P2 Revision Booklet

Circuits

Harder (Grade B-A*)

Q1.          (a)     The resistance of a 24 W, 12 V filament lamp depends on the current flowing through the lamp. For currents up to 0.8 A, the resistance has a constant value of 2.5 Ω.
(i)      Use the equation in the box to calculate the potential difference across the lamp when a current of 0.8 A flows through the lamp.
 
potential difference    =    current    ×    resistance	

Show clearly how you work out your answer.
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             Potential difference = ............................................................ V
(2)

(ii)     When the potential difference across the lamp is 12 V, the current through the lamp is 2 A.
On the axes below, draw a current–potential difference graph for the filament lamp over the range of potential difference from 0 to 12 volts.

(2)

(iii)    Why does the resistance of the lamp change when the current through the lamp exceeds 0.8 A?
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(1)

(b)     The lamp is now included in a circuit. The circuit is switched on for 2 minutes. During this time, 72 coulombs of charge pass through the lamp.

Use the equation in the box to calculate the energy transformed by the lamp while the circuit is switched on.
 
energy transformed    =    potential difference    ×    charge	

Show clearly how you work out your answer.
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            Energy transformed = ............................................................ J
(2)
(Total 7 marks)
 Q2.         The graph shows how the electric current through a 12 V filament bulb varies with the potential difference across the bulb.

(a)     What is the meaning of the following terms?
electric current
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potential difference
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(2)

(b)     The resistance of the metal filament inside the bulb increases as the potential difference across the bulb increases.
Explain why.
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(3)

(c)     Use data from the graph to calculate the rate at which the filament bulb transfers energy, when the potential difference across the bulb is 6 V.
Use the correct equation from the Physics Equations Sheet.
Show clearly how you work out your answer.
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                                       Rate of energy transfer = ................................... W
(2)
(Total 7 marks)
Q3.The picture shows an electric bicycle. The bicycle is usually powered using a combination of the rider pedalling and an electric motor.

(a)     A 36 volt battery powers the electric motor. The battery is made using individual 1.2 volt cells.
(i)      Explain how a 36 volt battery can be produced using individual 1.2 volt cells.
To gain full marks, you must include a calculation in your answer.
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(2)

(ii)     The battery supplies a direct current (d.c.).
What is a direct current (d.c.)?
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(1)

(iii)    When fully charged, the battery can deliver a current of 5 A for 2 hours. The battery is then fully discharged.
Use the equation in the box to calculate the maximum charge that the battery stores.
 
charge    =    current    ×    time	

Show clearly how you work out your answer and give the unit.
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                       Charge stored = ............................................................
(3)

(b)     When powered only by the electric motor, the bicycle can carry a 90 kg rider at a maximum speed of 6 m/s. Under these conditions, the maximum distance that the bicycle can cover before the battery needs recharging is 32 km.
The bicycle has a mass of 30 kg.
(i)      Use the equation in the box to calculate the maximum kinetic energy of the bicycle and rider when the rider is not pedalling.
 
kinetic energy   =      ×   mass   ×   speed2	

Show clearly how you work out your answer.
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                     Kinetic energy = ............................................................ J
(2)

(ii)     The bicycle can be fitted with panniers (bags) to carry a small amount of luggage.
What effect would fitting panniers and carrying luggage have on the distance the bicycle can cover before the battery needs recharging?
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Give a reason for your answer.
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(2)
(Total 10 marks)
 Q4.          A set of lights consists of 20 lamps connected in series to the 230 V mains electricity supply.

(a)     When the lights are switched on and working correctly, the current through each lamp is 0.25 A.
(i)      What is the total current drawn from the mains supply?
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(1)

(ii)     Use the equation in the box to calculate the charge passing through one of the lamps in 5 minutes.
 
charge    =    current    ×    time	

Show clearly how you work out your answer and give the unit.
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                                     Total charge = ..................................................
(3)

(b)     One of the lamps in the set is a fuse lamp. This contains a filament which melts if a fault occurs. A short time after the lights are switched on, a fault causes the filament inside the fuse lamp to melt and all the lamps go out.
The householder cannot find another fuse lamp so connects a piece of aluminium foil across the contacts inside the fuse lamp holder.
When switched on, the nineteen remaining lamps work.
What the householder has done is dangerous.
Explain why.
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(2)
(Total 6 marks)
Q5.          A set of Christmas tree lights is made from twenty identical lamps connected in series.

(a)     Each lamp is designed to take a current of 0.25 A. The set plugs directly into the 230 V mains electricity supply.
(i)      Write down the equation that links current, potential difference and resistance.
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(1)

(ii)     Calculate the resistance of one of the lamps. Show clearly how you work out your final answer and give the unit.
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Resistance = ......................................................................
(4)

(iii)     What is the total resistance of the set of lights?
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Total resistance = ........................................................
(1)

(b)     How does the resistance of a filament lamp change as the temperature of the filament changes?
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(1)
(Total 7 marks)
 Q6.          The diagram shows a type of electric immersion heater in a hot water tank. These hot water tanks are normally found in airing cupboards.

          Information on the immersion heater states:
                                        230 V
10 A

(a)     (i)      What is the equation which shows the relationship between power, current and voltage?
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(1)

(ii)     Calculate the power of the heater. Show clearly how you get to your answer and give the units.
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Power = ......................................................
(2)

(b)     (i)      What rating of fuse should be in the immersion heater circuit?
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(1)

(ii)     There are three wires in the cable to the immersion heater. Two of the wires are connected to the immersion heater. The third wire is connected to the copper tank.
         Explain the function of this third wire and the fuse in the circuit.
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(3)

(c)     (i)      What is the equation which shows the relationship between resistance, current and voltage?
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(1)

(ii)     Calculate the resistance of the heater. Show clearly how you get to your answer and give the units.
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Resistance = ....................................................
(2)
(Total 10 marks)
 Q7.          When a mains lamp is switched on it takes 0.5 seconds for the filament to reach its normal operating temperature. The way in which the current changes during the first second after switching on is shown in the sketch graph below. Mains voltage is 240 V.

(a)     Calculate the resistance of the filament whilst the lamp is drawing the maximum current.
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(3)

(b)     Describe how the resistance of the lamp changes after the current has reached its maximum value.
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(2)

(c)     Calculate the maximum power taken by the lamp.
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(2)

(d)     Calculate the power of the lamp in normal use.
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(2)

(e)     Calculate the energy used by the lamp in six hours of normal use.
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(3)
(Total 12 marks)
 Q8.          The circuit diagram below shows a circuit used to supply electrical energy to the two headlights of a car.

          The current through the filament of one car headlight is 3.0 A. The potential difference across each of the two headlights is 12 V.

(a)     Suggest a suitable fuse for the circuit.  ..............................................
(1)

(b)     Calculate the resistance of the headlight filament when in use.
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Answer ............................. W
(2)

(c)     Calculate the power supplied to the two headlights of the car.
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Answer ............................ W
(2)

(d)     The fully charged car battery can deliver 72 kJ of energy at 12 V. How long can the battery keep the headlights fully on?
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Answer .............................. s
(2)
(Total 7 marks)

 

Q9.          The diagram below shows how one type of fuel gauge in a car works. A sliding contact makes contact with a resistance wire wound in a coil (rheostat). It is connected to a float via a pivot P. When the petrol level changes the circuit resistance changes. This causes the pointer in the fuel gauge to move and show how much petrol is in the petrol tank.

          The circuit diagram is shown below.

          The petrol gauge is an ammeter. Explain why the reading on the ammeter falls as the petrol is used.
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(Total 3 marks)

 

Q10.          The diagram shows a 12 volt lighting system. Each lamp has a power of 32 watts.

(i)      Write down the equation that links current, potential difference and power.
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(1)

(ii)      Calculate the input current to the lighting system. Show clearly how you work out your answer.
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current = ........................................................................ A
(2)
(Total 3 marks)
 Circuits-Mark scheme

M1.         (a)      (i)     2
allow 1 mark for correct substitution i.e. 0.8 × 2.5 provided no further step shown
2

(ii)     straight line drawn from origin to 2, 0.8
or
their (a)(i), 0.8
1

curve from 2, 0.8 to 12,2or
their (a)(i) 0.8 to 12,2
accept curve from 2, 0.9 to 12,2
or
their (a)(i) 0.9 to 12,2
‘convex’ curve required 
accept a curve that flattens between 10 and 12V
1

(iii)    filament / lamp gets hot 
accept temperature increases
1

(b)     108
allow 1 mark for correct substitution i.e. 1.5 × 72 provided no further step shown
2
[7]
 
M2.         (a)     electric current
(rate of) flow of (electric) charge / electrons
accept 
with Q and t correctly named
1

potential difference
work done / energy transferred per coulomb of charge (that passes between two points in a circuit)
accept 
with W and Q correctly named
1

(b)     metals contain free electrons (and ions)
accept mobile for free
1

as temperature of filament increases ions vibrate faster / with a bigger amplitude
accept atoms for ions
accept ions/atoms gain energy
accept vibrate more for vibrate faster
do not accept start to vibrate 
1

electrons collide more (frequently) with the ions
or
(drift) velocity of electrons decreases
do not accept start to collide
accept increasing the p.d. increases the temperature (1 mark)
and
(and) resistance increases with temperature (1 mark) if no other marks scored
1

(c)     7.8
allow 1 mark for obtaining value 1.3 from graph
or allow 1 mark for a correct calculation using an incorrect current in the range 1.2-1.6 inclusive
2
[7]
 M3.         (a)      (i)     (connect) 30 (cells)
1

in series
1

(ii)     current always flows in the same directionorcurrent only flows one way
1

(iii)    36 000
allow 1 mark for correctly converting 2 hours to 7200 seconds 
answers 10 or 600 score 1 mark
2

coulombs / C
do not accept c
1

(b)     (i)      2160
allow 1 mark for correct substitution, ie ½ × 120 × 62
answers of 1620 or 540 score 1 mark
2

(ii)     reduce it
1

any one from:
•        draws a larger current (from battery)
•        motor draws greater power (from battery)
accept energy per second for power
accept more energy needed to move the bicycle
•        greater resistance force (to motion) / air resistance / drag / friction
accept less streamlined 
more mass to carry is insufficient
1
[10]
 M4.         (a)      (i)     0.25 (A)
1

(ii)     75
allow 1 mark for converting 5 minutes to 300 seconds
or allow 1 mark for correct substitution
ie 0.25 × 300
allow 1 mark for an answer 1.25
allow 1 mark only for their (a)(i) × 300 correctly calculated
2

coulombs or C
do not accept c
1

(b)     any two from:
•        fault not repaired
accept if a fault was to occur
•        larger current will (still) flow
•        aluminium foil will not melt (if a fault)
accept aluminium foil needs a higher current / charge to melt
•        wiring will overheat / (may) cause a fire
accept idea of fire hazard
do not accept explode etc
2
[6]

M5.          (a)     (i)      potential difference = current × resistance
accept voltage or pd for potential difference
accept V = I × R
accept correct transformation
do not accept V = C × R
do not accept V = A × R
accept  provided
 
subsequent use of Δ correct
do not accept an equation expressed in units
1

(ii)     46
credit correct transformation for 1 mark
allow 1 mark for use of 11.5 V or division of final resistance by 20
a final answer of 920 gains 2 marks only
3

         ohm(s)
accept symbol Ω
do not accept Ω s
unit / symbol mark can be awarded in (iii) provided unit / symbol is omitted in (ii)
1

(iii)     920 (ohms) or their (a)(ii) × 20
1

(b)     as temperature increases, resistance increases
accept hotter for temperature increase
do not accept a reference to resistance only i.e. it / resistance goes up
1
[7]

 

M6.          (a)     (i)      P = V × 1
or equivalent
credit a triangle if part (ii) correctly uses the relationship
credit power = volts × amps or watts V × A
do not accept C for current
1

(ii)     (P = 230 × 10 =) 2300
credit 2.3
1
         W or J/s
kW
1

(b)     (i)      15 A
credit 13 A or amps
1
(ii)     any three from
earth
         any short (to the metal tank) causes fuse to blow
fuse is in the live wire
to prevent damage to the heater
credit to stop the current
3

(c)     (i)      V = I × R
or equivalent
credit a triangle if part (ii) correctly uses the relationship
1
(ii)     (230 = 10 × R =) 23
ohms or Ω
2
[10]

 

M7.          (a)     Current = 0.4A (1) 
R = V/I or 240/0.4 (1)
R = 600 ohm (1)
3

(b)     Doubles
gets 2 marks
          OR gets bigger
gets 1 mark
2

(c)     P = V.I or 240 × 0.4
P = 96W
for 1 mark each
2

(d)     1 = 0.2A
P = 48W
for 1 mark each
BUT may get equation mark here if not in (c)
2

(e)     P = V.I.t (1)
P = 240 × 0.2 × 6 × 3600
OR P = 48 × 6 × 3600
gets 1 mark
P = 1036800 W
gets 1 mark
3
[12]
 M8.          (a)     in range 6 < I ≥ 13 A
for 1 mark
(no unit no mark)
1

(b)     4
gains 2 marks
          (else working
gains 1 mark
          (resistance of circuit correctly worked (2Ω))
2

(c)     72 (I2 R) ecf
gains 2 marks
          else working
gains 1 mark
          an answer of 36W (ie for one lamp) – (1)
2

(d)     1000 or 16.7 min (ecf from (c))
gains 2 marks
          else working
gains 1 mark
(formula with incorrect substitution – no mark (12V)
2
[7]
 M9.          level drops as petrol used;
causes circuit resistance to increase;
causes current to decrease 
for 1 mark each
          or if change not specified;
(one correct and two vague statements gains 2 marks,
three vague statements gains 1 mark)
e.g. level changes;       )
so resistance changes; ) = 1 mark
so current changes      )
[3]
 M10.          (i)      power = potential difference × current
accept voltage for potential difference
accept P = V × I
or correct transposition
accept  provided subsequent method correct
1
(ii)      8
allow 1 mark for correct substitution or transformation or an answer 2.67 / 2.7
2
[3]