1.
A battery of internal resistance 2 Ω is connected to an external resistance of 10 Ω. The current is
0.5 A.
What is the emf of the battery?
A.
1.0 V
B.
5.0 V
C.
6.0 V
D.
24.0 V
(Total 1 mark)
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2.
In the circuit below, which of the following will cause the greatest increase in the reading of the
voltmeter?
A.
An increase in temperature
B.
An increase in light intensity
C.
A decrease in temperature
D.
A decrease in light intensity
(Total 1 mark)
3.
This question is about electric circuits.
(a)
Define
(i)
electromotive force (emf ) of a battery.
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(1)
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(ii)
electrical resistance of a conductor.
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(1)
(b)
A battery of emf ε and negligible internal resistance is connected in series to two
resistors. The current in the circuit is I.
(i)
State an equation giving the total power delivered by the battery.
...........................................................................................................................
(1)
(ii)
The potential difference across resistor R1 is V1 and that across resistor R2 is V2.
Using the law of the conservation of energy, deduce the equation below.
ε = V1 + V2
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(2)
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(c)
The graph shows the I-V characteristics of two conductors, X and Y.
On the axes below, sketch graphs to show the variation with potential difference V of the
resistance of conductor X (label this graph X) and conductor Y (label this graph Y).
You do not need to put any numbers on the vertical axis.
(3)
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(d)
The conductors in (c) are connected in series to a battery of emf ε and negligible internal
resistance.
The power dissipated in each of the two resistors is the same.
Using the graph given in (c),
(i)
determine the emf of the battery.
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...........................................................................................................................
...........................................................................................................................
(2)
(ii)
calculate the total power dissipated in the circuit.
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(2)
(Total 12 marks)
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4.
Two electrodes, separated by a distance d, in a vacuum are maintained at a constant potential
difference. An electron, accelerated from one electrode to the other, gains kinetic energy Ek.
1
The distance between the electrodes is now changed to d.
3
What is the gain in kinetic energy of an electron that is accelerated from one electrode to the
other?
A.
Ek
3
B.
Ek
C.
3 Ek
D.
9 Ek
(Total 1 mark)
5.
The graph shows the I–V characteristics of two resistors.
When resistors X and Y are connected in series, the current in the resistors is 2.0 A. What is the
resistance of the series combination of X and Y?
A.
7.0 Ω
B.
1.3 Ω
C.
1.1 Ω
D.
0.14 Ω
(Total 1 mark)
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6.
This question is about electrical resistance.
(a)
A resistor of resistance 1.5 Ω is made from copper wire of radius 0.18 mm. The resistivity
of copper is 1.7 × 10–8 Ω m. Determine the length of copper wire used to make the
resistor.
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......................................................................................................................................
......................................................................................................................................
(2)
(b)
The manufacturer of the resistor in (a) guarantees that the resistance is within 10 % of 1.5
Ω , provided that the power dissipation in the resistor does not exceed 1.0 W.
(i)
Suggest why the resistance of the resistor might be greater than 1.65 Ω if the power
dissipation in the resistor is greater than 1.0 W.
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...........................................................................................................................
(2)
(ii)
Show that, for a power dissipation of 1.0 W, the current in a resistor of resistance
1.5 Ω is 0.82 A.
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(1)
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(iii)
The 1.5 Ω resistor is connected in series with a variable resistor and battery of emf
6.0 V and internal resistance 1.8 Ω.
Estimate the resistance R of the variable resistor that will limit the current to
0.82 A.
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(3)
(Total 8 marks)
7.
This question is about electric circuits
The components shown below are to be connected in a circuit to investigate how the current I in
a tungsten filament lamp varies with the potential difference V across it.
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(a)
Construct a circuit diagram to show how these components should be connected together
in order to obtain as large a range as possible for values of potential difference across the
lamp.
(4)
(b)
On the axes, sketch a graph of I against V for a filament lamp in the range V = 0 to its
normal working voltage.
(2)
(c)
The lamp is marked with the symbols “1.25 V, 300 mW”. Calculate the current in the
filament when it is working normally.
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......................................................................................................................................
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(1)
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(d)
The resistivity of tungsten at the lamp’s working temperature is 4 × 10–7 Ωm. The total
length of the tungsten filament is 0.80 m. Estimate the radius of the filament.
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(4)
(e)
The cell is connected to two identical lamps connected in parallel. The lamps are rated at
1.25 V, 300 mW. The cell has an emf of 1.5 V and an internal resistance of 1.2 Ω.
Determine whether the lamps will light normally.
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(4)
(Total 15 marks)
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8.
This question is about an electrical heater.
An electrical heater consists of two heating elements E1 and E2. The elements are connected in
parallel. Each element has a switch and is connected to a supply of emf 240 V. The supply has
negligible internal resistance.
Element E1 is made from wire that has a cross-sectional area of 6.8 × 10–8 m2. The resistivity of
the wire at the operating temperature of the element is 1.1 × 10–6 Ωm.
(a)
(i)
The total length of wire is 4.5 m. Show that the resistance of E1 is 73 Ω.
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
Calculate the power output of E1 with only this element connected to the supply.
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(2)
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(iii)
Element E2 is made of wire of the same cross-section and material as E1. The
length of wire used to make E2 is 1.5 m. Determine the total power output when
both E1 and E2 are connected to the supply.
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(3)
(iv)
With reference to the power output, explain why it would be inappropriate to
connect the heating elements in series.
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(3)
(b)
Each element in the electrical heater is wound as a coil as shown.
Each turn of the coil may be considered to act as a current-carrying long straight wire.
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(i)
On the diagram, draw the magnetic field around a current-carrying long straight
wire. The arrow shows the direction of the current.
(3)
(ii)
State and explain whether the turns of wire will attract or repel one another.
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(3)
(Total 15 marks)
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9.
This question is about an electric circuit.
A particular filament lamp is rated at 12 V, 6.0 mA. It just lights when the potential difference
across the filament is 6.0 V.
A student sets up an electric circuit to measure the I-V characteristic of the filament lamp.
In the circuit, shown below, the student has connected the voltmeter and the ammeter into the
circuit incorrectly.
The battery has emf 12 V and negligible internal resistance. The ammeter has negligible
resistance and the resistance of the voltmeter is 100 k. The maximum resistance of the
variable resistor is 15.
(a)
Explain, without doing any calculations, whether there is a position of the slide S at
which the lamp will be lit.
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...................................................................................................................................
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(3)
(b)
Estimate the maximum reading of the ammeter.
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(2)
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(c)
Complete the circuit diagram below showing the correct position of the voltmeter and of
the ammeter in order to determine the I-V characteristic of the filament lamp.
(2)
(Total 7 marks)
10.
This question is about electrical resistance.
(a)
A heating coil is to be made of wire of diameter 3.5 × 10–4 m. The heater is to dissipate
980 W when connected to a 230 V d.c. supply. The material of the wire has resistivity
1.3 × 10–6 Ω m at the working temperature of the heater.
(i)
Define electrical resistance.
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
Calculate the resistance of the heating coil at its normal working temperature.
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(2)
(iii)
Show that the length of wire needed to make the heating coil is approximately 4 m.
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(2)
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(b)
Three identical electrical heaters each provide power P when connected separately to a
supply S which has zero internal resistance. On the diagram below, complete the circuit
by drawing two switches so that the power provided by the heaters may be either P or 2P
or 3P.
(2)
(Total 7 marks)
11.
This question is about electric fields and electric circuits.
(a)
Two parallel, charged metal plates A and B are in a vacuum.
At a particular instant an electron is at point P.
On the diagram, draw
(i)
the electric field pattern due to the plates.
(3)
(ii)
an arrow to represent the direction of the force on the electron at P.
(1)
(b)
The acceleration of the electron at P is 8.8 × 1014 m s–2. Determine the magnitude of the
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electric field strength at the point P.
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(3)
(c)
The electric potential energy of the electron changes by 1.9 × 10–17 J as it moves from
one plate to the other. Show that the potential difference between the plates is 120 V.
......................................................................................................................................
......................................................................................................................................
(1)
(d)
A resistor R and a filament lamp L are connected in series with a battery. The battery has
an emf of 12 V and internal resistance 4.0 Ω. The potential difference across the filament
of the lamp is 3.0 V and the current in the filament is 0.25 A.
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(i)
Define emf and describe the concept of internal resistance.
emf:
...........................................................................................................................
...........................................................................................................................
Internal resistance:
...........................................................................................................................
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(2)
(ii)
Calculate the total power supplied by the battery.
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(1)
(iii)
Calculate the power dissipated in the external circuit.
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...........................................................................................................................
(2)
(iv)
Determine the resistance of the resistor R.
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(3)
(Total 16 marks)
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12.
(a)
Draw the complete diagram of the circuit that uses a potential divider, ammeter, voltmeter
and cell to measure the current-voltage characteristics for component X.
(3)
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(b)
The graph shows the current-voltage characteristics for the component X.
Component X is now connected across the terminals of a cell of emf 2.0 V and negligible
internal resistance. Use the graph to show that the resistance of X is 0.83 Ω.
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(2)
(c)
A resistor of constant resistance 1.0 Ω is connected in series with the cell in (b) and with
X. Use the graph to deduce that the current in the circuit is 1.3 A.
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(3)
(Total 8 marks)
13.
This question is about electrical resistance and electric circuits.
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(a)
Define resistance and state Ohm’s law.
Resistance: ...................................................................................................................
......................................................................................................................................
Ohm’s law: ..................................................................................................................
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(2)
(b)
A resistor made from a metal oxide has a resistance of 1.5 Ω. The resistor is in the form
of a cylinder of length 2.2 × 10–2 m and radius 1.2 × 10–3 m. Calculate the resistivity of
the metal oxide.
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......................................................................................................................................
......................................................................................................................................
(2)
(c)
The manufacturer of the resistor in (b) guarantees its resistance to be within ±10 % of
1.5 Ω provided the power dissipation in the resistor does not exceed 1.0 W. Calculate the
maximum current in the resistor for the power dissipation to be equal to 1.0 W.
......................................................................................................................................
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(2)
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(d)
The resistance of each of the resistors in the circuit below is measured to be 1.5 Ω with an
accuracy of ±10 %.
The cell has an emf of 2.0 V and negligible internal resistance.
(i)
Define emf.
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
Determine the minimum and the maximum power that could be dissipated in this
circuit.
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(3)
(Total 10 marks)
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