B.5 Current and circuits

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Practice exam-style IB Physics questions for Current and circuits, aligned with the syllabus and grouped by topic.

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Question 1

SL • Paper 1A

Easy

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SL • Paper 1A

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The emf of a cell is best described as the

A.

energy supplied by the cell per unit charge passing through it.

B.

force exerted by the cell on each electron in the circuit.

C.

energy dissipated per second in the external circuit only.

D.

rate at which charge passes through the cell terminals.

Question 2

SL • Paper 1A

Easy

Calculator Permitted

SL • Paper 1A

Easy

Calculator Permitted

A steady direct current transfers $18\ \text{C}$ of charge through a lamp in $12\ \text{s}$ .

The current in the lamp is

A.

$6.0\ \text{A}$

B.

$216\ \text{A}$

C.

$1.5\ \text{A}$

D.

$0.67\ \text{A}$

Question 3

SL • Paper 1A

Easy

Calculator Permitted

SL • Paper 1A

Easy

Calculator Permitted

A student needs to measure the current through resistor $R$ and the potential difference across resistor $R$ .

The correct arrangement of ideal meters is

A.

A simple circuit diagram with a cell and resistor R in the main loop. Both the ammeter symbol and voltmeter symbol are drawn in separate branches connected across R. Use standard circuit symbols and equal line weight.

B.

A simple circuit diagram with a cell, an ammeter symbol in the main series loop with resistor R, and a voltmeter symbol connected in a separate parallel branch across R. Use standard circuit symbols and equal line weight.

C.

A simple circuit diagram with a cell, an ammeter symbol, a voltmeter symbol, and resistor R all connected one after another in the same single series loop. Use standard circuit symbols and equal line weight.

D.

A simple circuit diagram with a cell and resistor R. The ammeter symbol is connected in a branch directly across R. The voltmeter symbol is placed in the main series path with R. Use standard circuit symbols and equal line weight.

Question 4

SL • Paper 1A

Easy

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SL • Paper 1A

Easy

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A uniform metal wire is replaced by a wire of the same material with twice the length and half the diameter.

The resistance of the new wire is

A.

$8$ times the original resistance.

B.

$\dfrac{1}{2}$ of the original resistance.

C.

$2$ times the original resistance.

D.

$4$ times the original resistance.

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Question 5

SL • Paper 1A

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SL • Paper 1A

Easy

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A $6.0\ \Omega$ resistor and a $3.0\ \Omega$ resistor are connected in parallel across an ideal $12\ \text{V}$ cell.

The current supplied by the cell is

A.

$6.0\ \text{A}$

B.

$2.0\ \text{A}$

C.

$1.3\ \text{A}$

D.

$4.0\ \text{A}$

Question 6

HL • Paper 1A

Easy

Calculator Permitted

HL • Paper 1A

Easy

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A cell has emf $9.0\ \text{V}$ and internal resistance $1.5\ \Omega$ . It is connected to an external resistor of resistance $4.5\ \Omega$ .

The terminal potential difference of the cell is

A.

$9.0\ \text{V}$

B.

$2.25\ \text{V}$

C.

$13.5\ \text{V}$

D.

$6.75\ \text{V}$

Question 7

HL • Paper 1A

Easy

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HL • Paper 1A

Easy

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A potentiometer consists of a uniform resistance wire connected across a $12\ \text{V}$ supply. The sliding contact is one quarter of the way along the wire from the zero-potential end. The output is measured using an ideal voltmeter between the zero-potential end and the sliding contact.

The output potential difference is

A potentiometer circuit with a uniform resistance wire connected across a 12 V dc supply. A sliding contact is positioned one quarter of the distance from the zero-potential end. An ideal voltmeter is connected between the zero-potential end and the sliding contact.

A.

$0\ \text{V}$

B.

$3.0\ \text{V}$

C.

$12\ \text{V}$

D.

$6.0\ \text{V}$

Question 8

SL • Paper 2

Easy

Calculator Permitted

SL • Paper 2

Easy

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A metal wire is connected to a dc cell. A charge of $18\ \text{C}$ passes through a cross-section of the wire in $45\ \text{s}$ . In the metal, the mobile charge carriers are electrons.

State what is meant by electric current.

[1]

Calculate the current in the wire.

[1]

State the direction of electron drift compared with conventional current in the wire.

[1]

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Question 9

SL • Paper 2

Easy

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SL • Paper 2

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A lamp is connected across a $12\ \text{V}$ dc supply. The current in the lamp is $0.50\ \text{A}$ for $2.0\ \text{min}$ .

Define electric potential difference.

[1]

Determine the total energy transferred in the lamp during this time.

[2]

Calculate the power dissipated by the lamp.

[1]

Question 10

SL • Paper 1A

Medium

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SL • Paper 1A

Medium

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An LDR and a fixed resistor are connected in series across a constant dc supply. The output potential difference is measured across the fixed resistor. The resistance of the LDR decreases when the light intensity increases.

When the light intensity on the LDR increases, the output potential difference

A potential divider circuit with a dc supply, an LDR in series with a fixed resistor, and an output voltage label connected across the fixed resistor. The LDR should be drawn above the fixed resistor in a single vertical branch; no component values are shown.

A.

stays constant because the supply potential difference is constant.

B.

increases because the current through the fixed resistor increases.

C.

decreases because the fixed resistor has a smaller resistance.

D.

decreases because the total current decreases.

Question 11

HL • Paper 1A

Medium

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HL • Paper 1A

Medium

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The terminal potential difference $V$ of a cell is measured for different currents $I$ . A graph of $V$ against $I$ is a straight line with vertical intercept $6.0\ \text{V}$ and it passes through $I=2.0\ \text{A}$ , $V=5.0\ \text{V}$ .

The emf and internal resistance of the cell are

Terminal potential difference of a cell against current.

A.

$\varepsilon=6.0\ \text{V}$ , $r=2.0\ \Omega$

B.

$\varepsilon=11\ \text{V}$ , $r=0.50\ \Omega$

C.

$\varepsilon=5.0\ \text{V}$ , $r=0.50\ \Omega$

D.

$\varepsilon=6.0\ \text{V}$ , $r=0.50\ \Omega$

Question 12

HL • Paper 1A

Medium

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HL • Paper 1A

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A filament lamp is tested by varying the potential difference in both directions. The axes are $V$ on the vertical axis and $I$ on the horizontal axis. As the magnitude of the current increases, the filament becomes hotter.

The expected graph is

A.

A graph with V on the vertical axis and I on the horizontal axis, origin at the centre. A horizontal straight line lies along the I axis through the origin, with no rise in V as I changes.

B.

A graph with V on the vertical axis and I on the horizontal axis, origin at the centre. A single straight diagonal line passes through the origin from the third quadrant to the first quadrant with constant gradient.

C.

A graph with V on the vertical axis and I on the horizontal axis, origin at the centre. A smooth curve passes through the origin and lies in the first and third quadrants. The curve becomes less steep as it moves away from the origin in both directions.

D.

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Question 13

SL • Paper 2

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SL • Paper 2

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Three resistors are connected to an ideal $9.0\ \text{V}$ cell. A $6.0\ \Omega$ resistor is in series with a parallel combination of a $12\ \Omega$ resistor and a $4.0\ \Omega$ resistor.

A simple circuit diagram with an ideal cell labelled $9.0\ \text{V}$. A $6.0\ \Omega$ resistor is in series with a two-branch parallel network. One parallel branch contains a $12\ \Omega$ resistor and the other contains a $4.0\ \Omega$ resistor. Conventional current direction is indicated in the external circuit.

Calculate the equivalent resistance of the parallel combination.

[1]

Calculate the current supplied by the cell.

[1]

Determine the power dissipated in the $6.0\ \Omega$ resistor.

[1]

Compare the currents in the $4.0\ \Omega$ and $12\ \Omega$ resistors.

[1]

Question 14

SL • Paper 2

Medium

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SL • Paper 2

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A light-dependent resistor (LDR) and a fixed $2.0\ \text{k}\Omega$ resistor are connected in series across a $6.0\ \text{V}$ supply. The output potential difference $V_\text{out}$ is measured across the fixed resistor. The resistance of the LDR is $8.0\ \text{k}\Omega$ in dim light and $1.0\ \text{k}\Omega$ in bright light.

A potential-divider circuit with a $6.0\ \text{V}$ dc supply. An LDR is in series with a fixed resistor labelled $2.0\ \text{k}\Omega$. The output terminals are connected across the fixed resistor and labelled $V_\text{out}$. The diagram should clearly show which resistor is the LDR and which resistor has the output measured across it.

State how the resistance of an LDR changes as the light intensity increases.

[1]

Calculate $V_\text{out}$ in bright light.

[1]

Determine $V_\text{out}$ in dim light.

[1]

Explain, in terms of charge carriers, why the resistance of the LDR changes with illumination.

[1]

Question 15

HL • Paper 2

Medium

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HL • Paper 2

Medium

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A potentiometer consists of a uniform $100\ \text{cm}$ resistance track connected across a $9.0\ \text{V}$ supply. A slider touches the track. The output potential difference is measured between the slider and the negative terminal of the supply using a high-resistance voltmeter.

A potentiometer circuit showing a uniform resistance track connected across a $9.0\ \text{V}$ dc supply. The negative terminal is connected to one end of the track and the positive terminal to the other. A movable slider contacts the track and an output voltmeter is connected between the slider and the negative end. Distances along the track from the negative end are indicated.

Calculate the output potential difference when the slider is $35\ \text{cm}$ from the negative end of the track.

[1]

The slider is moved to $80\ \text{cm}$ from the negative end. Determine the new output potential difference.

[1]

A low-resistance device is now connected across the output terminals. Explain why the output potential difference is no longer the value calculated from the slider position alone.

[2]

Question 16

HL • Paper 2

Medium

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HL • Paper 2

Medium

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A small solar panel contains $36$ identical solar cells connected in series. In bright sunlight each cell has an emf of $0.55\ \text{V}$ . The internal resistance of the panel may be neglected. The panel is connected to an $18\ \Omega$ resistor.

Determine the total emf of the solar panel.

[1]

Calculate the current in the resistor and the power dissipated in it.

[2]

Suggest one reason why a secondary chemical cell might be included with this solar panel in a practical system.

[1]

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Question 17

SL • Paper 1B

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SL • Paper 1B

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A remote weather station requires a dc supply. Three possible energy sources are compared using measurements made over one week.

Energy source	Average current / A	Average p.d. / V
Solar-cell panel	0.75	12.0
Primary chemical cell pack	1.0	12.0
Secondary chemical cell pack	1.5	12.0

Identify the source that converts electromagnetic radiation directly into electrical energy.

[1]

Use the table to determine the average electrical power supplied by the secondary chemical cell pack.

[1]

Suggest one advantage and one limitation of using the solar-cell panel rather than the primary chemical cell pack for the weather station.

[2]

Question 18

SL • Paper 1B

Medium

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SL • Paper 1B

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A data logger measures the charge that passes through a point in a metal wire connected to a dc cell. The positive terminal of the cell is on the left of the wire.

Charge passed through a point in a wire against time.

Use the graph to determine the current in the wire.

[2]

State the charge carriers in the metal wire.

[1]

Explain why the drift direction of the charge carriers is opposite to the direction of conventional current shown.

[1]

Question 19

HL • Paper 1A

Medium

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HL • Paper 1A

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A $10\ \Omega$ resistor is connected to an ideal $12\ \text{V}$ supply. A non-ideal voltmeter of resistance $30\ \Omega$ is connected in parallel with the resistor. An ideal ammeter in series with the supply measures the total current.

The ammeter reading is

A circuit diagram with an ideal 12 V dc supply, an ideal ammeter in series in the main loop, a 10 ohm resistor as the load, and a voltmeter connected in parallel across the 10 ohm resistor. The voltmeter is labelled with resistance 30 ohm.

A.

$1.2\ \text{A}$

B.

$0.30\ \text{A}$

C.

$4.8\ \text{A}$

D.

$1.6\ \text{A}$

Question 20

HL • Paper 1A

Medium

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HL • Paper 1A

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A $4.0\ \Omega$ resistor is connected in series with a parallel combination of $6.0\ \Omega$ and $3.0\ \Omega$ resistors. The combination is connected across an ideal $12\ \text{V}$ supply.

The power dissipated in the $4.0\ \Omega$ resistor is

A circuit diagram showing a 12 V ideal dc supply connected to a 4 ohm resistor in series with a parallel network. The parallel network contains a 6 ohm resistor in one branch and a 3 ohm resistor in the other branch. The 4 ohm resistor is clearly labelled as the resistor for which power is required.

A.

$24\ \text{W}$

B.

$8.0\ \text{W}$

C.

$16\ \text{W}$

D.

$36\ \text{W}$

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Question 21

SL • Paper 2

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SL • Paper 2

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A student investigates the resistance of a uniform metal wire. The diameter of the wire is $0.64\ \text{mm}$ . The graph shows how the resistance $R$ varies with the length $L$ between the contacts.

Resistance of a metal wire plotted against length.

State why the diameter should be measured at several positions along the wire.

[1]

Use the graph to determine the resistivity of the metal.

[2]

Suggest why the current in the wire should be kept small during the investigation.

[1]

Question 22

SL • Paper 2

Medium

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SL • Paper 2

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A cell is connected to a variable resistor. For different settings of the variable resistor, the current $I$ and terminal potential difference $V$ of the cell are measured. The graph shows the variation of $V$ with $I$ .

Terminal potential difference of a cell plotted against current.

State how the emf of the cell is obtained from the graph.

[1]

Determine the internal resistance of the cell from the graph.

[1]

The emf of the cell is $1.60\ \text{V}$ . Calculate the terminal potential difference when the current is $1.5\ \text{A}$ .

[1]

Explain why the terminal potential difference is less than the emf when current flows.

[1]

Question 23

HL • Paper 2

Medium

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HL • Paper 2

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A $4.0\ \text{k}\Omega$ resistor and a $6.0\ \text{k}\Omega$ resistor are connected in series across an ideal $12\ \text{V}$ supply. A voltmeter of resistance $12\ \text{k}\Omega$ is connected across the $6.0\ \text{k}\Omega$ resistor.

A circuit diagram with an ideal $12\ \text{V}$ dc supply connected to two series resistors labelled $4.0\ \text{k}\Omega$ and $6.0\ \text{k}\Omega$. A voltmeter is connected in parallel across the $6.0\ \text{k}\Omega$ resistor and labelled with resistance $12\ \text{k}\Omega$. The diagram should make clear that the voltmeter is non-ideal.

Calculate the equivalent resistance of the $6.0\ \text{k}\Omega$ resistor and voltmeter in parallel.

[1]

Determine the reading of the voltmeter.

[2]

Explain why the reading is different from that of an ideal voltmeter connected in the same position.

[1]

Question 24

HL • Paper 2

Medium

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HL • Paper 2

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The graph shows the current-voltage characteristic of a filament lamp. The lamp is operated from a variable dc supply and measurements are taken in both current directions.

Use the graph to determine the resistance of the lamp when the current is $0.40\ \text{A}$ .

[1]

Explain the shape of the graph for positive values of current.

[2]

State why the filament lamp does not obey Ohm's law over the full range shown.

[1]

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Question 25

HL • Paper 2

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HL • Paper 2

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A cell has emf $12.0\ \text{V}$ and internal resistance $0.80\ \Omega$ . It is connected to a variable load resistor.

Calculate the current when the load resistance is $5.2\ \Omega$ .

[1]

Determine the terminal potential difference of the cell for this load resistance.

[1]

The load resistance is reduced. Explain the effect on the terminal potential difference of the cell.

[2]

Question 26

HL • Paper 2

Medium

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HL • Paper 2

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Two solid samples have the same length and cross-sectional area. One sample is copper and the other is glass. The same potential difference is applied across each sample.

Distinguish between an electrical conductor and an electrical insulator in terms of charge carriers.

[2]

Explain the microscopic origin of resistance in the copper sample.

[2]

Question 27

SL • Paper 1B

Medium

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SL • Paper 1B

Medium

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A student investigates a metal wire using an ammeter and voltmeter. The wire is kept in a water bath to reduce temperature changes.

Potential difference against current for a wire.

Determine the resistance of the wire from the graph.

[2]

State one feature of the graph that supports the conclusion that the wire is ohmic.

[1]

Explain why controlling the temperature of the wire is important when testing Ohm's law.

[1]

Question 28

SL • Paper 1B

Medium

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SL • Paper 1B

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A uniform wire is tested by measuring the resistance between one end and a movable contact. The wire has a circular cross-section.

Measured resistance against contact length for a uniform wire; diameter 0.40 mm.

State the relationship between resistance and length indicated by the graph.

[1]

Use the graph and the diameter measurement to determine the resistivity of the wire material.

[3]

Suggest why the diameter should be measured at several positions along the wire.

[1]

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Question 29

SL • Paper 1B

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SL • Paper 1B

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A circuit contains a cell and three resistors. All meters are ideal.

An annotated circuit diagram with a dc cell connected to a series resistor followed by a junction splitting into two parallel resistors. The diagram includes ideal ammeters in the main branch and in one parallel branch, and ideal voltmeters across selected components. Resistor labels and some meter readings are shown, but one branch current and one potential difference are left for students to infer.

Use the meter readings to determine the current in the unmetered parallel branch.

[1]

Determine the potential difference across each resistor in the parallel section.

[1]

Calculate the equivalent resistance of the whole external circuit.

[2]

Explain why adding a further resistor in parallel with the existing parallel section would increase the main current.

[1]

Question 30

SL • Paper 1B

Medium

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SL • Paper 1B

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A cell is connected to different external load resistors. The terminal potential difference and current are recorded.

Terminal potential difference of a cell against current for different external loads.

Determine the emf of the cell.

[1]

Determine the internal resistance of the cell.

[2]

Explain why the terminal potential difference is less than the emf when the current is not zero.

[1]

Question 31

HL • Paper 1B

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HL • Paper 1B

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A student measures the potential difference across a high-value resistor using two different voltmeters. The meters have the constant resistances shown.

Component	Resistance / kΩ
Test resistor	100
Voltmeter 1	50
Voltmeter 2	1000

Explain why connecting the voltmeter changes the resistance of the part of the circuit being measured.

[1]

For the lower-resistance voltmeter, calculate the equivalent resistance of the voltmeter and test resistor in parallel.

[2]

Evaluate which voltmeter gives the better measurement of the potential difference that would exist across the test resistor with no meter connected.

[2]

Question 32

HL • Paper 1B

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HL • Paper 1B

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An automatic night-light uses a light-dependent resistor (LDR) and a fixed resistor as a potential divider. The output potential difference is measured across the fixed resistor.

Output potential difference across the fixed resistor.

Use the graph to determine the light intensity at which $V_\text{out}=3.0\ \text{V}$ .

[1]

Calculate the resistance of the LDR when $V_\text{out}=3.0\ \text{V}$ . The supply potential difference is $6.0\ \text{V}$ and the fixed resistor has resistance $2.0\ \text{k}\Omega$ .

[2]

Explain why $V_\text{out}$ increases as the light intensity increases.

[1]

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Question 33

HL • Paper 1B

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HL • Paper 1B

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A negative-temperature-coefficient thermistor is connected to a fixed potential difference. Its resistance is measured at different temperatures.

Condition	Temperature / $^\circ\text{C}$	Resistance / $\Omega$	Potential difference / V
Measured	20	1800	12.0
Measured	30	1200	12.0
Measured	40	800	12.0
Measured	50	450	12.0
Operating point	60	200	12.0
Measured	70	120	12.0
Measured	80	80	12.0

Describe the variation of thermistor resistance with temperature shown by the graph.

[1]

Calculate the power dissipated in the thermistor at the operating temperature shown in the table.

[2]

Suggest why the current may increase further after the thermistor has been connected for several seconds.

[1]

Question 34

HL • Paper 1B

Hard

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HL • Paper 1B

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The current and potential difference are measured for a filament lamp and for a fixed resistor.

Potential difference against current for a filament lamp and a fixed resistor, with a marked point on the lamp curve.

Use the graph to determine the resistance of the filament lamp at the marked operating point.

[2]

Compare the behaviour of the filament lamp with that of the fixed resistor.

[2]

Explain the change in resistance of the filament lamp at larger currents using a particle model.

[1]

Question 35

SL • Paper 2

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SL • Paper 2

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A student connects a cell to a variable resistor. An ideal ammeter measures the current from the cell and an ideal voltmeter measures the terminal potential difference of the cell. The graph shows the variation of terminal potential difference $V$ with current $I$ .

Graph of terminal potential difference against current for a cell with a straight-line relationship.

The cell is used to drive a current in the external circuit.

I.

Explain why the terminal potential difference is less than the emf when current is supplied by the cell.

[2]

II.

Use the graph to determine the emf $\varepsilon$ and internal resistance $r$ of the cell.

[3]

The variable resistor is adjusted so that its resistance is decreased. Discuss the effect on the useful power supplied to the external circuit and the power dissipated inside the cell.

[2]

Question 36

SL • Paper 2

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SL • Paper 2

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A uniform metal wire is tested by measuring the resistance $R$ of different lengths $L$ of the wire at approximately constant temperature. The graph shows the experimental results. The wire has diameter $0.32\ \text{mm}$ .

Experimental resistance-length data for a uniform metal wire.

The wire is assumed to have constant cross-sectional area.

I.

Show that the gradient of the graph is equal to $\rho/A$ , where $\rho$ is the resistivity and $A$ is the cross-sectional area of the wire.

[2]

II.

Use the graph to calculate the resistivity of the metal.

[2]

Explain why the current should be kept small during this investigation.

[2]

Evaluate why repeated measurements of the wire diameter at different positions are more important than repeated measurements of the length.

[2]

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Question 37

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SL • Paper 2

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The circuit contains a $12.0\ \text{V}$ ideal supply, three resistors and a switch. The switch is initially closed and is opened in part (b). Resistors $R_1=4.0\ \Omega$ and $R_2=6.0\ \Omega$ are connected in parallel. This parallel combination is connected in series with $R_3=3.0\ \Omega$ . The switch can disconnect only the branch containing $R_2$ .

A circuit diagram showing an ideal dc supply connected to a series resistor labelled $R_3$ and then to two parallel branches labelled $R_1$ and $R_2$. A switch is in series with the $R_2$ branch only. The component values and supply voltage are labelled.

The switch is closed.

I.

Calculate the equivalent resistance of the circuit.

[2]

II.

Determine the current in $R_3$ and the potential difference across $R_1$ .

[3]

The switch is opened. Discuss the change in the power dissipated in $R_1$ .

[2]

Question 38

SL • Paper 2

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SL • Paper 2

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A remote environmental sensor is to be powered either by primary chemical cells replaced every few months or by a solar panel charging a secondary cell. The sensor operates at $3.0\ \text{V}$ and draws a steady current of $45\ \text{mA}$ for $8.0\ \text{h}$ each day.

Consider the daily operation of the sensor.

I.

Calculate the charge passing through the sensor each day.

[2]

II.

Calculate the electrical energy transferred to the sensor each day.

[2]

Discuss the choice between the two energy-source systems for this application.

[3]

Question 39

HL • Paper 1B

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HL • Paper 1B

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A cell with internal resistance is connected to different load resistors. The power dissipated in the external load is calculated from measurements of current and terminal potential difference.

External power dissipated by a cell as load resistance changes.

Use the graph to identify the load resistance for which the external power is greatest.

[1]

Calculate the current in the circuit at this load resistance using the cell model.

[2]

Evaluate why using a much smaller load resistance is not a good way to obtain a larger useful power from this cell.

[2]

Question 40

HL • Paper 1B

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HL • Paper 1B

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A resistor network is connected to a dc supply. The switch can be open or closed. All connecting wires have negligible resistance.

An annotated circuit diagram showing a dc supply connected to a resistor network with one resistor in series with two branches. One branch contains a single resistor. The other branch contains two resistors in series and a switch that can bypass one of them when closed. Resistor values and the supply potential difference are labelled.

Determine the equivalent resistance of the network when the switch is open.

[2]

Calculate the total current from the supply when the switch is open.

[1]

When the switch is closed, one resistor is bypassed. Explain the effect on the total current from the supply.

[2]

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Question 41

SL • Paper 2

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SL • Paper 2

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A filament lamp is connected to a variable dc supply. The current $I$ through the lamp is measured for different values of potential difference $V$ across it. The graph shows the results for both current directions.

Current-voltage characteristic of a filament lamp with a marked operating point.

Consider the operating point marked on the graph.

I.

Determine the resistance of the lamp at the marked operating point.

[2]

II.

Calculate the electrical power dissipated in the lamp at the marked operating point.

[2]

Explain the shape of the graph in terms of the microscopic origin of resistance in a metal filament.

[3]

Compare the resistance found from $V/I$ at one point with the gradient of the curve at that point.

[1]

Question 42

SL • Paper 2

Hard

Calculator Permitted

SL • Paper 2

Hard

Calculator Permitted

A temperature-sensing circuit uses a $6.0\ \text{V}$ supply, a fixed resistor of resistance $2.0\ \text{k}\Omega$ and a negative-temperature-coefficient thermistor in series. At the temperature referred to in parts (a)(i) and (a)(ii), the thermistor resistance is $4.0\ \text{k}\Omega$ . The output potential difference $V_\text{out}$ is measured across the fixed resistor.

A potential divider circuit with a dc supply, a thermistor and a fixed resistor in series. The output voltage is labelled across the fixed resistor. A small graph or inset indicates that the thermistor resistance decreases as temperature increases, without giving exact data points.

At one temperature the thermistor resistance is $4.0\ \text{k}\Omega$ .

I.

Calculate the current in the circuit.

[2]

II.

Calculate $V_\text{out}$ at this temperature.

[2]

The temperature is increased. Explain the effect on $V_\text{out}$ .

[2]

Evaluate the effect of measuring $V_\text{out}$ with a voltmeter of finite resistance connected across the fixed resistor.

[1]

Question 43

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

Calculator Permitted

A cell of emf $\varepsilon$ and internal resistance $r$ is connected to a load resistor $R$ . The power delivered to the load is investigated as $R$ is varied.

A circuit diagram showing a cell modelled as an ideal emf source in series with an internal resistor labelled $r$, connected to an external variable load resistor labelled $R$. Ideal meters may be shown measuring load current and terminal potential difference.

The cell has $\varepsilon=9.0\ \text{V}$ and $r=1.5\ \Omega$ .

I.

Show that the power delivered to the load can be written as $P=\dfrac{\varepsilon^2R}{(R+r)^2}$ .

[2]

II.

Calculate the power delivered to the load when $R=3.0\ \Omega$ .

[2]

III.

State the load resistance for maximum power transfer.

[1]

Evaluate whether operating at maximum power transfer is the best choice for a portable device that must run for a long time from the cell.

[3]

Question 44

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

Calculator Permitted

A network is connected across an ideal $18.0\ \text{V}$ supply. Resistor $R_A=6.0\ \Omega$ is in series with a parallel combination. The parallel combination consists of a $12.0\ \Omega$ resistor in one branch and two $8.0\ \Omega$ resistors in series in the other branch.

A circuit diagram showing an ideal dc supply connected to a series resistor labelled $R_A$, followed by a two-branch parallel network. One branch contains a single resistor labelled $12.0\ \Omega$; the other branch contains two series resistors each labelled $8.0\ \Omega$. The supply voltage is labelled.

Analyse the circuit when all components are connected.

I.

Calculate the equivalent resistance of the network.

[3]

II.

Calculate the current in the $12.0\ \Omega$ resistor.

[3]

One of the $8.0\ \Omega$ resistors is short-circuited by a wire of negligible resistance. Discuss the change in total current from the supply.

[2]

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Question 45

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

Calculator Permitted

Two cylindrical conductors have the same length and cross-sectional area. One is copper and the other is a semiconductor thermistor material. Both are connected separately to the same small dc potential difference, and then their temperatures are increased.

Consider the copper conductor.

I.

Explain the microscopic origin of electrical resistance in the copper conductor.

[2]

II.

State and explain the effect of increasing temperature on the resistance of the copper conductor.

[1]

Compare the effect of increasing temperature on the thermistor material with the effect on copper.

[2]

Evaluate why the statement $R=V/I$ alone is not a statement of Ohm's law.

[2]

Question 46

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

Calculator Permitted

A portable charger uses solar cells. Each solar cell has emf $0.60\ \text{V}$ and internal resistance $0.20\ \Omega$ under the stated illumination. A module is made from ten identical cells connected in series and is connected to a $5.0\ \Omega$ load.

A circuit diagram showing a string of identical solar cells connected in series, modelled as a source with total emf and total internal resistance, connected to a single external load resistor. Labels identify the cell emf, cell internal resistance and load resistance.

Assume the illumination remains constant.

I.

Calculate the total emf and total internal resistance of the module.

[2]

II.

Calculate the current in the load and the terminal potential difference of the module.

[3]

Discuss two limitations of using this solar-cell module as the only energy source for the charger.

[3]

Question 47

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

Calculator Permitted

A potentiometer of total resistance $10.0\ \text{k}\Omega$ is connected across an ideal $5.00\ \text{V}$ supply. The slider is set so that the resistance between the lower end and the slider is $4.00\ \text{k}\Omega$ . A sensor input of resistance $6.00\ \text{k}\Omega$ is connected between the slider and the lower end.

A potentiometer connected across a dc supply with the lower end labelled zero potential and the upper end at the supply potential. A slider taps an output voltage relative to the lower end. A load resistor representing a sensor input is connected from the slider to the lower end, in parallel with the lower section of the potentiometer.

First ignore the sensor input, so that no current is drawn from the slider.

I.

Calculate the unloaded output potential difference.

[2]

II.

Explain why a potentiometer can provide a continuously variable output potential difference.

[1]

The sensor input is now connected.

I.

Calculate the loaded output potential difference.

[2]

II.

Explain why the loaded value is different from the unloaded value.

[1]

Evaluate one design change that would reduce the effect of connecting the sensor input.

[2]

Question 48

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

Calculator Permitted

A heating cable is made from a uniform resistive wire of resistivity $1.1\times10^{-6}\ \Omega\ \text{m}$ and cross-sectional area $2.0\times10^{-7}\ \text{m}^2$ . A length of the wire is to be connected across a $24\ \text{V}$ supply to dissipate $48\ \text{W}$ .

Assume the resistance of the wire is independent of temperature.

I.

Calculate the resistance required for the heating cable.

[2]

II.

Calculate the length of wire required.

[3]

In practice the wire becomes hot and its resistance increases. Evaluate the effect on the power dissipated and on the suitability of the design.

[3]

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B.4 Thermodynamics

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