Current electricity (3.5.1)
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Electric current is the rate of flow of electric charge. It is measured in amperes which is one of the seven SI base units.
The electric current in passing a point can be found using the formula below:
Where:
- is the charge passing the point in coulombs , and
- is the time taken for the electric charge to pass the point in
Particles like protons and electrons carry a physical property known as electric charge, which is positive for protons and negative for electrons. Other particles, such as neutrons, do not carry any electric charge.
- Charged objects exert electrostatic forces on each other.
- Charge can be positive or negative.
- Like charges repel.
- Opposite charges attract.
Electric charge is measured in coulombs The coulomb is a derived unit. The coulomb can be converted to SI units using the current equation:
Which means that:
A value of is defined as the electric charge passing a point in a time for an electric current of :
The elementary charge is
The electric charges of ions and particles can be expressed as relative charges in terms of the elementary charge.
- The electron has a relative charge of which corresponds to an electric charge of
- The proton has a relative charge of which corresponds to an electric charge of
Ions are labelled with their relative charge. The relative charge indicates the number of elementary charges on the ion. This value is typically expressed as the number of electrons gained or lost relative to the neutral atomic form of the element.
For example, a ion has a relative charge of since it has an extra two protons compared to its number of electrons. Therefore, it has an electric charge of:
Electric current is the flow of charge carriers. An electric current in a metal is due to the flow of electrons.
Metals consist of a regular lattice of positively charged metal ions with a sea of delocalised electrons, which are able to move between the ions.
Most of the electrons in a metal are localised to the atoms and do not contribute to an electric current.
Applying a voltage to a metal wire causes the delocalised electrons to move through the wire from the negative end to the positive end.
Conventional current is defined as the direction in which positive charges flow. Conventional current was defined before the discovery of the electron.
Even if the current flow is due to electrons, conventional current is still treated as flowing from a positive terminal to a negative terminal. Electron current is in the opposite direction to conventional current.
For example, the current in metals is due to electrons, which flow in the opposite direction to conventional current.
Potential difference is defined as the energy transferred per unit charge.
When a circuit component has a potential difference across it, electrical energy is transferred from the power supply to the charge carriers and then to the component. The greater the difference in electric potential between the battery terminals, the more energy each coulomb of charge receives as it passes through the cell.
An example of energy transfer is a filament bulb connected to a battery. The bulb converts electrical energy into light and thermal energy. A battery with a higher potential difference between its positive and negative terminals supplies more energy per unit charge, so it charges the bulb with more energy each second, making it shine more brightly.
The potential difference across a component is given by the equation:
Where:
- is the energy in joules transferred to the component ,
- is the charge in coulombs passing through the component, and
- Potential difference is measured in volts
It is important to note that is the potential difference across a component when of energy is transferred to the component by of charge, meaning that:
When a potential difference is applied across the ends of a wire, by the terminals of a cell or battery, electrons move through the wire.
Electrons move around a circuit from the negative terminal of a cell or battery to the positive terminal.
It is important to note that conventional current is the flow of positive charge, which is in the opposite direction to the flow of negatively charged electrons. This is called electron current.
As electrons move through a wire, they collide with static metal ions, causing them to be scattered in random directions. Electrons can also collide with defects in the wire.
Despite the collisions, the electric force due to the potential difference at the ends of the wires still causes a net movement of electrons through the wire. This is called electron drift.
- The velocity of the electrons is referred to as their mean drift velocity.
- Electrons move through wires much more slowly than through free space.
An example of this is the standard copper wire used in the laboratory carrying a current, electrons move as slowly as
The energy transferred to electric charges passing through a component due to an electromotive force (EMF) or a potential difference (p.d.) can be found using similar equations.
The energy transferred to a charge passing through a component with EMF, is:
The energy transferred by a charge passing through a component with p.d. is given by the formula:
- A greater EMF or p.d. leads to a greater energy transfer.
- A greater charge also leads to a greater energy transfer.
- The energy transfer to or from the charges is equal to the work done on or by the charges.
Resistance is the measure of how easily current can flow through an electrical component. Resistance is the opposition to the flow of electric charge. A higher resistance means that less current can flow for a given applied voltage.
It is important to note that you will only see this symbol (the box shape for a fixed resistor) in exam questions.
It is useful to note that you may sometimes see a resistor drawn as a jagged line, shown in the diagram on the right, but the rectangular symbol is the most common.
The resistance of an electrical component is defined as:
Where:
- is the voltage across the component in volts ,
- is the current flowing through the component in amperes , and
- resistance is measured in ohms
The ohm is a derived unit and is defined as one volt per ampere:
Ohm’s law states that for a metallic conductor, kept at a constant temperature, the current flowing is directly proportional to the applied voltage:
Where:
- across the voltage of the component in volts
- is the current flowing through the component in amperes and
- is the resistance in ohms
Conductors that obey Ohm’s law are called ohmic conductors, where under constant physical conditions.
Current is measured in electric circuits using ammeters. They can be assumed to have zero resistance, meaning they have no effect on the current flow.
Ammeters are placed in series with a component to measure the current flowing through it.
The circuit symbol for an ammeter is a circle with a capital A in the centre as shown below.
The potential difference across a component in a circuit is measured by connecting a voltmeter in parallel to the component. The circuit symbol for a voltmeter is a circle with a capital V in the centre.
For example, the diagram below shows a voltmeter connected in parallel to a filament bulb.
A voltmeter can be assumed to have infinite resistance, so that no current flows through it when it is connected in parallel to a component.
Note that in reality, a very small, non-zero current must flow through the voltmeter. This current is required for the voltmeter to function and measure the energy carried by each charge.
An ohmic conductor has a linear characteristic current–voltage graph. A rearranged form of Ohm’s law states that:
The left-hand side of the equation is equal to the gradient of a linear graph. Therefore, the gradient of an graph for a conductor is equal to the reciprocal of its resistance. The steeper the gradient of the graph, the lower the resistance of the conductor.
The general equation of a straight line is:
Where:
- is the gradient, and
- is the Y-intercept.
Setting and gives:
Comparing this equation to Ohm’s law confirms that , but also shows that when : the graph of an ohmic conductor passes through the origin.
It is important to note that exam questions can be set where either or is on the horizontal axis of the characteristic graph
Fixed resistors are ohmic conductors. The curve of a fixed resistor shows a linear relationship.
The resistance of a fixed resistor is equal to the inverse of the gradient of the curve. Therefore, a steeper graph means a lower resistance.
A filament lamp is a non-ohmic conductor:
At low current, a filament lamp is an ohmic conductor and has a linear curve. However, the filament lamp becomes a non-ohmic conductor at higher current:
- The temperature of a filament lamp increases with current.
- As a filament lamp heats up, its metal ions vibrate more, which increases the resistance.
- A large resistance leads to the gradient of the curve decreasing.
A diode is a non-ohmic conductor. Diodes only allow current to flow in one direction.
The two circuits above show how the curve for a diode relates to how it is connected in a circuit:
- Forward bias
- When the diode arrow is pointing in the direction from the positive terminal to the negative terminal, current flows through the circuit.
- For current to flow, the applied voltage must be greater than the threshold voltage, which is normally
- In the circuit diagrams above, the lamp will turn on when the diode is connected in forward bias.
- Reverse bias
- When the diode ‘arrow’ is pointing from the negative terminal to the positive terminal, no current can flow.
- The lamp does not turn on.
In forward bias, the diode has a small resistance, which can lead to very large currents flowing through the circuit. To prevent damage to the circuit components, a fixed resistor is included to reduce the current.
Question walkthrough
Comparing Filament Lamp and Thermistor Resistance
Explain how resistance changes with increasing current for a filament lamp and an NTC thermistor, linking each to the effect of temperature on charge carriers.
Question walkthrough
Designing an Experiment to Test Ohm's Law
Design a circuit and method to test whether a fixed resistor is ohmic, then adapt the method to investigate non-ohmic components like a lamp, diode, or thermistor.
Question walkthrough
Identifying a Non-Ohmic Component from Data
Identify a filament lamp as a non-ohmic conductor from current-voltage data and recognise its characteristic curved I-V graph shape.
The resistance of a wire depends on the material of the wire and its physical dimensions, specifically its length and cross-sectional area.
Resistivity is a property of the material the wire is made of. Wires made of the same material may have different resistances due to their varying dimensions, but they still possess the same resistivity.
The equation for the resistance of a wire is:
Where:
- is the resistivity of the wire material in ,
- is the length of the wire, and
- is the cross-sectional area of the wire.
The resistivity of a metal can be determined using the following circuit components in the setup below:
- A flying lead is used to adjust the length of a current-carrying test wire being measured.
- A voltmeter is connected in parallel to the test wire using the flying lead to measure the potential difference across it.
- An ammeter is connected in series to the test wire to measure the current flowing through it.
- A power source supplies a voltage to the circuit.
The potential difference across the test wire and the current through it are measured, allowing the resistance to be calculated by Ohm’s law:
The equation for the resistance of a wire can be rearranged for resistivity :
A graph of resistance against length will have a gradient equal to the resistivity of the material divided by the cross-sectional area:
Which can then be multiplied by the cross-sectional area of the wire to find the resistivity.
The graph below shows the resistance against length plots for copper and aluminium wires of the same cross-sectional area.
The gradient for the aluminium wire is steeper than that of the copper wire, indicating that aluminium has a higher resistivity than copper.
The resistivity of a metal increases with temperature. When the temperature of a wire increases, the positive metal ions gain thermal energy and vibrate with a greater amplitude around their mean positions.
- Larger vibrations of the metal ions in a current-carrying wire result in more collisions between the electrons and the metal ions.
- A greater number of collisions leads to the electrons losing more energy as they move through the wire, causing them to move through the wire more slowly.
- Slower-moving electrons result in a lower current for a given potential difference and therefore a larger resistance.
In some semiconductors, an increase in temperature results in a decrease in resistance, unlike in metals. These semiconductors exhibit a negative temperature coefficient (NTC).
In NTC semiconductors, an increase in temperature leads to an increase in number density which is the number of charge carriers per unit volume.
A larger number density leads to an increase in current for a given potential difference, and hence a decrease in resistance.
Question walkthrough
Resistivity
Sketch how resistivity varies with temperature for an intrinsic semiconductor, linking the shape of the graph to how charge carrier number density changes with temperature.
A thermistor is an electrical component made from a negative temperature coefficient (NTC) semiconductor. The thermistor circuit symbol is a fixed resistor with a line through it.
A thermistor is a variable resistor because its resistance, and hence resistivity, decreases with temperature.
It is useful to note that thermistors are used in temperature-sensing circuits. Thermistors are used to monitor the temperature of complex electrical devices, such as computers and mobile phones, as well as household appliances like kettles and toasters.
A thermistor is a non-ohmic conductor. The resistance of a thermistor depends on its temperature. For a negative temperature coefficient (NTC) thermistor, the resistance decreases as the temperature increases.
When the temperature of a thermistor increases, additional charge carriers are released which can contribute to a current, decreasing the resistance (since resistance is opposition to current flow).
The curve for a thermistor is linear at low currents. At high current, a thermistor’s temperature increases, decreasing its resistance, causing the gradient of the curve to become steeper.
The temperature dependence of thermistors makes them useful for thermometers and thermostats.
The resistance–temperature relationship for a thermistor can be determined using the experimental setup below.
- A waterproof thermistor is submerged in a hot water bath. The thermistor is connected to an ohmmeter to measure its resistance as the water cools.
- By taking readings of temperature and resistance using the thermometer and ohmmeter at set time intervals, respectively, you can observe the relationship between resistance and temperature of a thermistor experimentally.
Alternatively, if an ohmmeter is not available, the thermistor can be connected across a battery in series with an ammeter to measure the current, through it, and in parallel with a voltmeter to measure the potential difference, across it. The thermistor resistance can then be calculated from Ohm’s law:
The currents and voltages must be low to ensure the thermistor obeys Ohm’s law.
A diode is a non-ohmic conductor. Diodes only allow current to flow in one direction.
The two circuits above show how the curve for a diode relates to how it is connected in a circuit:
- Forward bias
- When the diode arrow is pointing in the direction from the positive terminal to the negative terminal, current flows through the circuit.
- For current to flow, the applied voltage must be greater than the threshold voltage, which is normally
- In the circuit diagrams above, the lamp will turn on when the diode is connected in forward bias.
- Reverse bias
- When the diode ‘arrow’ is pointing from the negative terminal to the positive terminal, no current can flow.
- The lamp does not turn on.
In forward bias, the diode has a small resistance, which can lead to very large currents flowing through the circuit. To prevent damage to the circuit components, a fixed resistor is included to reduce the current.
The law of conservation of charge states that the net charge of an isolated system remains constant.
Kirchhoff’s first law:
- is a direct consequence of the conservation of charge and applies to electric circuits.
- states that the current flowing into a point in an electric circuit is equal to the current flowing out of the point.
Kirchhoff’s first law can be expressed mathematically:
Where:
- The symbol means ‘sum of’,
- is the curruent into the junction of an electric circuit, and
- is the curruent out of the junction.
The junction below has currents of and flowing into it:
Using Kirchhoff’s first law, this must be equal to the current flowing out of the junction, so
A circuit diagram uses standardised symbols to visually represent an electrical circuit.
Circuit diagrams can include a variety of electrical components, ranging from simple setups that consist of a cell, wires, and a resistor to more complex designs that feature combinations of resistors, capacitors, thermistors, and other elements.
Rules for circuit diagrams:
- Use horizontal or vertical lines to represent wires only.
- Use the standardised circuit symbols.
- Do not leave any gaps between wires.
Drawing the direction of the current flow can be helpful, but is not essential. Current flows from the positive terminal to the negative terminal of the cell or battery.
For a circuit to be operational, it must include:
- a power source (i.e. a cell or battery)
- a closed path for the current to flow
- electrical components (e.g. resistors, capacitors, thermistors, etc.)
It is important to note that connecting a battery directly to a wire, without any other components, can cause the battery to short-circuit. Wires have very low resistance, which allows a high current to flow through them when a voltage is applied.
The simple circuit below consists of a cell, an ammeter, and a resistor.
- The battery serves as a power source, providing electrical energy to drive electrons around the circuit.
- The ammeter measures the current travelling through the wires.
- The resistor is used to control the amount of current travelling through the circuit.
It is important to note that some of the electrical energy travelling through the resistor and wires is dissipated as heat.
This simple circuit setup enables you to measure the current flowing through a resistor when a specific voltage is applied by the battery. This can be used to measure voltage if the resistance is known, or to measure resistance if the voltage is known.
The simple circuit below consists of a cell, a switch, and a lamp.
- The battery serves as a power source, providing electrical energy to drive electrons across the circuit.
- The switch prevents current from flowing through it when it is closed.
- The lamp converts electrical energy into light energy.
This simple circuit setup enables a light to be turned on and off using a switch.
Power is defined as the rate at which work is done, or the rate of energy transfer. The SI unit of power is the watt A higher power rating means a device transfers more energy per second:
Where:
- is the power in watts (W),
- is the energy transferred (work done) in joules (J), and
- is the time taken in seconds (s).
One watt is defined as the transfer of one joule of energy per second:
Electrical power is the rate at which electrical energy is transferred within a circuit. The electrical power supplied to a component can be calculated using:
Where:
- is the power in watts (W),
- is the potential difference in volts (V), and
- is the current in amperes (A).
A larger current or potential difference leads to a greater rate of energy transfer.
The electrical power dissipated by a component can be found using:
Substituting this equation with Ohm’s law:
Returns the following:
Where:
- is the power in watts (W),
- is the current in amperes (A), and
- is the resistance in ohms (Ω).
The current is squared, so a small increase in current causes a much larger increase in power dissipation.
This equation is commonly used for resistive heating in components such as heaters and filament lamps.
The electrical power dissipated by a component can also be found using:
Substituting this equation with Ohm’s law:
Returns the following:
Where:
- is the power in watts (W),
- is the potential difference in volts (V), and
- is the resistance in ohms (Ω).
For a fixed resistance, increasing the potential difference causes the power dissipated to increase rapidly because the voltage is squared.
There are three common equations for electrical power. To select the correct electrical power equation, first identify which quantities are given in the question.
These equations are all equivalent, but selecting the correct one first avoids unnecessary rearranging.
Avoid common exam pitfalls such as introducing extra steps or using incorrect formulas. These errors not only waste valuable time but also increase the risk of algebraic or unit mistakes.
A quick check of the given quantities in the question should immediately determine the correct equation.
In a series circuit with two unequal resistors, the current is the same through all components. The power dissipated in a component is given by:
Since the current is the same, the power dissipated in the component is directly proportional to the resistance of the component. Therefore, the component with the larger resistance dissipates more power.
The resistor with the greater resistance converts more electrical energy into heat and transfers it to the environment each second, thereby raising the temperature.
In a parallel circuit with two unequal resistors, the potential difference across each component is the same. The power dissipated in a component is given by:
Since the potential difference is the same, the power dissipated in the component is inversely proportional to the resistance of the component. Therefore, the component with the smaller resistance dissipates more power.
The resistor with the smaller resistance dissipates more power, resulting in a higher rate of electrical energy transfer to the surroundings and consequently, greater heating.
Question walkthrough
Power Dissipated by a Resistor
Convert a resistance from kilohms to ohms and use P = V²/R to calculate the power dissipated across a resistor connected to a battery.
Question walkthrough
Comparing Power Dissipation in Resistors
Identify which resistor in a mixed series-parallel network dissipates the most power, by comparing branch resistances and currents rather than calculating each power value directly.
The energy transferred (work done) is equal to the power multiplied by the time for which the energy is transferred. A system with a higher power transfers more energy each second:
Where:
- is the energy transferred (work done) in joules (J),
- is the power in watts (W), and
- is the time taken in seconds (s).
Electrical power in a circuit is given by:
Substituting this equation with the energy transferred equation:
Returns the following:
Where:
- is the energy transferred (work done) in joules (J),
- is the potential difference in volts (V),
- is current in amperes (A), and
- is time in seconds (s).
This shows energy transferred is proportional to current, voltage, and time.
A higher potential difference, current or time increases the energy transferred.
Electrical power in a circuit is given by:
Substituting this equation with the energy transferred equation:
Returns the following:
Where:
- is the energy transferred (work done) in joules (J),
- is the potential difference in volts (V),
- is current in amperes (A), and
- is time in seconds (s).
Question walkthrough
Comparing Power in Series vs Parallel
Compare the energy transferred by identical bulbs connected in series and in parallel across the same cell, using the potential divider effect and the power formula P = V²/R.
Kirchhoff’s second law states that the sum of the electromotive force (EMF) is equal to the sum of the potential difference (p.d.) in a loop of a circuit.
Alternatively, the sum of the EMF and the p.d. in a loop of a circuit is equal to zero:
- EMF is energy per unit charge (voltage) transferred from chemical to electrical energy. It is produced by an electrochemical cell or a changing magnetic field.
- p.d. across a component is energy per unit charge (voltage) dissipated across the component.
So, this law is a consequence of the conservation of energy.
In any circuit loop, potential rises across batteries or cells by their EMF and drops across components by their resistance multiplied by the current flowing through them.
The sum of the EMF is equal to the sum of the p.d. in any loop of a circuit.
If the direction of the current is negative in any part of a loop, then the direction of the p.d. is negative.
Only the red parts of the circuit are the loop being analysed in the examples above. Black sections are part of the real circuit but aren’t used in that loop’s equation.
Curved arrows show the direction you’re tracing the loop, not the actual current direction.
Trace with the current and the p.d. is positive; trace against it and the p.d. is negative, even though the resistor’s real p.d. hasn’t changed.
Question walkthrough
Using Kirchhoff's Second Law to Find Voltage
Apply Kirchhoff's second law to a series circuit with a thermistor and filament lamp to find a missing voltmeter reading from the cell EMF and one known p.d.
Question walkthrough
Finding Potential Difference Between Two Points
Calculate the potential difference between two points in a circuit by finding the p.d. across each branch with Ohm's law and taking their difference.
Kirchhoff’s first law states that the sum of the current flowing into a junction is equal to the current flowing out of a junction.
Question walkthrough
Applying Kirchhoff's Current Law at Junctions
Determine three unknown branch currents by applying Kirchhoff's current law at successive junctions in a multi-branch circuit.
Question walkthrough
Solving for Unknown Ammeter and Voltmeter Readings
Find ammeter and voltmeter readings in a series-parallel circuit using Ohm's law and current splitting across parallel resistors, with an alternative potential-divider method.
In a series circuit:
- the current through each resistor is the same.
- the sum of the voltages across the resistors is equal to the total voltage.
The total resistance of two or more resistors in series is given by:
Question walkthrough
Calculating Current in a Series Circuit
Find the current in a series circuit by summing three resistances to get the total resistance, then applying Ohm's law.
Question walkthrough
Deriving the Series Resistors Formula
Derive the total resistance formula for three resistors in series from Kirchhoff's voltage law and Ohm's law, showing each algebraic step.
In a parallel circuit:
- the voltage across each resistor is the same,
- the sum of the currents through the resistors is equal to the total current.
The total resistance of two or more resistors in parallel is given by:
It is important to recall the correct formula for a circuit in parallel.
Question walkthrough
Find total resistance in a circuit
By analysing and interpreting a circuit diagram, determine the total resistance in a circuit and the EMF of the power source.
Question walkthrough
Deriving the Parallel Resistors Formula
Derive the total resistance formula for three parallel resistors from Kirchhoff's current law and Ohm's law, showing each algebraic step.
Some circuits contain both series (denoted in the diagram as ) and parallel combinations. In such cases, the equations for series and parallel resistors can be combined.
Question walkthrough
Finding LED Resistance in a Mixed Circuit
Calculate an LED's resistance in a circuit combining series and parallel resistors, using Ohm's law and the reciprocal rule for parallel combinations.
Question walkthrough
Combining Three Parallel Resistor Branches
Practise finding total resistance for a network with three parallel branches, including a branch made of two series resistors, using the reciprocal formula for parallel combinations.
Question walkthrough
Finding Cell Current Using a Filament Graph
Uses a non-linear voltage-current graph for a filament lamp to find branch currents in a series-parallel circuit and the total current in the cell.
A potential divider circuit is used to vary the potential difference (p.d.) output , connected to a fixed potential difference input A simple potential divider circuit consists of two resistors in series.
A potential divider is used to supply an external circuit with any p.d. between zero and the p.d supplied by the power source,
Kirchhoff’s second law states that the total p.d. supplied by the power source equals the sum of the p.d. across each resistor.
The resistances of the resistors determine the p.d. output. The resistor with the larger share of the total resistance receives a greater share of the total p.d.
A potential divider is used to split the potential difference of a power supply, but in some applications, the output voltage needs to vary.
The output voltage of a potential divider can be varied by replacing one of the fixed resistors with a variable resistor. As the resistance of the variable resistor changes, so does its share of the input p.d. causing to change in response.
Thermistors can be used as one of the resistors in a potential divider circuit, in order to provide a that varies with temperature input. This circuit could form part of a temperature sensor.
The resistance of a thermistor varies with its temperature:
- The higher the temperature of a thermistor, the lower its resistance.
- A higher temperature excites charge carriers in the thermistor, reducing the resistance.
When the temperature increases, the thermistor’s resistance drops. This results in the thermistor receiving a smaller fraction of the input voltage leading to a decrease in the output voltage Conversely, will rise when the temperature decreases.
A light-dependent resistor (LDR) can also be used as part of a potential divider circuit to provide an output voltage that varies in proportion to the intensity of the light. For example, an LDR could form part of a light sensor.
The resistance of a light-dependent resistor (LDR) varies with the light intensity incident on it:
- The higher the light intensity incident on an LDR, the lower its resistance.
- Incident light (of a sufficiently high frequency) excites charge carriers in an LDR, thereby reducing the resistance.
When light intensity is high, the LDR’s resistance is low. Consequently, it receives a smaller fraction of the input voltage resulting in a decrease in the output voltage Conversely, when the light intensity is low, the output voltage will increase.
Circuits with a low that require a varying may use a potentiometer instead of two separate fixed resistors. A potentiometer consists of three terminals and a sliding contact.
The position of the contact determines how the p.d. is shared between the two terminals and therefore the value of
As the slider is moved down, becomes smaller and becomes larger. now has a smaller share of the overall resistance and receives a smaller share of the overall voltage, resulting in a decrease in The inverse will happen if the slider is moved up.
An example of this type of circuit would be a sound volume control. Adjusting the sliding contact on the volume control changes the share of resistance and, therefore, the voltage output. The output would be connected to a speaker whose volume would change in response to the voltage level.
The electromotive force (EMF) of a source in a circuit, such as a cell or battery, is the energy per unit charge transferred from chemical energy to electrical energy.
Internal resistance Real cells and batteries have some resistance to the flow of current within themselves. This resistance causes energy to be lost as heat inside the source.
Generally, the voltage across the terminals of a cell or battery is less than its EMF as some energy is lost due to internal resistance.
A real cell of EMF, and internal resistance, can be modelled as an ideal cell (defined as a cell with no internal resistance) of EMF, in series with a fixed resistor of resistance
The electromotive force, (EMF) of a source in a circuit such as a cell or battery is energy per unit charge transferred from chemical energy to electrical energy. Note that some of this electrical energy will be dissipated as heat across the internal resistance.
The terminal potential difference, of a cell or battery is the energy per unit charge transferred to electrical energy in the external circuit. The terminal potential difference of a cell or battery can be measured by connecting a voltmeter across its terminals.
‘Lost volts’ refers to the energy per unit charge wasted as heat inside a battery or cell. It is the drop in potential across the battery or cell’s internal resistance.
Due to Kirchhoff’s second law (conservation of energy), we have:
It is important to recall the potential difference across the terminals of a battery or cell.
Question walkthrough
Explaining Why Terminal Voltage Is Less Than EMF
Explain why the terminal voltage of a cell in series with a resistor is less than its EMF, in terms of internal resistance and energy loss.
Lost volts, due to internal resistance inside a source of EMF is given by:
Where:
- is the current flowing through the source of EMF, and
- is its internal resistance.
Terminal potential difference, of a source of EMF is given by:
Where:
- is the current flowing through the source of EMF, and
- is the total resistance of the external circuit.
The EMF of a source is given by:
which may be written as:
To determine internal resistance and EMF of a power source:
- Set up a circuit with a variable resistor connected in series with the power source.
- Vary the resistance of the variable resistor and record voltage and current.
- Plot a graph of against
- The equation, tells us that the Y intercept gives the EMF and the gradient of the line gives the negative internal resistance
Question walkthrough
Finding Internal Resistance from Voltmeter Percentage Drop
Determine the internal resistance of a cell in terms of the external resistance, given the percentage decrease in voltmeter reading when a switch is closed.
Question walkthrough
Finding EMF in Two Opposing Cells Circuit
Calculate the EMF of a cell using two cells with opposing EMFs and internal resistance connected to an external resistor, applying Kirchhoff's voltage law to a single-loop circuit.
The electromotive force (EMF) of a power source is the amount of energy converted to electrical energy per unit charge.
EMF is similar to potential difference but is used when work is done on the charge carriers, such as by a power source like a cell or battery.
Examples of this include:
- Common batteries used in electrical circuits convert chemical energy into electrical energy.
- Solar cells, which convert light energy into electrical energy, and thermocouples which convert thermal energy into electrical energy.
EMF in is given by the formula:
Where:
- is the work done in on the charges by the power source
- is the charge in passing through the power source.
It is important to note that EMF is not a force and is measured in volts the same as potential difference.
Moreover, the word ‘force’ in electromotive force originates from the way a power source transfers energy to the charges moving through it, which drives them around a circuit.
EMF and potential difference are both measured in and are both defined as the energy transferred per unit charge. However, they both have a discrete key distinction:
- EMF is used when work is done on the charge carriers, and the charge carriers gain energy.
- Potential difference is used when work is done by the charge carriers, and the charge carriers lose energy.
An example of this is illustrated in the diagram above.
- Work is done on charge carriers as they move through a battery and are given energy.
- However, work is done by the charge carriers when they move through a filament bulb; the electrical energy of the charge carriers is converted into thermal energy and light energy.
The energy transferred to electric charges passing through a component due to an electromotive force (EMF) or a potential difference (p.d.) can be found using similar equations.
The energy transferred to a charge passing through a component with EMF, is:
The energy transferred by a charge passing through a component with p.d. is given by the formula:
- A greater EMF or p.d. leads to a greater energy transfer.
- A greater charge also leads to a greater energy transfer.
- The energy transfer to or from the charges is equal to the work done on or by the charges.