What a cell does

An electric cell is a device that transfers energy to moving charges in a circuit by converting energy from another store into electrical energy. It isn’t a tiny electron pump; the metal wires already have mobile charge carriers inside them. What the cell does is set up an electric field around the circuit, and that field causes the charges to drift.

Electromotive force is an energy-per-charge quantity. It describes the energy a source supplies to charge as the charge passes through it. The name is a historical one: emf is not a force. Its unit is the volt, the same as potential difference, since both are measured as joules per coulomb.

A complete dc circuit works like a system with a source and sinks. The cell acts as the source, transferring energy to charges. Resistors, lamps and motors act as sinks, transferring that energy into internal energy, light or mechanical work. This is why comparing a circuit with a heat engine or the atmosphere makes sense: each involves flows driven by differences, with energy transferred between parts of a system. The difference provides the drive. A heat engine is driven by a temperature difference; a chemical cell is driven by chemical reactions.

Direct-current operation

A cell in this topic is treated as a direct-current source, meaning a source that drives charge round the external circuit in one direction only. Alternating-current circuits are not needed here. If a question says “cell” or shows a simple battery symbol, assume dc unless told otherwise.

Chemical cells

A chemical cell is an electric cell that transfers chemical energy to electrical energy through chemical reactions at its electrodes. A primary cell is a chemical cell designed to be used until its reactants are depleted, then discarded. A secondary cell is a chemical cell whose discharge reactions can be reversed during charging, so it can be used many times.

Chemical cells are portable and quiet. They’re also convenient, since they can supply steady dc without mains electricity. That makes them useful when flexibility matters, such as in small sensors, handheld devices, emergency lighting and transport applications. The trade-off is clear enough: cells store a finite amount of energy, add mass, may have limited lifetimes, and use materials that must be mined, transported and recycled responsibly.

Solar cells

A solar cell is an electrical energy source that converts electromagnetic radiation into electrical energy using a photovoltaic material. A single solar cell has a small emf, so practical panels connect many cells together to produce useful currents and voltages.

Solar cells draw their input energy from the Sun, and no fuel is consumed during operation. Their drawbacks matter too. Output depends on illumination, panels can be expensive to install, and storage is usually needed if energy is required at night or during poor weather.

Compares primary cells, secondary cells and solar cells as circuit energy sources.

Why circuit diagrams matter

A circuit diagram uses symbols to show how electrical components are connected. It doesn’t show where they happen to be placed on the bench. The real circuit might look messy, but the diagram should make the electrical relationships easy to read.

Use the circuit symbols from the IB Physics data booklet. Watch the cell and battery symbols carefully: a battery is a collection of cells connected together, even though people often say “battery” when they mean a single cell.

A dot at a junction shows that wires are electrically connected. If two drawn wires cross with no dot, treat them as not joined. When they matter, component values, meter ranges and supply values are usually written beside the relevant symbol.

Building and checking circuits

When you build a circuit, translate the diagram one connection at a time. In a measurement circuit, put the ammeter in series with the component whose current you want, and put the voltmeter in parallel with the component whose potential difference you want. If the circuit doesn’t behave as expected, check the power supply, loose leads, meter ranges, and whether the actual layout matches the diagram.

Current and charge flow

An electric current is the rate at which electric charge flows through a point in a circuit. A charge carrier is a mobile charged particle that contributes to current. In metals, the charge carriers are electrons; in liquids and gases, they may be positive and negative ions.

For a direct current,

A coulomb is a large amount of charge compared with the charge on a single electron. Since charge in coulombs can be written in ampere seconds, use $C = A\,s$ when reducing units to SI base units.

Conventional current and electron current

Conventional current is a model for current direction: it points the way positive charge would move in a circuit. In a metal wire, electrons drift the other way because they are negatively charged. We still use conventional current because many electricity and magnetism rules were developed using that direction.

Electrons drift slowly through a metal. A lamp lights almost immediately, but not because one electron shoots from the switch to the lamp. The electromagnetic disturbance is set up through the circuit very quickly, so charges throughout the circuit begin to drift almost together.

Fields link

An electric field is a region where an electric charge experiences a force. In this topic, the field matters as the cause of charge-carrier drift. Later fields topics compare electric, gravitational and magnetic fields: electric and gravitational fields can both have inverse-square forms around point sources, but electric fields involve positive and negative charge whereas gravitational fields involve mass only. Magnetic fields are different again because isolated magnetic poles are not observed.

Energy per unit charge

Electric potential difference is the energy transferred per charge: the work done per unit positive charge as it moves between two points along the path of the current.

One volt means one joule per coulomb. A large potential difference across a component, then, means each coulomb of charge transfers a large amount of energy there.

In a simple lamp circuit, the cell gives energy to the charges. The connecting wires are usually treated as having negligible potential difference, because very little energy is transferred to them. Across the lamp, the potential difference is significant: the lamp is designed to transfer electrical energy into internal energy and light.

Positive charge, if free to move, goes from higher potential to lower potential. Electrons move the other way, but the energy accounting still works when we use conventional current and positive charge.

Mobility of charge carriers

An electrical conductor is a material with charge carriers mobile enough to produce a significant current when an electric field is applied. In a metal, the outer electrons are delocalized, so they can drift through a lattice of positive ions.

An electrical insulator is a material where charge carriers have very low mobility. Under ordinary conditions, an applied electric field produces little current. Charged particles may still be present; they just aren’t free to travel through the material.

A semiconductor is a material with charge-carrier availability between that of a conductor and an insulator. Its availability can change strongly with conditions such as temperature or illumination, which is the idea behind thermistors and LDRs later in the topic.

In liquids and gases, conduction can happen when ions are free to move. Positive ions drift in the direction of the electric field; negative ions drift the other way. The same rule applies in every material: current requires mobile charge carriers.

Microscopic origin

Electric resistance is a property of a component or material that describes how strongly it transfers electrical energy from moving charges to the material for a given current. In a metal, electrons gain energy from the electric field, then pass energy to the vibrating ion lattice through interactions. Seen on the larger scale, that energy transfer shows up as heating.

The particle model is useful here. Resistance is not some mysterious “friction in the wire”; it’s an energy-transfer process between mobile charge carriers and the material structure. In a hotter metal, the lattice vibrates more vigorously, so electrons interact more often and resistance usually increases.

This connects straight back to thermal physics. Energy transferred to the lattice increases the internal energy of the conductor. If energy leaves the conductor more slowly than electrical work supplies it, the temperature rises.

Measuring resistance in practice

To measure the resistance of a wire, connect an ammeter in series and a voltmeter across the wire. Record several pairs of current and potential-difference readings, keeping the current small enough that the wire’s temperature does not change appreciably. Calculate the resistance for each pair, then use a mean value, with uncertainties and significant figures matched to the instrument precision.

Definition and units

Electrical resistance is the ratio of the potential difference across a component to the current through it:

One ohm is the same as one volt per ampere. So, for a component with resistance 1 $\Omega$, a potential difference of 1 V across it gives a current of 1 A, as long as its resistance has that value under those conditions.

You can use this definition for any component, ohmic or non-ohmic. For a non-ohmic component, $V/I$ may change when the current changes.

Meters and their effect

An ideal ammeter has zero resistance, so adding it in series does not alter the circuit current. An ideal voltmeter has infinite resistance, so connecting it in parallel draws no current. Unless the question says otherwise, IB problems assume ammeters and voltmeters are ideal.

Real meters do have resistance. When a non-ideal meter is given, treat its resistance as constant and include it in the circuit: an ammeter adds resistance in series, while a voltmeter makes a parallel branch across the component it is measuring.

Separating material from shape

Resistivity is a property of the material itself. It tells you how strongly that material opposes current flow, without depending on the sample’s particular length or cross-sectional area.

Rearrange it to get $R = \rho L/A$. A longer wire therefore has a larger resistance; a thicker wire has a smaller one. For a circular wire, increasing the diameter reduces resistance because the area depends on diameter squared.

The unit is ohm metre, $\Omega\,\text{m}$, not ohm per metre. That small wording difference matters.

Finding resistivity experimentally

A good resistivity experiment measures the resistance of a uniform sample, along with its dimensions. For a wire, measure the length between the contacts. Then measure the diameter at several positions with a micrometer or digital callipers before calculating the area. To test the relationships, plot $R$ against $L$ for wires of the same material and diameter, or plot $R$ against $1/d^2$ for equal lengths of the same material.

Thermal and electrical conduction

There’s a useful parallel with thermal conduction. In a metal, free electrons help carry charge and also contribute to thermal energy transfer. The large-scale equations look similar as well: a gradient drives a flow. In electrical conduction, current is associated with a potential gradient; in thermal conduction, energy-transfer rate is associated with a temperature gradient. The details are different, but the modelling idea is the same: microscopic carriers produce a measurable macroscopic transport property.

The law, carefully stated

Ohm’s law is an empirical rule: the potential difference across a metallic conductor is directly proportional to the current through it, as long as the conductor’s physical conditions stay constant.

In this syllabus, you treat a metal conductor at constant temperature as an ohmic device. That temperature condition isn’t just a tidy add-on; it’s central to the law. If the conductor heats up noticeably, the relationship may no longer be proportional.

A straight-line graph of $V$ against $I$ through the origin shows constant resistance. The gradient gives the resistance. Watch the wording here: $R = \frac{V}{I}$ is the definition of resistance, not Ohm’s law. Ohm’s law is the proportional relationship under fixed physical conditions.

Investigating an ohmic conductor

To test a metal wire, change the supply potential difference gently, measure $I$ and $V$, then plot $V$ on the vertical axis against $I$ on the horizontal axis. Keep the range small enough that the wire temperature stays effectively constant. A straight best-fit line through the origin supports ohmic behaviour.

Ohmic and non-ohmic devices

An ohmic conductor has potential difference directly proportional to current, provided the physical conditions stay constant. A non-ohmic conductor does not have potential difference directly proportional to current, so its resistance changes as the operating conditions change.

A filament lamp is the standard lab example. As the current rises, the filament heats up. Its hotter lattice vibrates more strongly, and moving electrons transfer energy to it more easily. Resistance increases, so the $V$-$I$ graph bends instead of staying as a straight line.

You can explain resistor heating using ideas from elsewhere in physics: the electric field does work on charge carriers, interactions with the lattice transfer energy, and the material’s internal energy increases. That’s conservation of energy, together with the particle model of matter.

Investigating non-ohmic behaviour

For a lamp investigation, use the same basic ammeter-voltmeter circuit as for a wire, but take readings in both current directions. Plot $V$ against $I$ with the origin in the centre, so the positive and negative readings can be compared. The curve should pass through the origin, but it should not be straight. Calculate $R$ from $\frac{V}{I}$ for individual points; do not use the tangent gradient as the resistance.

Rate of energy transfer

Electrical power is the rate at which a component transfers electrical energy.

These three forms say the same thing, just rearranged using the resistance relationship. Use $P = IV$ when you know the current and potential difference. Use $P = I^2R$ when you know the current and resistance. Use $P = \frac{V^2}{R}$ when you know the potential difference and resistance.

Over a time interval, the energy transferred is

Put this together with the power equations for heating calculations involving resistors, lamps, heaters and other devices where electrical energy is converted mainly to internal energy.

For a resistor connected to the same supply potential difference, a lower resistance gives a higher power because $P = \frac{V^2}{R}$. For a resistor carrying the same current, a higher resistance gives a higher power because $P = I^2R$. Always check which quantity stays constant.

Series circuits

A series connection is an arrangement where components are joined one after another, so the same current passes through every component.

For resistors in series:

$$I = I_1 = I_2 = \dots$$ $$V = V_1 + V_2 + \dots$$

The current stays the same because charge cannot pile up indefinitely between components. The potential differences add because each coulomb transfers energy as it passes through each component in turn.

Parallel circuits

A parallel connection is an arrangement where components are connected across the same two nodes, so each branch has the same potential difference.

For resistors in parallel:

$$I = I_1 + I_2 + \dots$$ $$V = V_1 = V_2 = \dots$$

Branch currents add because charge flow splits at a junction and recombines later. A parallel combination has an equivalent resistance smaller than the smallest branch resistance, because adding a branch gives charge another route.

Practical check

You can check these rules with a multimeter used as an ohmmeter. First measure the individual resistor values, noting tolerances. Then measure combinations in series and in parallel. For a complicated network, simplify the obvious parallel groups first, then combine the series parts. Repeat until one equivalent resistance remains.

A model of a real cell

A real cell can be modelled as an ideal source of emf in series with an internal resistance, which is a resistance inside the cell that causes energy transfer within the cell when current flows.

When current flows, the external circuit gets a smaller potential difference than the emf. Some energy per coulomb is transferred inside the cell instead. The terminal potential difference is given by $V = \varepsilon - Ir$. The term $Ir$ is sometimes called the lost volts; it isn’t lost in terms of energy conservation, just unavailable to the external circuit.

The emf of a cell is the open-circuit terminal potential difference: the terminal potential difference when no current is drawn. If the load resistance decreases, the current increases and the terminal potential difference usually falls.

Measuring emf and internal resistance

To measure $\varepsilon$ and $r$, connect a variable resistor across the cell, then measure the terminal potential difference and current for several settings. Plot $V$ on the vertical axis against $I$ on the horizontal axis. Since $V = \varepsilon - Ir$ is a straight-line equation, the vertical intercept gives $\varepsilon$ and the gradient is $-r$. Use a range that does not overheat or rapidly discharge the cell.

A simple model with fixed emf and fixed internal resistance is deliberately idealized. It still helps, because it predicts the main trend: higher current means more energy transferred inside the cell and a lower terminal potential difference.

Devices whose resistance can change

A variable resistor is a resistor whose resistance can be adjusted, or one whose resistance changes because of a physical condition. In this syllabus, variable resistance is limited to thermistors, light-dependent resistors and potentiometers.

A thermistor is a semiconductor resistor whose resistance varies with temperature. Here, the type used is a negative-temperature-coefficient thermistor: as temperature increases, resistance decreases. The explanation comes from the particles in the material. A higher temperature makes the lattice vibrate more, which on its own would make charge motion harder, but it also releases many more mobile charge carriers in the semiconductor. That increase in carriers has the larger effect.

A light-dependent resistor is a semiconductor resistor whose resistance decreases as light intensity increases. Incoming photons transfer energy to the material and free more charge carriers, so the same potential difference can produce a larger current.

Potentiometers and potential dividers

A potentiometer is a three-terminal variable resistor used as a potential divider, with a sliding contact that selects a fraction of the supply potential difference. In this arrangement, it can give a smoothly adjustable output potential difference from nearly zero up to nearly the full supply value.

A two-terminal variable resistor in series can control current, but it may not give a wide range of potential difference across a load unless its maximum resistance is much larger than the load resistance. A potentiometer is usually the better choice when the aim is to supply an adjustable voltage to another part of a circuit.

In a sensor circuit, a thermistor or LDR is often connected in series with a fixed resistor. The supply potential difference is shared in proportion to resistance, so as the sensor resistance changes, the potential difference across the sensor and across the fixed resistor change in predictable opposite ways.