Physics 9702 · AS & A Level
Potential difference and power
100 practice questions on Potential difference and power, with worked solutions and instant marking.
Two large parallel plates X and Y are separated by a distance of $5.0\,\text{mm}$ and linked to the terminals of a $200\,\text{V}$ d.c. supply, as shown. At P, a small oil drop has one extra electron. What is the size of the electrostatic force on the oil drop caused by the electric field between the plates?
Feb/March 2016
A fixed resistor with resistance $12\,\Omega$ is linked to a battery. The current through the resistor is $0.20\,\text{A}$. The current is then doubled. What is the new power dissipated in the resistor?
Feb/March 2016
A $12\,\text{V}$ battery is connected to a source of electromotive force (e.m.f.) and left to charge for $20$ minutes. In this period, the battery receives $7.2 \times 10^4\,\text{J}$ of energy. What quantity of charge flows through the battery?
Feb/March 2016
The potential difference across a resistor is $12\,\text{V}$. The current through the resistor is $2.0\,\text{A}$.\n\nA charge of $4.0\,\text{C}$ moves through the resistor.\n\nWhat is the energy transferred in the resistor and the time taken for the charge to move through the resistor?
Feb/March 2017
Three resistors with resistances $R_1$, $R_2$ and $R_3$ are arranged as in Fig. 6.1. The current through the resistor network is $I$ and the potential difference across it is $V$. Show that the overall resistance $R$ of the network is given by the equation $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$.
Feb/March 2017
An electron moves into the region between two parallel plates that are $5.0\ \text{cm}$ apart and are kept at electric potentials of $+2000\ \text{V}$ and $-500\ \text{V}$, respectively. What is the electric force acting on the electron?
Feb/March 2018
Which statement concerning electric charges in a uniform electric field is incorrect?
Feb/March 2018
A resistor has resistance $R$. If the potential difference across the resistor is $V$, the current in the resistor is $I$. The power dissipated in the resistor is $P$. Work $W$ is done when charge $Q$ passes through the resistor. Which of the following is not a valid relationship between these variables?
Feb/March 2018
A crane is being used to raise containers from a ship. One container has a mass of $14\,000\,\text{kg}$ and is lifted straight up at a speed of $3.2\,\text{m s}^{-1}$. The electric motor providing the power to lift the container draws a current of $240\,\text{A}$ with a potential difference of $2200\,\text{V}$. What is the efficiency of the system?
Feb/March 2019
A pair of horizontal parallel plate conductors is spaced by 5.0\ \text{mm} in air. The lower plate is earthed, while the upper plate is at +50\ \text{V}. What is the electric field strength E at the midpoint between the plates?
Feb/March 2019
As shown, three resistors are arranged in parallel across a power supply. The power dissipated in the resistors with resistances $2\,\Omega$, $3\,\Omega$ and $4\,\Omega$ is $P_2$, $P_3$ and $P_4$ respectively. What is the ratio $P_2 : P_3 : P_4$?
Feb/March 2019
Define the term electric field strength.
Feb/March 2019
Using energy changes, describe the electromotive force (e.m.f.) of a battery and the potential difference (p.d.) across a resistor. Describe: - e.m.f. - p.d.
Feb/March 2019
A negatively charged oil drop remains at rest, midway between two plates linked to a high voltage supply, as shown. Which alteration would not make the upward electrical force on the drop greater?
Feb/March 2020
As illustrated, a battery is connected to three resistors with resistances $12\,\Omega$, $6\,\Omega$ and $2\,\Omega$. The current supplied by the battery is $3\,\text{A}$. What is the value of the ratio $\dfrac{\text{power dissipated in the resistor of resistance } 6\,\Omega}{\text{power dissipated in the resistor of resistance } 2\,\Omega}$?
Feb/March 2020
A uniform electric field is set up between two parallel metal plates. The electric field strength is $1.4 \times 10^{4}\,\text{N C}^{-1}$. The potential difference across the plates is $350\,\text{V}$.
Feb/March 2020
The figure depicts a thundercloud with its base $500\,\text{m}$ above the ground. The potential difference between the cloud base and the ground is $200\,\text{MV}$. A raindrop carrying a charge of $4.0 \times 10^{-12}\,\text{C}$ is located in the region between the cloud and the ground. What is the electrical force acting on the raindrop?
Feb/March 2021
A cell with negligible internal resistance is joined to resistors $R_1$, $R_2$ and $R_3$, as illustrated. The cell supplies energy to the circuit and energy is lost in the resistors. Which word equation has to be correct?
Feb/March 2021
For the circuit diagram below, lamp P is rated $250\,\text{V},\,50\,\text{W}$ and lamp Q is rated $250\,\text{V},\,200\,\text{W}$. Both lamps are joined in series to a $250\,\text{V}$ power supply. Take the resistance of each lamp to be constant. Which statement most accurately describes what happens when the switch is closed?
Feb/March 2022
A cell with electromotive force (e.m.f.) $E$ and internal resistance $r$ is connected to a variable resistor, as illustrated. The resistance of the variable resistor is increased steadily from $r$ to $3r$. Which graph shows how the potential difference (p.d.) $v$ across the internal resistance varies with the p.d. $V$ across the variable resistor?
Feb/March 2022
How are potential difference (p.d.) and electromotive force (e.m.f.) defined in terms of energy transfer $W$ and charge $q$?
Feb/March 2024
A resistor dissipates $25\,\text{W}$ of power when the potential difference (p.d.) across it is $4.0\,\text{V}$. What is the resistance of this resistor?
Feb/March 2024
A thermistor is joined to a cell with negligible internal resistance. Which graph shows how the power, $P$, dissipated in the thermistor changes with temperature?
Feb/March 2025
A cell with electromotive force (e.m.f.) $E$ and internal resistance $r$ is connected in series to a switch $S$ and an external resistor of resistance $R$. The potential difference (p.d.) across P and Q is $V$. Which statement is correct when $S$ is moved from open to closed?
Feb/March 2025
In base units, the SI unit of potential difference, the volt, is written as
May/June 2010
Which row shows the conditions in which forces act on a charged particle in a uniform electric field?
May/June 2010
The diagram illustrates two points $P$ and $Q$ on a circle of radius $r$, separated by an angle of $90^\circ$. A positive point charge placed at the centre of the circle produces an electric field of magnitude $E$ at both $P$ and $Q$. Which expression represents the work done in transferring a unit positive charge from $P$ to $Q$?
May/June 2010
Two parallel plates with opposite charges are set up as shown. An electron is released from rest at the surface of the negatively charged plate. The electron moves away from the negatively charged plate and towards the positively charged plate. Which graph shows how the force $F$ on the electron changes with its distance $x$ from the negative plate?
May/June 2010
Using energy transfer $W$ and charge $q$, how are potential difference (p.d.) and electromotive force (e.m.f.) defined?
May/June 2010
Resistors P, Q and R in the circuit each have the same resistance. The battery, which has negligible internal resistance, provides a total power of $12\,\text{W}$. What is the power dissipated as heating in resistor R?
May/June 2010
In base units, the SI unit of potential difference (the volt) is expressed as
May/June 2010
As illustrated, two parallel plates carry opposite charges. An electron is let go from rest at the surface of the negatively charged plate. It moves from the negatively charged plate towards the positively charged plate. Which graph represents how the force $F$ on the electron changes with its distance $x$ from the negative plate?
May/June 2010
The diagram depicts two points $P$ and $Q$ separated by an angle of $90^{\circ}$ on a circle with radius $r$. A positive point charge placed at the centre of the circle produces an electric field of magnitude $E$ at both $P$ and $Q$. Which expression represents the work done in moving a unit positive charge from $P$ to $Q$?
May/June 2010
Which row gives the circumstances under which a charged particle experiences forces in a uniform electric field?
May/June 2010
With respect to energy transfer $W$ and charge $q$, what is meant by potential difference (p.d.) and electromotive force (e.m.f.)?
May/June 2010
Resistors P, Q and R in the circuit each have the same resistance. The battery, with negligible internal resistance, delivers a total power of $12\,\text{W}$. What is the power dissipated as heat in resistor R?
May/June 2010
Two parallel plates with opposite charges are set up as shown. An electron is released from rest at the surface of the negatively charged plate. The electron moves away from the negatively charged plate towards the positively charged plate. Which graph shows how the force $F$ acting on the electron changes with its distance $x$ from the negative plate?
May/June 2010
The diagram indicates two points P and Q that are separated by $90^{\circ}$, on a circle of radius $r$. A positive point charge placed at the centre of the circle produces an electric field of magnitude $E$ at both P and Q. Which expression gives the work done in moving a unit positive charge from P to Q?
May/June 2010
Using energy transfer $W$ and charge $q$, how are potential difference (p.d.) and electromotive force (e.m.f.) defined?
May/June 2010
In base units, the SI unit of potential difference (the volt) is written as
May/June 2010
State the meaning of an electric field.
May/June 2010
A potential difference is placed across two metal plates that are not parallel. Which diagram shows the electric field between the plates?
May/June 2011
A pair of parallel plates are separated by $25\ \text{mm}$, and the potential difference across them is $12\ \text{kV}$. What is the force on an electron when it is located in the uniform electric field between the plates?
May/June 2011
A battery is labelled $9.0\ \text{V}$. What is meant by this?
May/June 2011
Four resistors with the same value are connected as shown. How do the powers dissipated by the resistors change when resistor W is removed?
May/June 2011
An electric motor delivers $120\,\text{W}$ of useful mechanical output power. The motor has an efficiency of $60\%$. Which row is correct?
May/June 2011
The diagram depicts two parallel metal plates linked to a d.c. power supply via a resistor. A uniform electric field exists in the space between the plates. Which change would lead to a decrease in the electric field strength?
May/June 2011
In each electric field diagram, a positively charged particle is transferred from X to Y. In which diagram does the particle feel a repulsive force that gets larger?
May/June 2011
What term is used for the electric potential difference between two points in a wire carrying a current?
May/June 2011
An e.m.f. source $E$ has a fixed internal resistance $r$ and is connected to an external variable resistor of resistance $R$. As $R$ is raised from a value smaller than $r$ to a value larger than $r$, which statement is correct?
May/June 2011
A potential difference of $12\,\text{kV}$ is applied across two parallel plates separated by a gap of $25\,\text{mm}$. What force acts on an electron located in the uniform electric field between the plates?
May/June 2011
A potential difference is applied across two metal plates that are not parallel. Which diagram represents the electric field between the plates?
May/June 2011
A battery is labelled $9.0\,$V. What is the meaning of this?
May/June 2011
What could be one possible unit for the quantity $VI$, if $V$ is the potential difference across a resistor and $I$ is the current through that same resistor?
May/June 2012
A lightning discharge may take place between a charged cloud and the Earth’s surface once the electric field strength in the air between them reaches $25\,\text{kN C}^{-1}$. The diagram illustrates the electric field between the cloud base and the Earth’s surface. What is the least potential difference between the Earth and the base of a cloud, $2\,\text{km}$ high, needed for lightning to occur?
May/June 2012
The circuit shown below carries a current $I$ through the resistor $R$. What information must be known to find the value of $I$?
May/June 2012
An electric field is present in the region between two charged metal plates. Which graph shows how electric field strength $E$ varies with distance $d$ from $X$ along the line $XY$?
May/June 2012
A power cable $X$ has resistance $R$ and carries current $I$. A second cable $Y$ has resistance $2R$ and carries current $\frac{1}{2}I$. What is the ratio $\dfrac{\text{power dissipated in }Y}{\text{power dissipated in }X}$?
May/June 2012
Which unit could be used for the product $VI$, where $V$ represents the potential difference across a resistor and $I$ represents the current through that same resistor?
May/June 2012
A lightning discharge can take place between a charged cloud and the Earth’s surface when the electric field strength in the air between them reaches $25\,\text{kN C}^{-1}$. The diagram illustrates the electric field between the bottom of a cloud and the Earth’s surface. What is the least potential difference between the Earth and the bottom of a cloud, $2\,\text{km}$ above the ground, for lightning to occur?
May/June 2012
Define electric field strength in terms of force per unit charge.
May/June 2012
A tiny water droplet with mass $3.0\,\mu\text{g}$ has a charge of $-6.0 \times 10^{-11}\,\text{C}$. It is placed in the Earth’s gravitational field between two horizontal metal plates. The upper plate is at a potential of $+500\,\text{V}$, while the lower plate is at a potential of $-500\,\text{V}$. The plates are $2.0\,\text{mm}$ apart. What is the droplet’s motion?
May/June 2013
As shown, two parallel plates carry opposite charges. An electron is let go from rest at the surface of the negatively charged plate, and it moves from that plate towards the positively charged plate. Which graph indicates how the force $F$ acting on the electron changes with its distance $x$ from the negative plate?
May/June 2013
A $13\,\Omega$ resistor is connected in series to a power supply whose electromotive force (e.m.f.) is $12\,\text{V}$ and whose internal resistance is $2.0\,\Omega$. What power is dissipated in the $13\,\Omega$ resistor?
May/June 2013
When a battery is connected to a resistor, the battery slowly heats up. This makes the battery's internal resistance rise while its e.m.f. remains the same. As the internal resistance of the battery rises, what happens, if anything, to the terminal potential difference and the output power?
May/June 2013
In a calculator’s liquid crystal display, the two conducting layers are $8\,\mu\text{m}$ apart. When the calculator is switched on, a $1.5\,\text{V}$ cell is connected across the conducting layers. What is the electric field strength between the layers?
May/June 2013
A low-voltage source having an e.m.f. of $20\,\text{V}$ and an internal resistance of $1.5\,\Omega$ supplies a heater with resistance $6.5\,\Omega$ in a fish tank. What power is transferred to the water in the fish tank?
May/June 2013
A filament lamp has a resistance of $180\,\Omega$ when the current through it is $500\,\text{mA}$. What power is transformed in the lamp?
May/June 2013
A $12\,\text{V}$ battery is connected in series with an ammeter, a $2\,\Omega$ fixed resistor and a $0\! -\! 10\,\Omega$ variable resistor. High-resistance voltmeters $P$ and $Q$ are placed across the variable resistor and the fixed resistor respectively, as shown. The resistance of the variable resistor is altered from its maximum value to zero. Which graph shows how the voltmeter readings vary with current?
May/June 2013
Two metal plates are positioned horizontally and parallel to each other, $5.0\,\text{cm}$ apart. The plates have potentials of $+100\,\text{V}$ and $+20\,\text{V}$. What force acts on an electron within the electric field between the plates?
May/June 2013
The cross-sectional area of a metal wire is circular and changes as you move along its length. A current flows through the wire. The thinner end of the wire is at a reference potential taken as zero. Which graph most accurately shows how the potential difference $V$, relative to the zero reference, varies with distance $x$ along the wire?
May/June 2013
What is meant by charge?
May/June 2013
What is the mean power output of a laser that delivers $0.20\,\text{J}$ of energy in $10\,\text{ns}$?
May/June 2014
A horizontal beam of electrons is directed between two horizontal parallel plates that are $2.0\,\text{cm}$ apart. The top plate is at an electrical potential of $+4.0\,\text{V}$, and the bottom plate is at an electrical potential of $-4.0\,\text{V}$. What is the force on each electron while it is between the plates?
May/June 2014
In the diagram, the two points $P$ and $Q$ are positioned on a circle of radius $r$ so that they are $90^\circ$ apart. A positive point charge at the centre of the circle produces an electric field of magnitude $E$ at both $P$ and $Q$. Which expression gives the work done when a unit positive charge is moved from $P$ to $Q$?
May/June 2014
A battery, having a constant internal resistance, is connected to a resistor with resistance $250\,\Omega$, as shown. The current in the resistor is $40\,\text{mA}$ for $60\,\text{s}$. Over this interval, $6.0\,\text{J}$ of energy is dissipated in the internal resistance. What are the energy delivered to the external resistor in the $60\,\text{s}$ and the e.m.f. of the battery?
May/June 2014
A component in a circuit has a potential difference of $2.0\,\text{V}$ across it. How many electrons must pass through the component for $4.8\,\text{J}$ of energy to be transferred to it?
May/June 2014
Two horizontal metal plates carrying opposite charges are positioned in a vacuum. A particle with positive charge begins at rest and travels from one plate to the other plate, as shown. Which graph shows how the kinetic energy $E_K$ of the particle changes with the distance $x$ travelled from the positive plate?
May/June 2014
Two parallel plates X and Y are spaced a distance $d$ apart in a vacuum. A potential difference exists between the plates, creating a uniform electric field. A charge $-q$ starts from rest at the surface of plate X and moves towards plate Y. By the time the charge arrives at plate Y, its kinetic energy is $K$. Which expression gives the electric field strength between the plates?
May/June 2014
A cell has an electromotive force (e.m.f.) of $6\,\text{V}$ and internal resistance $R$. An external resistor, which also has resistance $R$, is connected across the cell, as illustrated. Power $P$ is dissipated in the external resistor. The cell is then replaced with another cell that has an e.m.f. of $6\,\text{V}$ and negligible internal resistance. What is the new power dissipated in the external resistor?
May/June 2014
The diagram depicts a low-voltage circuit used to heat the water in a fish tank. The heater has a resistance of $3.0\,\Omega$. The power supply has an e.m.f. of $12\,\text{V}$ and an internal resistance of $1.0\,\Omega$. At what rate is energy transferred to the heater?
May/June 2014
A battery is joined in series with resistors X and Y, as illustrated in Fig. 6.1. X has a fixed resistance, whereas Y has resistance $6.0\,\Omega$. The battery has electromotive force (e.m.f.) $24\,\text{V}$ and zero internal resistance. A variable resistor with resistance $R$ is connected in parallel with X. The battery current $I$ is altered by changing $R$ from $5.0\,\Omega$ to $20\,\Omega$. Fig. 6.2 shows how $I$ changes with $R$.
May/June 2014
A potential difference of $1000\,\text{V}$ is applied across two parallel metal plates that are separated by a distance of $2\,\text{mm}$. What is the electric field strength in the region between the plates?
May/June 2015
A droplet of oil carries charge $-q$ and lies between two horizontal metal plates, as illustrated. The plates are separated by a distance $d$. It is found to remain at rest when the upper plate is at potential $+V$ and the lower plate is at potential $-V$. Under these conditions, what is the weight of the droplet?
May/June 2015
The diagrams illustrate two different circuits. In each circuit, the cells have the same electromotive force and zero internal resistance. Each of the three resistors has resistance $R$. In the circuit on the left, the power dissipated in the resistor is $P$. What is the total power dissipated in the circuit on the right?
May/June 2015
Which one of these equations correctly connects some of the following quantities: potential difference (p.d.) $V$, current $I$, resistance $R$, charge $Q$, energy $E$, power $P$, time $t$?
May/June 2015
An electric battery’s deliverable charge is measured in ampere-hours. For instance, a battery with capacity $40$ ampere-hours could, if fully charged, provide $0.2\,\text{A}$ for $200$ hours. What is the maximum energy a fully charged $12\,\text{V}$, $40$ ampere-hour battery could supply?
May/June 2015
A battery of e.m.f. $E$ and internal resistance $r$ is connected in series with a variable external resistor. The external resistance $R$ is gradually raised from zero. Which statement is correct? (Ignore any temperature effects.)
May/June 2015
A battery with electromotive force (e.m.f.) $6.0\,\text{V}$ and negligible internal resistance is joined in series to a resistor of resistance $6.0\,\Omega$ and a variable resistor whose resistance can vary from zero to $4.0\,\Omega$. A voltmeter is placed across the variable resistor. The resistance of the variable resistor is adjusted. What range of readings can the voltmeter show?
May/June 2015
An oil drop of mass $m$, containing $n$ extra electrons, is kept at rest in the uniform electric field between two horizontal plates spaced a distance $d$ apart. The voltage across the plates is $V$, the elementary charge is $e$ and the acceleration of free fall is $g$. Determine the value of $n$.
May/June 2015
A cell with e.m.f. $E$ transfers a charge $Q$ to an external circuit. Which statement is correct?
May/June 2015
An electric motor is attached to a pedal bicycle. The cyclist activates the motor for $3.0\,\text{minutes}$. A steady current of $3.5\,\text{A}$ is taken by the electric motor from a battery with a terminal voltage of $24\,\text{V}$. What is the energy supplied by the battery?
May/June 2015
Apply the definition of power to demonstrate that the SI base units of power are $\text{kg m}^2\text{ s}^{-3}$.
May/June 2015
What does the term electric field mean?
May/June 2015
Apply the definition of work done to demonstrate that the SI base units of energy are $\text{kg m}^2\text{s}^{-2}$.
May/June 2015
On Fig. 5.1, sketch the thermistor’s temperature characteristic.
May/June 2015
A resistor carries a current for an unknown length of time. Which two quantities can be used to determine the energy dissipated by the resistor?
May/June 2016
A $100\,\Omega$ resistor carries a current whose direction and magnitude vary, as shown. What is the average power dissipated in the resistor?
May/June 2016
Which diagram illustrates the arrangement of the electric field between a positively charged metal sphere and a negatively charged metal plate?
May/June 2016
Two parallel metal plates, $4.0\,\text{cm}$ apart, have electric potentials of $800\,\text{V}$ and $2000\,\text{V}$. Points X, Y and Z lie in the region between the plates at distances of $1.0\,\text{cm}$, $2.0\,\text{cm}$ and $3.0\,\text{cm}$ from the lower plate. Calculate the electric field strength, in $\text{V m}^{-1}$, at X, Y and Z?
May/June 2016