What a cell does

An electric cell 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 supplied by a source to the charge that passes through it. The name is historical: emf is not a force. Its unit is the volt, the same as potential difference, since both are measured in joules per coulomb.

A complete dc circuit acts like a system with a source and sinks. The cell is the source, transferring energy to charges. Resistors, lamps and motors are 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 one 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: a source that drives charge round the external circuit in one direction only. Alternating-current circuits are not required here. If a question says “cell” or shows a simple battery symbol, assume dc unless told otherwise.

Chemical cells

A chemical cell transfers chemical energy to electrical energy through chemical reactions at its electrodes. A primary cell is designed to be used until its reactants run out, then discarded. A secondary cell has discharge reactions that can be reversed during charging, so the cell can be used many times.

Chemical cells are portable, quiet and convenient. They can also provide steady dc without a mains supply, which makes them useful in situations where flexibility matters: small sensors, handheld devices, emergency lighting and transport applications. The trade-off is clear. Cells store only a finite amount of energy, add mass, may have limited lifetimes, and use materials that need to be mined, transported and recycled responsibly.

Solar cells

A solar cell is an electrical energy source that uses a photovoltaic material to convert electromagnetic radiation into electrical energy. 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 while they operate. There are drawbacks too: the 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 connect, rather than where they happen to sit on the bench. The real circuit might look messy; the diagram's job is to make the electrical relationships clear.

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. Two drawn wires that cross without a dot should be treated as not joined. When they matter, component values, meter ranges and supply values are normally written beside the relevant symbol.

Building and checking circuits

When you set up a circuit, translate the diagram one connection at a time. In a measurement circuit, put the ammeter in series with the component whose current is being measured, and put the voltmeter in parallel with the component whose potential difference is being measured. 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 helps produce that current. In metals, the charge carriers are electrons; in liquids and gases, they may be positive and negative ions.

For a direct current,

I = Δq/Δt, where I is direct current (A), Δq is the charge passing a point (C), and Δt is the time interval (s).

A coulomb is huge 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 means the current direction defined by 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 themselves drift slowly through a metal. A lamp lights almost immediately not because one electron shoots from the switch to the lamp, but because 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 in which an electric charge experiences a force. For this topic, we only need the field 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 work done per unit positive charge as charge moves between two points along the path of the current.

V = W/q, where V is electric potential difference (V), W is work done or energy transferred (J), and q is the charge moved (C).

One volt is one joule per coulomb. A larger potential difference across a component means each coulomb of charge transfers more energy there.

In a simple lamp circuit, the cell transfers energy to the charges. We usually model the connecting wires as having negligible potential difference, since very little energy is transferred to them. The lamp has a significant potential difference across it because it is made to transfer electrical energy into internal energy and light.

If positive charge is free to move, it moves from higher potential to lower potential. Electrons move the opposite way, but the same 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 that can move easily enough to produce a significant current when an electric field is applied. In metals, 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. That doesn’t mean the material contains no charged particles; they just aren’t free to travel through it.

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. That idea is used later in the topic for thermistors and LDRs.

In liquids and gases, conduction can happen when ions are free to move. Positive ions drift in the direction of the electric field, while negative ions drift in the opposite direction. The rule is the same for 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 during interactions. At the macroscopic scale, that energy transfer shows up as heating.

Here the particle model does useful work. Resistance is not some mysterious “friction in the wire”; it is 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 frequently and resistance usually increases.

The idea also connects straight to thermal physics. Energy transferred to the lattice increases the internal energy of the conductor. If energy leaves the conductor more slowly than it is supplied electrically, the conductor’s 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:

R = V/I, where R is electrical resistance (Ω).

One ohm is the same as one volt per ampere. A component with a resistance of 1 Ω will have a current of 1 A when a potential difference of 1 V is applied across it, provided its resistance is 1 Ω under those conditions.

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

Meters and their effect

An ideal ammeter has zero resistance, so when you place it in series, it doesn’t change the circuit current. An ideal voltmeter has infinite resistance, so when you place it in parallel, it draws no current. Unless the question states otherwise, IB problems treat ammeters and voltmeters as ideal.

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

Separating material from shape

Resistivity is a material property: it tells us how strongly a material opposes current flow, without depending on the sample’s particular length or cross-sectional area.

ρ = RA/L, where ρ is resistivity (Ω m), A is cross-sectional area (m²), and L is conductor length (m).

Rearrange it and you get R = ρL/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, Ω m, not ohm per metre. That small wording difference matters.

Finding resistivity experimentally

In a good resistivity experiment, you measure the resistance of a uniform sample and also measure 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 with the same material and diameter, or plot R against 1/d² for equal lengths of the same material.

Thermal and electrical conduction

There’s a useful parallel with thermal conduction. In a metal, free electrons carry charge and also help transfer thermal energy. The large-scale equations look similar as well: a gradient drives a flow. For electrical conduction, current is linked to a potential gradient; for thermal conduction, energy-transfer rate is linked to a temperature gradient. The details are different, but the modelling idea matches: 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 physical conditions of the conductor remain constant.

In this syllabus, a metal conductor at constant temperature counts 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 significantly, the relationship may no longer be proportional.

On a graph of V against I, a straight line through the origin shows constant resistance. The gradient gives the resistance. Watch the wording here: R = V/I defines resistance, but it is not Ohm’s law. Ohm’s law is the proportional relationship under fixed physical conditions.

Investigating an ohmic conductor

To test a metal wire, gently vary the supply potential difference, 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 is a conductor where potential difference is directly proportional to current, as long as the physical conditions stay constant. A non-ohmic conductor is a component where potential difference is not directly proportional to current, so its resistance changes with operating conditions.

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

You can explain the heating of a resistor using ideas from other parts of physics. The electric field does work on charge carriers, energy is transferred when they interact with the lattice, and the material’s internal energy rises. It’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 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.

P = IV = I²R = V²/R, where P is electrical power dissipated by a resistor (W).

Each form says the same thing, just with the resistance relationship substituted in. Use P = IV when current and potential difference are known. If current and resistance are known, use P = I²R. If potential difference and resistance are known, use P = V²/R.

Over a time interval, the energy transferred is E = PΔt, where E is energy transferred (J). Combine this 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, reducing its resistance increases the power because P = V²/R. For a resistor carrying the same current, increasing its resistance increases the power because P = I²R. Always check which quantity is being held constant.

Series circuits

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

For resistors in series:

I = I₁ = I₂ = …
V = V₁ + V₂ + …
Rₛ = R₁ + R₂ + …

where I₁ and I₂ are currents in individual series components (A), V₁ and V₂ are potential differences across individual series components (V), Rₛ is equivalent series resistance (Ω), and R₁ and R₂ are individual resistor values (Ω).

The current stays the same because charge cannot pile up indefinitely between components. The potential differences add, since each coulomb transfers energy in 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 = I₁ + I₂ + …
V = V₁ = V₂ = …
1/Rₚ = 1/R₁ + 1/R₂ + …

where Rₚ is equivalent parallel resistance (Ω).

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. Measure the individual resistor values first, noting tolerances, then measure combinations in series and in parallel. For a complicated network, simplify the obvious parallel groups first, then combine series parts. Repeat until one equivalent resistance remains.

A model of a real cell

A real cell can be treated 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.

ε = I(R + r), where ε is emf of the cell (V) and r is internal resistance (Ω).

When current flows, the external circuit gets a smaller potential difference than the emf, because some energy per coulomb is transferred inside the cell. The terminal potential difference is given by V = ε − Ir. The term Ir is sometimes called the lost volts; it hasn’t disappeared from energy conservation, it’s 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, current increases, and the terminal potential difference usually falls.

Measuring emf and internal resistance

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

A simple fixed-emf, fixed-internal-resistance model is deliberately idealized. Even so, it remains useful because it predicts the main trend: higher current means more energy transferred inside the cell and a lower terminal potential difference.