 ### Capacitor Questions

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March 2013

8.1 Write down the main function of a capacitor in a circuit. (1)
8.1 Stores (electric) charge (energy).

OR

Releases (stored) charge instantly/very fast.

A high-resistance light bulb and an uncharged parallel plate capacitor are connected in series with a 12V battery and a switch S, as shown below. The internal resistance of the battery and the resistance of the connecting wires should be ignored. 8.2 Describe how the brightness of the light bulb changes during the charging process. (1)
8.2 The brightness of the bulb decreases (gradually) until it stops glowing (dies).

OR

The bulb glows dimmer until it stops glowing (dies).

This is bacause as the capacitor gets charged, it develops an increasing opposing potential difference to the very battery that is charging it. This opposition gradually decreases the current in the cicuit, until the currecnt becomes zero.

The capacitor is NOW fully charged.

8.3 Write down the potential difference across the:

8.3.1 Light bulb (1)
8.3.1 0 V (zero volts)

no current flowing, therefore no potential difference.

8.3.2 Capacitor (1)
8.3.2   12V

8.4 The distance between the plates of the capacitor is 5,4 mm. For the fully charged capacitor, calculate the magnitude of the:

8.4.1 Electric field between the plates (3)
8.4.1 • The direction is from positive plate to negative plate.
• The electric field is UNIFORM, which means of constant strength and direction.

8.4.2 Electrostatic force exerted on an electron between the plates (3)
8.4.2 Since the electric field is uniform, the electron would experience the same size (constant) force ANYWHERE in between the plates, even close to the negative plate.
As a result of the constant force, the acceleration of the electron would be constant as well. (Newton's Second Law)

8.5 An electron is positioned 3,8 mm from the positive plate of the capacitor.
Calculate the:

8.5.1 Distance (in mm) between the electron and the negative plate (1)
8.5.1   5,4mm - 3,8mm = 1,6mm

8.5.2 Work that must be done to move the electron to the negative plate (Ignore the effects of gravitational force.) (4)
8.5.2 (a) Calculate the work involved when an electron moves from rest from the negative plate to the positive plate.

W = VQ
W = 12(1,6 x 10-19)
W = 1,92 x 10-18J

OR

W = FΔcosΘ
W = (3,56 x 10-16)(5,4 x 10-3)(1)
W = 1,92 x 10-18J

NOTE: If the electron is to be moved TO the negative plate, work must be done to it by an external source. (a kind of "repulsion" to be overcome.)
If the electron is to be moved to the positive plate, an external source is not required, since this is a natural movement.

(b) Calculate the velocity of the electron when it reaches the positive plate. (Work energy theorem) (c) How would this magnitude of work calculated in (a), be affected if the distance between the plates was halved?

The work done would be the same.
None of the variables in W = VQ would have changed. Only d changed, and d is not part of this equation.

NOTE:
But E would have increased
E = V/d

Hence F would have increased since F = QE (same Q, greater E)

Hence acceleration would have increased since larger F.

(d) How would the final velocity of the electron be affected if the distance between the plates was halved.

No change.
No change to variables Ek, m and vi in the equation. Hence vf would be the same.

Nov 2012

8 In the circuit represented below, an uncharged capacitor is connected in series with
a 1 000Ω resistor. The emf of the battery is 12 V. Ignore the internal resistance of the battery and the ammeter. 8.1 Calculate the initial current in the circuit when switch S is closed. (3)
8.1 8.2 Write down the potential difference across the plates of the capacitor when it is fully charged. (1)
8.2 12 V

The capacitor has a capacitance of 120µF and the space between its plates is filled with air.

8.3 Calculate the charge stored on the plates of the capacitor when it is fully charged. (3)
8.3 After discharging the capacitor, it is connected in the same circuit to a resistor of HIGHER resistance and switch S is closed again.

8.4 How would this change affect each of the following:
(Write down INCREASES, DECREASES or REMAINS THE SAME.)

8.4.1 The initial charging current (1)
8.4.1 Decreases

8.4.2 The time it takes for the capacitor to become fully charged (1)
8.4.2 Increases

8.5 The two parallel plates of the fully charged capacitor are 12mm apart.

8.5.1 Sketch the electric field pattern between the parallel plates. (3)
8.5.1 8.5.2 Calculate the magnitude of the electric field at a point midway between the plates. (3)
8.5.2 March 2010

10 Capacitors are circuit devices used to store electrical energy. The capacitance of capacitors depends, amongst other factors, on the plate area. The larger the plate area, the more the energy that can be stored.

10.1 Apart from plate area, state TWO other factors that can influence the capacitance of a capacitor. (2)
10.1 Dielectric
Distance between plates 

10.2 A certain parallel plate capacitor consists of two plates, each having dimensions of 2cm by 10cm. The plates are 0,2 mm apart and are held at a potential difference of 20 V. The space between the plates is filled with air.

10.2.1 Sketch the electric field pattern between the two oppositely charged parallel plates of the capacitor. (3)
10.2.1 10.2.2 Calculate the capacitance of this capacitor. (5)
10.2.2 Calculate the area A of the plates as length x breadth by convertng the centimeters to meters.

Nov 2010

9 A certain parallel plate capacitor consists of two plates, each of dimension 15mm by 20mm, separated by a distance of 1,5 mm. The space between the plates is occupied by air.

9.1 Define the term capacitance, in words. (2)
9.1 The ratio of the (amount of) charge (transferred) to the (resulting) potential difference.

9.2 Calculate the capacitance of this capacitor. (5)
9.2 Calculate the area A by converting the mm into m.

The circuit diagram below shows the ABOVE CAPACITOR, initially uncharged, connected in series to a resistor, an ammeter of negligible resistance and a source with an emf of 12 V. The internal resistance of the battery is negligible. Switch S is now closed.

9.3 Draw a sketch graph of current versus time to show how the ammeter reading changes with time as the capacitor charges. (2)
9.3 The capacitor is now fully charged.

9.4 Calculate the magnitude of the charge on each plate of the capacitor. (3)
9.4 9.5 One of the molecules in the air between the plates of the capacitor becomes ionised. This ion carries a charge of +3,2 x 10-19C. Calculate the magnitude of the electrostatic force experienced by this ion between the plates. (5)
9.5 Then March 2009

10 Each plate of a parallel plate capacitor has an area of 40cm2 . The plates are 1cm apart. The capacitor is connected to a 12V DC supply.

10.1 Calculate the magnitude of the charge on each plate. (5)
10.1 Convert the 40cm2 into meter squared. (4 x 10-3 m2)

10.2 By which factor will the charge calculated in QUESTION 10.1 change if the area of each parallel plate is changed to 20cm2 ?
Explain your answer in terms of physics principles and the charge stored in the capacitor. (NO calculations needed.) (3)
10.2 half
Half the area will store half the amount of charge

OR

C ∝ A
and C ∝ Q,
thus C is halved

10.3 What is the net charge on the capacitor? (1)
10.3 net charge = 0 C

10.4 Capacitors are used in flash cameras. Give a reason for this use. (1)
10.4 Discharges almost instantly to deliver flash light

Nov 2009 Unused

10 The ability of capacitors to store charge makes them essential components in electrical appliances. Users are often warned of the dangers associated with capacitors inside appliances.

10.1 Briefly explain why it can be dangerous to touch a charged capacitor. (2)
10.1 Discharges very fast when touched and can cause an electric shock that can be fatal

10.2 A certain parallel plate capacitor consists of two identical aluminium plates, each of area 2 x 10-4 m2. The plates are separated by a distance of 0,03 mm, with air occupying the space between the plates.

10.2.1 Calculate the capacitance of the capacitor. (4)
10.2.1 10.2.2 Calculate the charge stored on the plates of the capacitor when connected to a 6 V battery. (3)
10.2.2 The second step is Q = CV

10.3 How will the capacitance of the capacitor in QUESTION 10.2 change (INCREASES, DECREASES or REMAINS THE SAME) if:

10.3.1 Paper is used to fill the gap between the plates instead of air (1)
10.3.1 Increases

10.3.2 The distance between the plates is increased (1)
10.3.2 Decreases

Nov 2008

10 An ink-jet printer makes use of the electric field between two oppositely charged parallel plates to control the position of an ink drop on paper. In the diagram below, the generator (G) of the printer shoots out ink drops that are charged in the charging unit C. The input signal from a computer controls the charge given to each ink drop. P is a negatively charged ink drop. 10.1 Define the electric field at a point in space. (2)
10.1 Electric force experienced per positive charge placed at the point

OR

A point /space where a charge will experience an electric force

10.2 Is plate B negatively or positively charged? Give a reason for your answer. (2)
10.2 Negative
• Negative ink droplets deflect away from B
• Are attracted towards A
• B repels P
• like charges repel

10.3 Sketch the electric field pattern between plates A and B. (2)
10.3 The plates A and B are 6,4 x 10-4 m apart and ink drop P has a charge of
magnitude 1,5 x 10-13 C. When the ink drop enters the field it experiences an electrical force of 2,1 x 10-7 N.

10.4 Calculate the potential difference across the parallel plates. (5)
10.4 Prep Paper 2008

11 Two parallel plates are arranged to form a capacitor. The area of each plate is 0,04m2. The plates are separated by a 0,002 m air gap.

11.1 Calculate the capacitance of the capacitor. (4)
11.1 This capacitor is connected across a 250 V source as shown below. 11.2 Calculate the charge that accumulates on each plate. (3)
11.2 11.3 State how the amount of the charge stored on each plate can be increased without altering the design of the capacitor. (2)
11.3 Increase the potential difference

The term "design" means the area A of the plates, and the distance d between the plates. Therefore you must not alter A or d.

11.4 Write down the general name for the insulating material that is used to fill the space between the plates of a capacitor. (1)
11.4 dielectric

11.5 Use your knowledge of capacitors to explain why it is dangerous to open an amplifier while it is in operation. (2)
11.5 The capacitor stores charge. This large amount of charge can cause shock to the body.

Exemplar 2008

10 A learner sets up a circuit as illustrated in the circuit diagram below to investigate the change in electric current over time while a capacitor is being charged. Initially there is no charge on the capacitor. After closing the switch, the learner takes the ammeter readings every 20 seconds. The table below shows the results obtained during the investigation. 10.1 Draw a graph of electric current (on the dependent, y-axis) versus time (on the independent, x-axis) on the attached GRAPH PAPER. Draw the axes and choose an appropriate scale. Plot the points and then draw the best fitting line. Supply a suitable heading for your graph.
[HINT: The graph is not a straight-line.] (5)
10.1    Graph of electric current versus time 10.2 Use the graph in QUESTION 10.1 to determine the reading on the ammeter
after 30 s. (1)
10.2   56µA

10.3 Consider the change in the ammeter reading and change in the potential difference to explain the shape of the graph. (2)
10.3 As the potential difference across the plates of the capacitor increases during charging, the potential difference of the battery is opposed, causing the current in the circuit to gradually decrease. 

A capacitor is rated 9 V, 50 µF.

10.4 Calculate the charge on the fully charged capacitor. (3)
10.4 10.5 Capacitors are seen as batteries of the future. State ONE advantage that capacitors have over batteries such as torch batteries. (2)
10.5 Any one
• Supply electrical energy faster
• Can be recharged almost indefinitely
• No spilling of dangerous chemicals

10.6 Appliances such as TVs contain large capacitors. Give a reason why such capacitors are discharged before servicing the appliances. (2)
10.6 The high voltage across plates can cause electric shock or even death when the capacitor discharges.

10 A capacitor's function is to store charge or electrical energy. Capacitors also function as filters, passing alternating current (AC) and blocking direct current (DC).

10.1 Briefly explain how a capacitor can block direct current (DC). (2)
10.1 As the capacitor charges, the direct current decreases and eventually becomes zero when the capacitor is fully charged. 

10.2 You are requested to design a parallel plate capacitor with a capacitance of 200pF using the following materials:

• Two connecting wires
• A whole sheet of aluminium foil of area 0,2m2

Use the following steps as guidance in your design:

10.2.1 Calculate the distance between the plates of the capacitor. (4)
10.2.1 10.2.2 Make a sketch of your design and indicate the dimensions of the capacitor on the sketch. (4)
10.2.2 10.2.3 What change will you make to your design, still using all the supplied materials, to change the capacitance of the capacitor to 100pF?
10.2.3 Double the distance between the plates / Increase the distance between the plates to 8,86 mm 

10.3 Supercapacitors (capacitors of 1 farad and more) are well suited to replace batteries in many applications. This is because their scale is comparable to that of batteries at the moment, from small ones used in cellular phones to large ones that can be found in cars. Even though supercapacitors have a lower energy density compared to batteries, they avoid many of the disadvantages of batteries.

10.3.1 Compare the way in which capacitors and batteries store energy. (2)
10.3.1 Batteries store energy in chemical reactions
Capacitors store energy in electric fields

10.3.2 Name ONE disadvantage of batteries when disposed of in the environment. (1)
10.3.2 Any one:
Chemicals e.g. acid or heavy metals can leach into soil and groundwater.
Plastic casings can pollute environment.

10.3.3 The following statement appears in an advertisement of a certain type of battery:

'Capacitors cannot function without batteries - they need a source of energy. On the other hand, batteries don't need capacitors.'

Briefly explain why this is a valid statement.
10.3.3 Capacitors need a source of energy e.g. batteries to obtain charge.
 Batteries produce their own energy (electricity) from chemical reactions inside the battery. 