Physics 9702 · AS & A Level
Resistance and resistivity
100 practice questions on Resistance and resistivity, with worked solutions and instant marking.
Which measurements are required to calculate the resistivity of the metal in a piece of wire?
Feb/March 2016
A network of three resistors, each having resistance $R$, is connected as shown. The combined resistance measured between points X and Y is $8.0\,\Omega$. Determine the value of $R$?
Feb/March 2016
State the meaning of electric current.
Feb/March 2016
A coil is made from $N$ turns of insulated copper wire wrapped around a cylindrical iron core whose diameter is $D$. The copper wire has diameter $d$. The resistivity of copper is $\rho$. Diameter $D$ is much greater than diameter $d$. What is the total resistance between the two ends of the coil?
Feb/March 2017
Six resistors, each with resistance $R$, are arranged as illustrated. Their total resistance is $66\,\text{k}\Omega$. Determine the value of $R$.
Feb/March 2017
A wire with a resistance of $9.55\ \Omega$ has a diameter measuring $0.280\ \text{mm}$. The wire is made from a metal whose resistivity is $4.90 \times 10^{-7}\ \Omega\ \text{m}$. Determine the wire's length.
Feb/March 2018
Five resistors are arranged as shown. What is the combined resistance between points $P$ and $Q$?
Feb/March 2018
Which graph illustrates how the potential difference $V$ of a filament lamp varies with current $I$?
Feb/March 2019
A wire with cross-sectional area $5.0 \times 10^{-6}\,\text{m}^2$ is constructed from a metal whose resistivity is $50 \times 10^{-8}\,\Omega\,\text{m}$. The potential difference across the wire is $6.0\,\text{V}$ and the current flowing through it is $3.0\,\text{A}$. What is the wire's length?
Feb/March 2019
Identical resistors are arranged in four combinations $P$, $Q$, $R$ and $S$ between terminals $X$ and $Y$. In descending order of combined resistance between $X$ and $Y$ (with the greatest first), what is the sequence?
Feb/March 2019
A manufacturer advises that, when an electric drill is used with a longer extension cord, the cord should have a larger cross-sectional area. What is one reason for this recommendation?
Feb/March 2020
Define the ohm in terms of V and A.
Feb/March 2020
A electrical cable is made up of seven copper-wire strands, each with a diameter of $0.30\,\text{mm}$, linked in parallel. The resistivity of copper is $1.72 \times 10^{-8}\,\Omega\,\text{m}$. The current flowing in the cable is $13\,\text{A}$. What is the potential difference (p.d.) between two points on the cable separated by a distance of $1.0\,\text{m}$?
Feb/March 2021
A wire has a length of $0.80\,\text{m}$ and a diameter of $5.0 \times 10^{-4}\,\text{m}$. Its $I$-$V$ characteristic is shown. What is the resistivity of the metal that the wire is made from?
Feb/March 2022
As illustrated in Fig. 6.1, the two ends of a metal resistance wire are attached to a battery with electromotive force (e.m.f.) $8.0\,\text{V}$ and negligible internal resistance. The resistance wire dissipates $36\,\text{W}$ of power.
Feb/March 2022
The diagram represents a network made up of three resistors. What is the total resistance of the network between terminal $X$ and terminal $Y$?
Feb/March 2024
A copper wire has a length of $6.4\,\text{m}$ and a resistance of $0.92\,\Omega$. The resistivity of copper is $1.8 \times 10^{-8}\,\Omega\,\text{m}$. What is the wire’s diameter?
Feb/March 2025
What unit is used for resistivity?
May/June 2010
The resistance of a thermistor varies with its temperature, and the resistance of a light-dependent resistor (LDR) varies with the illumination level. In what conditions would both the thermistor and the LDR have the greatest resistance?
May/June 2010
A thermistor’s resistance varies with its temperature, while a light-dependent resistor (LDR) has a resistance that varies with the illumination. In which conditions is the resistance of both a thermistor and an LDR greatest?
May/June 2010
What unit is resistivity measured in?
May/June 2010
What unit is used for resistivity?
May/June 2010
A thermistor’s resistance varies with temperature, whereas the resistance of a light-dependent resistor (LDR) varies with the illumination. In what conditions will both the thermistor and the LDR have their greatest resistance?
May/June 2010
A heater is being made from nichrome wire. At the heater’s operating temperature, nichrome has a resistivity of $1.0 \times 10^{-6}\,\Omega\,\text{m}$. The heater must dissipate $60\,\text{W}$ when the potential difference across its terminals is $12\,\text{V}$.
May/June 2010
State what electric current means.
May/June 2010
The graphs illustrate possible current-voltage ($I$-$V$) relationships for a filament lamp and for a semiconductor diode. Which row correctly gives the $I$-$V$ graphs for the lamp and the diode?
May/June 2011
The resistance of a metal cube is determined by placing it between two parallel plates, as illustrated. The cube has volume $V$ and is formed from a material of resistivity $\rho$. The connections to the cube have negligible resistance. Which expression gives the electrical resistance of the metal cube between X and Y?
May/June 2011
A soft, electrically-conducting cylindrical sample has resistance $R$. It is rolled out so that its length becomes twice as great, while its volume remains constant. What is its new resistance?
May/June 2011
Which graph most accurately shows how the current $I$ through a thermistor varies with the potential difference $V$ across it?
May/June 2011
The diagram illustrates a d.c. circuit. What is the resistance between points $P$ and $Q$ caused by the resistance network?
May/June 2011
The graphs illustrate possible current-voltage ($I$-$V$) characteristics for a filament lamp and for a semiconductor diode. Which row most accurately states the correct $I$-$V$ graphs for the lamp and the diode?
May/June 2011
The resistance of a metal cube is determined by putting it between two parallel plates, as illustrated. The cube has volume $V$ and is made from a material of resistivity $\rho$. The connections to the cube have negligible resistance. Which expression gives the electrical resistance of the metal cube between X and Y?
May/June 2011
In Fig. 5.1, sketch the $I$-$V$ characteristic of a filament lamp.
May/June 2011
An iron wire is $8.0\,\text{m}$ long and its diameter is $0.50\,\text{mm}$. Its resistance is $R$. Another iron wire is $2.0\,\text{m}$ long and has diameter $1.0\,\text{mm}$. What resistance does the second wire have?
May/June 2012
An iron wire is $8.0\,\text{m}$ long and has a diameter of $0.50\,\text{mm}$. Its resistance is $R$. A second iron wire is $2.0\,\text{m}$ long and has a diameter of $1.0\,\text{mm}$. What is the resistance of the second wire?
May/June 2012
The heater delivers $2.5\,\text{kW}$ when it is connected to a $220\,\text{V}$ supply.
May/June 2012
The SI base-unit form of resistivity is given by $\text{kg } x^3 y^{-2} z^{-3}$. What are $x$, $y$ and $z$?
May/June 2013
A power cable is $2000\,\text{m}$ long. It consists of twelve parallel strands of copper wire, each strand having a diameter of $0.51\,\text{mm}$. Calculate the resistance of the cable. (resistivity of copper = $1.7 \times 10^{-8}\,\Omega\,\text{m}$)
May/June 2013
Two wires $P$ and $Q$, both formed from the same material, are attached to the same electrical supply. $P$ is twice as long as $Q$ and has one-third of the diameter of $Q$, as shown in the diagram. Determine the ratio $\dfrac{\text{current in }P}{\text{current in }Q}$?
May/June 2013
Five resistors are arranged as shown. Calculate the total resistance between $P$ and $Q$.
May/June 2013
The diagram presents a thermistor calibration curve, plotted using a non-standard scale on the vertical axis. At a temperature of $40\,^{\circ}\text{C}$, what is the corresponding thermistor resistance?
May/June 2013
The graph illustrates the way current $I$ depends on voltage $V$ for a filament lamp. Because the graph is not a straight line, the lamp's resistance changes with $V$. Which row gives the correct resistance for the stated value of $V$?
May/June 2013
An electric power cable is made up of six copper wires $c$ that surround a steel core $s$. For a $1.0\,\text{km}$ section of one copper wire, the resistance is $10\,\Omega$ and, for a $1.0\,\text{km}$ section of the steel core, the resistance is $100\,\Omega$. What is the approximate resistance of a $1.0\,\text{km}$ section of the power cable?
May/June 2013
The figure depicts a length of model-railway track connected to a battery, a resistor and a relay coil. When no train is on the track, current flows in the relay coil, which makes a switch operate and turn on a light. When a train is in that section of track, most of the current travels through the train’s wheels and axles instead of through the relay coil. The switch in the relay then turns off the light. What is the reason for fitting a resistor between the battery and the track?
May/June 2013
An ammeter, a $2\,\Omega$ fixed resistor and a $0\text{-}10\,\Omega$ variable resistor are connected in series with a $12\,\text{V}$ battery. A high-resistance voltmeter is connected across the fixed resistor. The resistance of the variable resistor is then altered from zero to its maximum value. Which graph shows the way the potential difference (p.d.) recorded by the voltmeter changes with the current recorded by the ammeter?
May/June 2013
A student records the current through a resistor with constant resistance and the potential difference (p.d.) across it. The data are then used to produce a graph of current against p.d. The current readings include a systematic error. How could this be identified from the graph?
May/June 2013
Resistors A and B have resistances $R_1$ and $R_2$ respectively. As shown in Fig. 6.1, they are joined in series with a battery. The battery provides electromotive force (e.m.f.) $E$ and has zero internal resistance.
May/June 2013
Two electrically conducting cylinders $X$ and $Y$ are made from the same material. Their dimensions are shown. The resistance measured across the ends of each cylinder is taken. What is the ratio $\frac{\text{resistance of } X}{\text{resistance of } Y}$?
May/June 2014
A practical investigation is done to determine the resistance of a wire. The current in the wire is $(1.0 \pm 0.2)\,\text{A}$ and the potential difference across the wire is $(8.0 \pm 0.4)\,\text{V}$. Calculate the resistance of the wire and its uncertainty.
May/June 2014
What SI base units are used to express resistance?
May/June 2014
A copper wire is to be substituted with an aluminium alloy wire that has the same length and the same resistance. The resistivity of copper is half that of the alloy. What is the ratio $\frac{\text{diameter of alloy wire}}{\text{diameter of copper wire}}$ ?
May/June 2014
The diagram shows an electric pump for a garden fountain that is linked to a $230\,\text{V}$ mains electrical supply by an $18\,\text{m}$ cable. The pump is considered to be performing acceptably when the potential difference (p.d.) across it is at least $218\,\text{V}$. At that point, the current through it is $0.83\,\text{A}$. What is the greatest resistance per metre of each of the two wires in the cable if the pump is to perform acceptably?
May/June 2014
Wires P and Q are made from the same material and have the same length. They are connected in parallel to one voltage supply. The diameter of wire P is $2\,\text{mm}$ and the diameter of wire Q is $1\,\text{mm}$. Determine the ratio $\dfrac{\text{current in P}}{\text{current in Q}}$?
May/June 2014
The wire RST is joined to a second wire XY, as illustrated. Each wire has length $100\,\text{cm}$ and a resistance per unit length of $10\,\Omega\,\text{m}^{-1}$. Calculate the total resistance between X and Y.
May/June 2015
If a thin metal wire is pulled taut, its length increases while its thickness decreases. As a result, the resistance of the wire changes. The wire’s volume stays unchanged. Which graph could show how the resistance $R$ varies with extension $x$ of the wire?
May/June 2015
The current $I$ against potential difference (p.d.) $V$ relationship for a semiconductor diode is shown in Fig. 5.1.
May/June 2015
Uniform resistance wire AB is $50\text{ cm}$ long and has a diameter of $0.36\text{ mm}$. The metal used for the wire has resistivity $5.1 \times 10^{-7}\,\Omega\text{ m}$.
May/June 2015
A pair of copper wires with the same length are joined in parallel. A potential difference is applied across the two ends of this parallel arrangement. Wire S has a diameter of $3.0\,\text{mm}$. Wire T has a diameter of $1.5\,\text{mm}$. What is the value of the ratio $\dfrac{\text{current in S}}{\text{current in T}}$?
May/June 2016
Which graph displays the $I$-$V$ characteristic of a filament lamp?
May/June 2016
A pair of resistors with resistances $R_1$ and $R_2$ are joined in parallel. What is the total resistance between X and Y?
May/June 2016
The potential difference $V$ across a filament lamp is gradually increased from zero until it reaches its normal operating value. Which graph shows how the current $I$ in the lamp varies with $V$?
May/June 2016
Which equation is used to express resistance?
May/June 2016
The graph illustrates how the resistance of a uniform metal wire changes as its length changes. The graph’s gradient is $G$. The wire has cross-sectional area $A$. Which expression could be used to calculate the resistivity of the metal in the wire?
May/June 2016
Possible current-voltage ($I$-$V$) characteristics for a filament lamp and a semiconductor diode are shown in the graphs. Which row in the table gives the correct $I$-$V$ graphs for the lamp and for the diode?
May/June 2016
What does the ohm mean?
May/June 2016
Which component is represented by the $I$-$V$ graph shown?
May/June 2017
Two wires have equal lengths and equal resistances. Wire X is formed from a metal with resistivity $1.7 \times 10^{-8}\,\Omega\,\text{m}$, and wire Y is formed from a metal with resistivity $5.6 \times 10^{-8}\,\Omega\,\text{m}$. The diameter of wire X is $0.315\,\text{mm}$. What diameter does wire Y have?
May/June 2017
A semiconductor block carries a current of $30.0\,\text{mA}$ when the potential difference (p.d.) across it is $10.0\,\text{V}$. The block’s dimensions and the direction of current flow are shown. The electrical meters used have accuracies of $\pm 0.1\,\text{mA}$ and $\pm 0.1\,\text{V}$. The block dimensions are accurate to $\pm 0.2\,\text{mm}$. What is the resistivity of the semiconductor?
May/June 2017
A metal cube whose side length is $a$ has an electrical resistance of $R$ measured across opposite faces. What is the resistance across the opposite faces of another cube made of the same metal, but with side length $3a$?
May/June 2017
Define the ohm in electrical terms.
May/June 2017
State two SI base units besides kilogram, metre and second.
May/June 2017
Describe the $I$-$V$ characteristic of a metallic conductor under constant temperature conditions.
May/June 2017
A cylindrical sample made of a soft material that conducts electricity has resistance $R$. It is rolled out so that its length becomes twice as large, while its volume remains unchanged. What will its new resistance be?
May/June 2018
Which graph illustrates how voltage $V$ varies with current $I$ for a semiconductor diode?
May/June 2018
The graph illustrates the $I$-$V$ characteristic of an electrical component. What is the component?
May/June 2018
A metal wire with a length of $1.4\,\text{m}$ has a constant cross-sectional area of $7.8 \times 10^{-7}\,\text{m}^2$. The metal’s resistivity is $1.7 \times 10^{-8}\,\Omega\,\text{m}$. What is the wire’s resistance?
May/June 2018
Define a volt.
May/June 2018
Wire X has a resistance per unit length that remains constant at $3.0\,\Omega\,\text{m}^{-1}$, and its diameter measures $0.48\,\text{mm}$.
May/June 2018
Which graph most accurately shows how potential difference $V$ varies with current $I$ in a filament lamp?
May/June 2019
Four wires are all made from the same metal. Their cross-sectional areas, lengths and thermodynamic temperatures are shown. Which wire has the greatest resistance?
May/June 2019
The graph illustrates how the resistance of a uniform metal wire changes with length. The gradient of the graph is $G$. The wire has cross-sectional area $A$. Which expression could be used to find the resistivity of the metal in the wire?
May/June 2019
Define what resistance is.
May/June 2019
Define the ohm in terms of potential difference and current.
May/June 2019
Which graph most accurately shows how the current $I$ through a filament lamp changes with the potential difference $V$ across the lamp?
May/June 2020
A cylindrical metal wire $X$ has resistance $R$. The same volume of this metal is reshaped into a cylindrical wire $Y$ with twice the length. What resistance does wire $Y$ have?
May/June 2020
It is possible to join three identical resistors in four distinct arrangements. Two of these arrangements have resistances of $4.0\,\Omega$ and $9.0\,\Omega$. Determine the resistance of one resistor.
May/June 2020
Measurements are taken of the current $I$ at different voltages $V$ across a fixed resistor. The outcomes are then plotted on a graph to show how $I$ varies with $V$. What is the most appropriate description of the errors in the readings?
May/June 2020
A heating-element wire has resistance $R$. It snaps and a different wire is fitted in its place. The table gives data for the original wire and the replacement wire. Original wire: length $l$, diameter $d$, resistivity of metal $\rho$. Replacement wire: length $l$, diameter $2d$, resistivity of metal $2\rho$. What is the resistance of the replacement wire?
May/June 2020
A metal wire joins a power supply to a lamp. Its total resistance is $3.4\,\Omega$ and the metal’s resistivity is $2.6 \times 10^{-8}\,\Omega\,\text{m}$. The complete length of the wire is $59\,\text{m}$.
May/June 2020
A wire is placed in an electric circuit, and the current in the wire is measured. Which single change could increase the current in the wire?
May/June 2021
The diagram depicts a resistor network. Every resistor has resistance $R$. What is the overall resistance of the network between points X and Y?
May/June 2021
The graph illustrates how current $I$ varies with potential difference $V$ for components X, Y and Z. Which row correctly identifies the components?
May/June 2021
A wire has a resistance of $9.55\,\Omega$ and a diameter of $0.280\,\text{mm}$. The wire is made from a metal with resistivity $4.90 \times 10^{-7}\,\Omega\,\text{m}$. What length is the wire?
May/June 2021
Define the term ohm.
May/June 2021
A wire has a resistance of $30\,\Omega$. A second wire is made from the same material, has the same mass and is three times the length of the first wire. What is the resistance of the second wire?
May/June 2022
The light intensity falling on a light-dependent resistor (LDR) is increased. The temperature of a thermistor is increased. In each case, the current through the component is kept constant. What happens to the potential difference across each component?
May/June 2022
An iron wire is $8.0\,\text{m}$ long and has a diameter of $0.50\,\text{mm}$. Its resistance is $R$. A second iron wire is $2.0\,\text{m}$ long and has a diameter of $1.0\,\text{mm}$. What resistance does the second wire have?
May/June 2022
A fixed resistor and a filament lamp are connected in series to a power supply. The $I$-$V$ characteristics of both components are shown. The current in the fixed resistor is $0.34\,\text{A}$. What is the resistance of the filament lamp?
May/June 2022
A lump of conducting putty (modelling clay) with constant resistivity is shaped into a cylinder. The resistance $R$ across its flat ends (shaded) is recorded. The same volume of putty is then reshaped into cylinders with different lengths $L$, and for each value of $L$ the resistance $R$ across the flat ends is measured. Which graph best shows how $R$ varies with $L$?
May/June 2022
On Fig. 6.1, sketch the $I$-$V$ characteristic for a filament lamp.
May/June 2022