Syllabus Edition

First teaching 2023

First exams 2025

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Resistance & Resistivity (CIE AS Physics)

Exam Questions

3 hours71 questions
1
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1 mark

Which equation is used to define resistance?

  • energy = (current)2 × resistance × time  

  • potential difference = current × resistance

  • power = (current)2 × resistance

  • resistivity = resistance × area ÷ length

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2
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What is the unit of resistance when expressed in SI base units?

  • kg m2 s–2 A–1

  • kg m2 s–3 A–2

  • kg m s–2 A–1

  • kg m s–3 A–1

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3
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Which graph shows the IV characteristic of a filament lamp ?

cie-ial-physics-images-9-2-e-q3-

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    4
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    The resistance R of a resistor is determined by measuring the potential difference V across it and the current I in it. The value of R is then calculated using the equation

    begin mathsize 16px style R equals V over I end style

     The values measured are V = 1.00 ± 0.05 V and I  = 0.50 ± 0.01 A.

     What is the percentage uncertainty in the value of R ?

    • 2.5 %

    • 3.0 %

    • 7.0 %

    • 10.0 %

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    5
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    The graph shows how the electric current I  through a conducting liquid varies with the potential difference V across it.

     At which point on the graph does the liquid have the smallest resistance?

    cie-ial-images449png

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      6
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       The graphs show the variation with potential difference V of the current I for three circuit components.

      cie-ial-images451png

      The components are a metal wire at constant temperature, a semiconductor diode and a filament lamp.

       Which row of the table correctly identifies these graphs?

       

       

      Metal wire at constant temperature

      Semiconductor diode

      Filament lamp

      A

      B

      C

      D

      X

      Y

      Y

      Z

      Z

      X

      Z

      X

      Y

      Z

      X

      Y

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        7
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        What is a correct statement of Ohm's Law?

        • the potential difference across a component equals the current providing the resistance and other physical conditions stay constant

        • the potential difference across a component equals the current multiplied by the resistance

        • the potential difference across a component is proportional to its resistance.

        • the potential difference across a component is proportional to the current in it providing physical conditions stay constant

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        8
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        The graphs show possible current-voltage (I–V) relationships for a filament lamp and a semiconductor diode.

        cie-ial-images452png

        Which row best specifies the correct I–V graphs for the lamp and the diode?

         

         

        Filament lamp

        Semiconductor diode

        A

        B

        C

        D

        P

        P

        Q

        Q

        R

        S

        R

        S

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          9
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          An electrical component has a potential difference V across it and a current I  through it. A graph of I against V is drawn and is marked in three sections WX, XY and YZ.

          cie-ial-images453png

          In which ways does the resistance of the component vary within each of the three sections?

           

           

          WX

          XY

          YZ

          A

          B

          C

          D

          constant

          constant

          increases

          increases

          decreases

          increases

          decreases

          increases

          increases

          increases

          constant

          decreases

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            10
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            The graph shows the variation with potential difference (p. d.) of the current in a lamp filament.

            cie-ial-images455png

            Which statement explains the shape of this graph?

            • as the filament temperature rises, electrons can pass more easily through the filament

            • it takes time for the filament to reach its working temperature

            • the power output of the filament is proportional to the square of the current in it

            • the resistance of the filament increases with a rise in temperature

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            11
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            The unit of resistivity, expressed in terms of base units, is given by                                            

                         kg space straight x cubed space straight y to the power of negative 2 space end exponent straight z to the power of negative 3 end exponent         

            Which base units are x, y and z ?

             

            x

            y

            z

            A

            B

            C

            D

            ampere

            metre

            metre

            second

            metre

            ampere

            second

            ampere

            second

            second

            ampere

            metre

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              12
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              A cylindrical wire of length 10 m and diameter 2.0 mm has a resistance of 0.050 Ω.

               From which material is the wire made?

               

              Material

              Resistivity / Ω m

              A

              bronze

              1.6 × 10–7

              B

              nichrome

              1.6 ×10–6

              C

              silver

              1.6 × 10–8

              D

              zinc

              6.3 × 10–8

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                13
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                The resistance of one device R1 is designed to change with temperature; the resistance of another device R2 is designed to change with illumination.

                 What are the names of these devices ?

                 

                R1

                R2

                A

                thermistor 

                light-dependent resistor

                B

                thermistor

                potential divider

                C

                semiconductor diode 

                light-dependent resistor

                D

                semiconductor diode 

                potential divider

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                  14
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                  A light-dependent resistor (LDR) is connected in series with a resistor R and a battery.

                  cie-ial-images498png

                  The resistance of the LDR is equal to the resistance of R when no light falls on the LDR. When the light intensity falling on the LDR increases, which statement is correct?

                  • the current in R decreases

                  • the current through the LDR decreases

                  • the p. d. across R decreases

                  • the p .d. across the LDR decreases

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                  15
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                  A copper wire is stretched so that its diameter is reduced from 1.0 mm to a uniform 0.5 mm. The resistance of the unstretched copper wire is 0.2 Ω.

                  What is the resistance of the stretched wire?

                  • 0.4 Ω

                  • 0.8 Ω

                  • 1.6 Ω

                  • 3.2 Ω

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                  16
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                  Which graph best represents the way in which the current I through a thermistor depends upon the potential difference V across it ?

                  cie-ial-physics-images-9-3-e-q6

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                    17
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                    A power cable has length 2000 m. The cable is made of twelve parallel strands of copper wire, each with diameter 0.51 mm.

                     What is the resistance of the cable ? (resistivity of copper = 1.7 × 10–8 Ω m)

                    • 0.014 Ω

                    • 3.5 Ω

                    • 14 Ω

                    • 166 Ω

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                    18
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                    A circuit is set up with an LDR and a fixed resistor as shown.

                     cie-ial-images504png

                    The voltmeter reads 4 V.

                    The light intensity is increased.

                     What is a possible voltmeter reading?

                    • 3V

                    • 4V

                    • 6V

                    • 8V

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                    19
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                    A cylindrical wire 4.0 m long has a resistance of 31 Ω and is made of metal of resistivity 1.0 × 10–6 Ω m.

                     What is the radius of cross-section of the wire?

                    • 1.0 × 10–8 m

                    • 2.0 × 10–8 m

                    • 6.4 × 10–8 m

                    • 2.0 × 10–4 m

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                    20
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                    When a thin metal wire is stretched, it becomes longer and thinner. This causes a change in the resistance of the wire. The volume of the wire remains constant.

                     Which graph could represent the variation with extension x of the resistance R of the wire ?

                    cie-ial-physics-images-9-3-e-q10

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                      1
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                      The graph shows how current I varies with voltage V for a filament lamp.

                      cie-ial-images456png

                      Since the graph is not a straight line, the resistance of the lamp varies with V.

                       Which row gives the correct resistance at the stated value of V?

                       

                       

                      V / V

                      R / Ω

                      A

                      B

                      C

                      D

                      2.0

                      4.0

                      6.0

                      8.0

                      1.5

                      3.2

                      1.9

                      0.9

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                        2
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                        A charge of 8.0 C passes through a resistor of resistance 30 Ω at a constant rate in a time of 20 s.

                         What is the potential difference across the resistor?

                        • 0.40 V

                        • 5.3 V

                        • 12 V

                        • 75 V

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                        3
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                        The I -V characteristics of two electrical components P and Q are shown below.

                        cie-ial-images457png

                        Which statement is correct ?

                        • P is a resistor and Q is a filament lamp

                        • the resistance of Q increases as the current in it increases

                        • for a current of 1.9 A, the resistance of Q is approximately half that of P

                        • for a current of 0.5 A, the power dissipated in Q is double that in P

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                        4
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                        The resistance R of a resistor is to be determined. The current I in the resistor and the potential difference V across it are measured.

                         The results, with their uncertainties, are

                                          I = (2.0 ± 0.2) A                     V = (15.0 ± 0.5) V

                         What is the uncertainty in this value for R ?

                        • ± 0.3 Ω

                        • ± 0.5 Ω

                        • ± 0.7 Ω

                        • ± 1 Ω

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                        5
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                        The variation with potential difference V of the current I in a semiconductor diode is shown below.

                        cie-ial-images458png

                        What is the resistance of the diode for applied potential differences of +1.0 V and –1.0 V ?

                         

                         

                        Resistance

                        at +1.0 V

                        at –1.0 V

                        A

                        B

                        C

                        D

                        20 Ω

                        20 Ω

                        0.05 Ω

                        0.05 Ω

                        infinite

                        zero

                        infinite

                        zero

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                          6
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                          A battery of negligible internal resistance is connected to two 10 Ω resistors in series.

                          cie-ial-images459png

                          What charge flows through each of the 10 Ω resistors in 1 minute?

                          • 0.30 C

                          • 0.60 C

                          • 3.0 C

                          • 18 C

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                          7
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                          Two heating coils X and Y, of resistance RX and RY respectively, deliver the same power when 12 V is applied across X and 6 V is applied across Y.

                           What is the ratio R subscript X over R subscript Y  ?

                          • 1 fourth

                          • 1 half

                          • 2

                          • 4

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                          8
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                          A student found two unmarked resistors. To determine the resistance of the resistors, the circuit below was set up. The resistors were connected in turn between P and Q, noting the current readings.

                           The voltage readings were noted without the resistors and with each resistor in turn.

                          cie-ial-images460png

                          The results were entered into a spreadsheet, as shown.

                          1.5

                          1.3

                          28

                          46

                          1.5

                          1.4

                          14

                          100

                          The student forgot to enter the column headings.

                           Which order of the headings would be correct?

                          A

                          e.m.f / V

                          V / V

                          R / Ω

                          I / mA

                          B

                          V / V

                          e.m.f / V

                          R / Ω

                          I / mA

                          C

                          V / V

                          e.m.f / V

                          I / mA

                          R / Ω

                          D

                          e.m.f / V

                          V / V

                          I / mA

                          R / Ω

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                            9
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                            A 2 Ω resistor and a 4 Ω resistor are connected to a cell.

                            cie-ial-images461png

                            Which graph shows how the potential V varies with distance between X and Y ?

                            cie-ial-physics-images-9-2-m-q9

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                              10
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                              The diagram shows a length of track from a model railway connected to a battery, a resistor and a relay coil.

                              cie-ial-images466png

                              With no train present, there is a current in the relay coil which operates a switch to turn on a light.

                               When a train occupies the section of track, most of the current flows through the wheels and axles of the train in preference to the relay coil. The switch in the relay turns off the light.

                               Why is a resistor placed between the battery and the track?

                              • to limit the heating of the wheels of the train

                              • to limit the energy lost in the relay coil when a train is present

                              • to prevent a short circuit of the battery when a train is present

                              • to protect the relay when a train is present

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                              11
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                              Two wires P and Q made of the same material are connected to the same electrical supply.

                               P has twice the length of Q and one-third of the diameter of Q, as shown in the diagram.

                              cie-ial-images509png

                              What is the ratio  fraction numerator c u r r e n t space i n space P over denominator c u r r e n t space i n space Q end fraction ?

                              • 2 over 3

                              • 2 over 9

                              • 1 over 6

                              • 1 over 18

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                              12
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                              In the circuit below, the reading VT on the voltmeter changes from high to low as the temperature of the thermistor changes. The reading VL on the voltmeter changes from high to low as the level of light on the light-dependent resistor (LDR) changes.

                              cie-ial-images510png

                              The readings VT and VL are both high.

                               What are the conditions of temperature and light level ?

                               

                              Temperature

                              Light level

                              A

                              B

                              C

                              D

                              low

                              low

                              high

                              high

                              low

                              high

                              low

                              high

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                                13
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                                In a fire alarm system, a thermistor T has a resistance of 2000 Ω at room temperature. Its resistance decreases as the temperature increases. The alarm is triggered when the potential difference between X and Y reaches 4.5 V.

                                cie-ial-images511png

                                What is the resistance of the thermistor when the alarm is triggered ?

                                • 90 Ω

                                • 150 Ω

                                • 250 Ω

                                • 1300 Ω

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                                14
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                                Two electrically-conducting cylinders X and Y are made from the same material.

                                Their dimensions are as shown.

                                cie-ial-images512png

                                The resistance between the ends of each cylinder is measured.

                                 What is the ratio fraction numerator r e s i s tan c e space o f space X over denominator r e s i s tan c e space o f space Y end fraction ?

                                • 2 over 1

                                • 1 over 1

                                • 1 half

                                • 1 fourth

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                                15
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                                The graph shows the variation with length l of resistance R for two wires X and Y made from the same material.

                                cie-ial-images513png

                                What does the graph show?

                                • cross-sectional area of X = 2 × cross - sectional area of Y

                                • resistivity of X = 2 × resistivity of Y

                                • when equal lengths of X and Y are connected in series to a battery, power in X = 2 × power in Y

                                • when equal lengths of X and Y are connected in parallel to a battery, current in X = 2 × current in Y

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                                16
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                                A light-dependent resistor R has a resistance of about 1 MΩ in the dark and about 1 kΩ when illuminated. It is connected in series with a 5 kΩ resistor to a 1.5 V cell of negligible internal resistance.

                                cie-ial-images514png

                                The light-dependent resistor is illuminated (in an otherwise dark room) by a flashing light.

                                 Which graph best shows the variation with time t of potential difference V across R ?

                                cie-ial-physics-images-9-3-m-q6

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                                  17
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                                  Tensile strain may be measured by the change in electrical resistance of a strain gauge.

                                   A strain gauge consists of folded fine metal wire mounted on a flexible insulating backing sheet.

                                   The strain gauge is firmly attached to the specimen, so that the strain in the metal wire is always identical to that in the specimen.

                                  cie-ial-images519png

                                  When the strain in the specimen is increased, what happens to the resistance of the wire?

                                  • it decreases, because the length decreases and the cross-sectional area increases

                                  • it decreases, because the length increases and the cross-sectional area decreases

                                  • it increases, because the length decreases and the cross-sectional area increases

                                  • it increases, because the length increases and the cross-sectional area decreases

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                                  18
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                                  The resistance of a thermistor depends on its temperature, and the resistance of a light-dependent resistor (LDR) depends on the illumination.

                                   Under which conditions will the resistance of both a thermistor and an LDR be highest ?

                                   

                                  Thermistor

                                  LDR

                                  A

                                  B

                                  C

                                  D

                                  highest temperature

                                  highest temperature

                                  lowest temperature

                                  lowest temperature

                                  highest illumination

                                  lowest illumination

                                  highest illumination

                                  lowest illumination

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                                    19
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                                    A researcher has two pieces of copper of the same volume. All of the first piece is made into a cylindrical resistor P of length x.

                                    cie-ial-images520png

                                    All of the second piece is made into uniform wires each of the same length x which he connects between two bars of negligible resistance to form a resistor Q.

                                    cie-ial-images521png

                                    How do the electrical resistances of P and Q compare ?

                                    • P has a larger resistance than Q

                                    • Q has a larger resistance than P

                                    • P and Q have equal resistance

                                    • Q may have a larger or smaller resistance than P, depending on the number of wires made

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                                    20
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                                    Two wires have the same length and the same resistance. Wire X is made of a metal of resistivity 1.7 × 10–8 Ωm, and wire Y is made of a metal of resistivity 5.6 × 10–8 Ωm.

                                     The diameter of wire X is 0.315 mm.

                                     What is the diameter of wire Y?

                                    • 0.17 mm

                                    • 0.33 mm

                                    • 0.57 mm

                                    • 1.0 mm

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                                    1
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                                    The diagram shows an electric pump for a garden fountain connected by an 18 m cable to a 230 V mains electrical supply.

                                    cie-ial-images467png

                                    The performance of the pump is acceptable if the potential difference (p.d.) across it is at least 218 V. The current through it is then 0.83 A.

                                     What is the maximum resistance per meter of each of the two wires in the cable if the pump is to perform acceptably?

                                    • 0.40 Ω m–1

                                    • 0.80 Ω m–1

                                    • 1.3 Ω m–1

                                    • 1.4 Ω m–1

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                                    2
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                                    The graph below shows the variation of the current I through a lamp with potential difference V across it.

                                    cie-ial-images468png

                                    Which of the following graphs best represents the variation of power P dissipated in the same lamp with I 2 ?

                                    cie-ial-physics-images-9-2-h-q2

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                                      3
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                                      Circuit contains three identical lamps A, B and C. Circuit also contains three switches, S1, S2 and S3, as shown.

                                      cie-ial-images473png

                                      One of the lamps is faulty. In order to detect the fault, an ohm-meter is connected between terminals X and Y.

                                       When measuring resistance, the ohm-meter causes negligible current in the circuit. Readings of the ohm-meter for different switch positions are shown in the table.

                                      Switch

                                      Meter reading / Ω

                                      S1

                                      S2

                                      S3

                                      open

                                      closed

                                      open

                                      open

                                      open

                                      open

                                      closed

                                      closed

                                      open

                                      open

                                      open

                                      closed

                                      15

                                      30

                                      15

                                      Which lamps are faulty?

                                      • A & B

                                      • B only

                                      • B & C

                                      • C only

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                                      4
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                                      The current flowing through a component varies with the potential difference V across it as shown.

                                      cie-ial-images474png

                                      Which graph best represents how the resistance R varies with V ?

                                      cie-ial-physics-images-9-2-h-q4

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                                        5
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                                        The circular cross-sectional area of a uniform metal wire varies along its length. There is a current in the wire. The narrow end of the wire is at a reference potential of zero.

                                        cie-ial-images479png

                                        Which graph best represents the variation with distance x along the wire of the potential difference V relative to the reference zero?

                                        cie-ial-physics-images-9-2-h-q5

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                                          6
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                                          The graph shows the I -V characteristics of a semiconductor diode

                                          cie-ial-images484png

                                          A cell of e. m .f. 1.2 V and negligible internal resistance is connected in series to a semiconductor diode and a resistor R1, as shown below

                                          cie-ial-images485png

                                          A resistor R2 of resistance 375 Ω is connected across the cell. The diode has the characteristic shown in the graph. The current supplied by the cell is 7.6 mA.

                                           What is the resistance of R1?

                                          • 82 Ω

                                          • 114 Ω

                                          • 160 Ω

                                          • 260 Ω

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                                          7
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                                          The graph shows how the current I varies with potential difference V for an electrical component.

                                          9-2-q27-cie-ial-physics-mcq-h

                                          Which row of the table gives the resistance of the component at V2 and describes how the resistance changes from V1 to V2 ?

                                           

                                          Resistance at V2

                                          Change in resistance from V1 to V2

                                          A

                                          fraction numerator V subscript 2 minus V subscript 1 over denominator I subscript 2 minus I subscript 1 end fraction 

                                          increases

                                          B

                                          fraction numerator V subscript 2 minus V subscript 1 over denominator I subscript 2 minus I subscript 1 end fraction 

                                          decreases

                                          C

                                          V subscript 2 over I subscript 2 

                                          increases

                                          D

                                           V subscript 2 over I subscript 2

                                          decreases

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                                            8
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                                            The graph shows the relationship between potential difference V and current I for a fixed 20 Ω resistor and a filament lamp.

                                            cie-ial-images487png

                                            The resistor and lamp are placed in series with a 9 V battery of negligible internal resistance. What is the current in the circuit ?

                                            • 0.1 A

                                            • 0.2 A

                                            • 0.3 A

                                            • 0.4 A

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                                            9
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                                            The graphs show the I -V characteristics for a metal conductor and a thermistor

                                            cie-ial-images490png

                                            What is the ratio fraction numerator r e s i s tan c e space o f space t h e r m i s t o r space a t space p o i n t space A over denominator r e s i s tan c e space o f space m e t a l space c o n d u c t o r end fraction  ?

                                            • 2 over 5

                                            • 1 half

                                            • 2 over 1

                                            • 5 over 2

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                                            10
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                                            1 mark

                                            One style of light bulb, very different from the "incandescent" design which works on the principle of a super-heated wire filament emitting light, is called a gas discharge tube.

                                             In this design of light bulb, light is produced by the direct excitation of gas molecules as electric current passes between two electrodes.

                                            cie-ial-images492png

                                            What will the I - V graphs of these bulbs look like?

                                            cie-ial-physics-images-9-2-h-q10

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                                              11
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                                              1 mark

                                              A thermistor and another component are connected to a constant voltage supply. A voltmeter is connected across one of the components. The temperature of the thermistor is then reduced, but no other changes are made.

                                               In which circuit will the voltmeter reading increase ?

                                              cie-ial-physics-images-9-3-h-q1

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                                                12
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                                                1 mark

                                                A copper wire is to be replaced by an aluminum alloy wire of the same length and resistance.

                                                 Copper has half the resistivity of the alloy.

                                                 What is the ratio  fraction numerator d i a m e t e r space o f space a l l o y space w i r e over denominator d i a m e t e r space o f space c o p p e r space w i r e end fraction  ?

                                                • square root of 2

                                                • 2

                                                • square root of 2

                                                • 4

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                                                13
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                                                1 mark

                                                The current in a block of semiconductor is 30.0 mA when there is a potential difference (p.d.) of 10.0 V across it. The dimensions of the block and the direction of the current in it are as shown.

                                                cie-ial-images526png

                                                The electrical meters used are accurate to ± 0.1 mA and ± 0.1 V. The dimensions of the block are accurate to ± 0.2 mm.

                                                 What is the resistivity of the semiconductor?

                                                • 10.0 ± 0.2 Ω m

                                                • 10.0 ± 0.3 Ω m

                                                • 10.0 ± 0.5 Ω m

                                                • 10.0 ± 0.8 Ω m

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                                                14
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                                                1 mark

                                                The resistance of a metal cube is measured by placing it between two parallel plates, as shown.


                                                cie-ial-images527png

                                                The cube has volume V and is made of a material with resistivity ρ. The connections to the cube have negligible resistance.

                                                Which expression gives the electrical resistance of the metal cube between X and Y? 

                                                • rho V to the power of 1 third end exponent

                                                • rho V to the power of 2 over 3 end exponent

                                                • rho over V to the power of 1 third end exponent

                                                • rho over V to the power of 2 over 3 end exponent

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                                                15
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                                                1 mark

                                                A wire PQ is made of three different materials, with resistivities ρ, 2ρ and 3ρ. There is a current I in this composite wire, as shown.

                                                cie-ial-images528png

                                                Which graph best shows how the potential V along the wire varies with distance x from P ?

                                                cie-ial-images529png

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                                                  16
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                                                  1 mark

                                                  A strain gauge consists of a length of wire with a uniform cross-sectional area. Its resistance is 2.50 kΩ. It is attached to a large pipe.

                                                   When the pipe expands, the strain gauge changes in dimensions, such that the length increases by 4% and the diameter reduced by 1%.

                                                   What is the new resistance of the strain gauge?

                                                  • 2.60 kΩ

                                                  • 2.65 kΩ

                                                  • 2.80 kΩ

                                                  • 3.00 kΩ

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                                                  17
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                                                  1 mark

                                                  The variation with temperature of the resistance RT of a thermistor is shown on the graph.

                                                  cie-ial-images530png

                                                  The thermistor is connected into the circuit shown below.

                                                  The battery has an e. m .f. of 9.0 V and negligible internal resistance. The voltmeter has infinite resistance.

                                                  cie-ial-images531png

                                                   What is the temperature of the thermistor when the reading on the voltmeter is 4.0 V?

                                                  • 2.5 °C

                                                  • 13.0 °C

                                                  • 16.0 °C

                                                  • 24.0 °C

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                                                  18
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                                                  1 mark

                                                  A conducting liquid fills a cylinder metal case to a depth y as shown in the diagram.

                                                  cie-ial-images533png

                                                  The resistance between the case and the metal rod is

                                                  • proportional to y

                                                  • proportional to y2

                                                  • inversely proportional to y

                                                  • inversely proportional to y2

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                                                  19
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                                                  1 mark

                                                  The following strain gauge consists of a fine metal wire, so that an applied tension on the strain gauge results in changes in the length and cross-sectional area of the wire.

                                                  cie-ial-images535png

                                                  When the length of the wire is stretched by 5%, what is the percentage change in the resistance of the wire? Assume that the volume of a wire remains constant when it is stretched.

                                                  • + 5%

                                                  • – 5%

                                                  • + 10%

                                                  • – 10%

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                                                  20
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                                                  1 mark

                                                  Aluminum and copper rods are designed to have the same length and the same resistance.

                                                   The resistivity of copper is half that of aluminum, but its density is three times that of aluminum.

                                                   Determine the ratio of the mass of the aluminum rod to the mass of the copper rod.

                                                  • 1 over 6

                                                  • 2 over 3

                                                  • 3 over 2

                                                  • 6 over 1

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