold nucleus.

(2)

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(c) An alpha particle that is moving directly towards a gold nucleus is deflected back along its original path. The minimum separation between the alpha particle and the gold nucleus is 3.8 × 10–14 m.

atomic number of gold = 79(i) Calculate the electrostatic force on the alpha particle when it is at the minimum separation from the gold nucleus.

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Force on alpha particle = ...........................................................

(ii) The initial kinetic energy of the alpha particle is 6.0 MeV.Calculate the change in momentum of the alpha particle, in N s, as it travels to its minimum separation from the gold nucleus.

(3) .............................................................................................................................................

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Change in momentum = ........................................................... N s

(Total for question = 8 marks) Q20.Which graph shows how the electric field strength E due to a negative point charge varies with distance r from the charge?

A

B

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C

D

(Total for question = 1 mark)Q21.A 4.0 μF capacitor discharges through a 560 kΩ resistor. What is the time constant of the circuit?

A 2.2 × 10–3 s

B 4.5 × 10–1 s

C 2.2 × 100 s

D 4.5 × 102 s



Two parallel conducting plates are separated by a distance d. A potential difference V is applied between the plates and a charge Q is placed halfway between them, as shown.

Which of the following gives the magnitude of the force acting on the charge?



A potential difference V is applied across two identical capacitors of capacitance C connected in series.

Which of the following expressions is the total energy stored on the capacitors?

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Which of the following units is equivalent to the farad?

A C J–1

B C V–1

C J C–1

D V C–1

(Total for question = 1 mark) Q25.Two charges +Q and –Q are located as shown on the diagram. is the point halfway between the two charges.

A small positive charge moves from +Q to –Q. Which statement about the resultant force on this charge, as it passes through , is correct?

A The magnitude of the resultant force is a maximum.

B The magnitude of the resultant force is a minimum.

C The resultant force changes direction.

D The resultant force is zero.


Q26.A student is investigating capacitance. She sets up the circuit shown.

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(a) When the switch is closed there is a maximum current, which decreases to zero over a period of time as the capacitor charges. Explain why.

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(b) The student discharged the capacitor. She set the variable resistor to its maximum resistance and closed the switch. As the capacitor charged, the student decreased the resistance of the variable resistor so that the current remained constant until the capacitor was fully charged.

A graph of current against time is shown.

(i) Determine the capacitance of the capacitor.(3)

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(ii) Hence determine the energy stored by the capacitor when it is fully charged.(2)

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(c) Capacitance can also be determined by measuring the current I at regular time intervals, as a capacitor discharges through a resistor, and plotting a graph of ln I against time.

(i) Explain how capacitance can be determined using this graph.(3)

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(ii) A capacitor was discharged through a 390 Ω resistor. The capacitance of the capacitor was calculated

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as 2200 μF.

Explain why the data for the graph for this circuit would be difficult to obtain using an ammeter. Your answer should include a calculation.

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(Total for question = 14 marks) Q27.A student was investigating the charge and discharge of a capacitor.

He set up the following circuit.

(a) Calculate the time constant for the circuit.

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............................................................................................................................................. (b) The student wanted to plot a current-time graph as the capacitor charged, but found that the current changed too rapidly for him to take readings.

Instead, he modelled the experiment using a spreadsheet. The switch was closed at time t = 0 s. V is the potential difference across the capacitor.

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Explain how the value in cell B5 is calculated.(2)

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(c) Some of the data from the spreadsheet has been plotted on a graph of current I against time t.

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(i) Plot the missing points and draw a line of best fit.(2)

(ii) Use the graph to determine a second value for the time constant.(2)

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(iii) Suggest how the student might change his spreadsheet to give a more accurate model of the charging of the capacitor.

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*(d) An alternative method of determining the time constant is to use a straight line graph.

State and explain the variables that the student should plot and how he should determine the time constant from this graph.

(3)

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Two identical point charges Q1 and Q2 are placed a small distance apart.

The force acting on Q1 has magnitude F.

The charge Q1 and the distance between the charges are both doubled. The charge Q2 is unchanged.

What is the magnitude of the new force on Q1?

(Total for question = 1 mark) Q29.(a) Two point charges of 3.1 × 10−9 C and −2.4 × 10−8 C are placed a distance of 0.043 m apart in a vacuum.

Calculate the magnitude of the force between the charges.(2)

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Force = ...........................................................

(b) The diagram represents the electric field around two point charges of equal magnitude. A is a positive charge and B is a negative charge.

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(i) State the meaning of electric field strength.(1)

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(ii) By considering the electric field at X due to A and due to B separately, explain the direction of the electric field at X.

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(Total for question = 7 marks) Q30.The potential difference across a charged capacitor is V0. The capacitor discharges through a fixed resistor. After a time equal to the time constant, the potential difference has reduced to V.

Which of the following is a correct expression for V?

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(Total for question = 1 mark) Q31.Which of the following is a correct statement about uniform electric fields?

A The field strength is the same at all points.

B The field strength is the same in all directions.

C The field produces no force on a stationary charged particle.

D The force on a charged particle is perpendicular to the field

(Total for question = 1 mark) Q32.Which of the following is a unit of the permittivity of free space ε0?

(Total for question = 1 mark) Q33.Which of the following is not a unit of electric field strength?

A J C m−1

B J C−1 m−1

C N A−1 s−1

D N C−1


Q34.An alpha particle is travelling directly towards the nucleus of a gold atom The graph shows how the force F between the particles varies with their separation r over a short distance.

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(a) The relationship between F and r obeys an inverse square law. With reference to points A and B on the graph, explain what this means.

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(b) Calculate the force between the alpha particle and the gold nucleus when their separation is at its minimum value of 4.5 × 10−14 m.

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Force = ...........................................................

(Total for question = 5 marks) Q35.A teacher is using an electron beam tube to demonstrate the deflection of electrons in a uniform electric field.

A potential difference (p.d.) of 4800 V is applied between the cathode and anode of the tube. The cathode is heated and electrons are emitted from its surface. These electrons are then accelerated from rest and pass through a hole in the anode.

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(a) State the name of the process by which electrons are emitted from the cathode.

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(b) Show that the speed v of the electrons as they leave the anode is about 4 × 107 m s−1.

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(c) After leaving the anode, the electrons follow a parabolic path as they pass between a pair of parallel plates with a p.d. of 800 V between them. There is a uniform electric field between the plates.

(i) Calculate the force due to the electric field that acts on an electron while it is between the plates.(3)

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(ii) An electron experiences an upward acceleration a as it travels between the plates. Its vertical displacement h after a time t is given by

Calculate the value of h as the electron leaves the plates.(4)

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............................................................................................................................................. (d) (i) Keeping the p.d. between the cathode and anode at 4800 V, the p.d. between the parallel plates is decreased. Draw the new path of the electrons on the diagram in (c). Label this path A.

(1)(ii) Keeping the p.d. between the parallel plates at 800 V, the p.d. between the cathode and anode is decreased. Draw the new path of the electrons on the diagram in (c). Label this path B.

(1)(Total for question = 13 marks)

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