Current & Charge Notes | Leaving Cert Physics

Electric current is the rate of flow of electric charge, propelled by potential difference and resisted by conductors. Across metallic lattices, electrolytes, and semiconductors, distinct charge carriers govern conduction, producing universal heating, magnetic, and chemical effects while obeying strict conservation laws.

Electric Charge, Electrostatics, and Charge Carriers

Matter contains equal amounts of positive and negative charge under normal conditions. Protons hold a positive elementary charge, while electrons carry an equal negative elementary charge of $1.6 \times 10^{-19}\text{ C}$ . Because these quantities balance, everyday atoms remain electrically neutral. Removing or adding electrons upsets this balance, leaving an object with a net electric charge $Q$ , measured in coulombs ( $\text{C}$ ).

Electrostatic interactions

Charged bodies exert electrostatic forces across space: like charges repel, whereas opposite charges attract. If you are asked for Coulomb's law on Section B, the definition examiners look for states that the electrostatic force between two point charges varies directly with the product of their charges and varies inversely with the square of their separation:

F = \frac{Q_1 Q_2}{4 \pi \varepsilon d^2}

The electric field strength $E$ describes the force per unit charge experienced by a small positive test charge placed in the field, giving $E = \frac{F}{Q}$ with units of $\text{N C}^{-1}$ or $\text{V m}^{-1}$ . Outside a uniformly charged sphere, this field behaves as if all charge were concentrated at the centre: $E = \frac{Q}{4 \pi \varepsilon d^2}$ , where $d$ represents the distance from the centre of the sphere (radius plus distance from the surface). Electric field lines run radially outwards from a positive sphere and radially inwards toward a negative sphere, always meeting conducting surfaces at right angles.

Electrostatic charging occurs through friction, which transfers electrons mechanically, or by induction. In charging by induction, bringing an external charged body near a neutral conductor displaces mobile charges; earthing the far side drains like charge away, leaving the conductor with the opposite net charge once the earth connection and then the charging body are removed. Whenever a conductor has sharp corners or points, charge crowds together at those regions of high curvature. This causes point discharge: the intense field ionises nearby air molecules, repelling ions to create an electric wind—which is why lightning conductors have pointed tips and Van de Graaff generators use sharp spray combs.

Conduction across media

Materials carry charge through distinct mobile entities:

In metals, charge carriers are free (delocalised) electrons drifting through a fixed lattice of positive metal ions.
In an electrolyte, conduction occurs via mobile positive and negative ions.
In gases subjected to high potential differences, ions and electrons carry current.
In semiconductors, conduction depends on both electrons and positive holes.
In a vacuum, thermionic emission produces streams of free electrons.

Electric Current, Voltage, and Circuit Laws

Electric current is the rate of flow of charge along a conducting pathway. Expressed mathematically:

I = \frac{Q}{t}

The SI base unit of current is the ampere ( $\text{A}$ ), while one coulomb represents the charge transported by a current of one ampere flowing for one second ( $1\text{ C} = 1\text{ A s}$ ).

Conventional current and drift

The direction of current was agreed on before the electron was discovered, which is why conventional current runs from the positive terminal to the negative terminal, opposite to the physical electron drift in metallic conductors. Circuit problems assume conventional current unless electron motion is specifically asked for.

Potential difference and electromotive force

Charge drifts through a circuit only when driven by an energy difference. Potential difference between two points is the work done in transferring unit charge from one point to the other ( $V = \frac{W}{Q}$ ). The volt ( $\text{V}$ ) equals one joule of work performed per coulomb transferred ( $1\text{ V} = 1\text{ J C}^{-1}$ ). Electromotive force (emf) describes the total electrical energy supplied to each unit of charge passing through a source.

Circuit rules and Kirchhoff's junction law

In circuit analysis, a junction simply means any meeting place where two or more conductors join together. Because charge cannot pile up or vanish into thin air, Kirchhoff's current law states that the sum of the currents entering a junction equals the sum of the currents leaving that junction ( $\sum I_{\text{in}} = \sum I_{\text{out}}$ ), reflecting the fundamental principle of conservation of charge.

Feature	Series Circuit	Parallel Circuit
Current	Identical through every component	Divides across branches: $I = I_1 + I_2 + \dots$
Voltage	Shared: $V_{\text{total}} = V_1 + V_2 + \dots$	Same full voltage across every parallel branch
Total Resistance	Increases: $R_T = R_1 + R_2 + \dots$	Decreases: $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$
Broken component	Circuit breaks; all current stops	Remaining branches continue operating

Resistance, Resistivity, and Temperature Effects

Whenever charge flows through a component, the material resists that movement. The definition they are looking for in the marking scheme for resistance is the ratio of the potential difference across a conductor to the current flowing through it ( $R = \frac{V}{I}$ ). We measure this electrical opposition in ohms ( $\Omega$ ). Think of the unit definition straight from that relationship: a conductor has a resistance of one ohm if a potential difference of one volt across it drives a current of one ampere through it.

For the exam, learn the precise wording for Ohm's law: the current flowing through a conductor is directly proportional to the potential difference across it, provided temperature and other physical conditions remain constant ( $V \propto I$ ). A plot of $V$ against $I$ yielding a straight line through the origin confirms ohmic behaviour; any curvature proves that Ohm's law is not obeyed, and calculating resistance along a curve requires reading the coordinate ratio $\frac{V}{I}$ directly rather than taking the slope.

Resistivity

If you stretch out a uniform piece of wire, three separate physical factors determine its resistance. Its length $l$ adds up opposition, a wider cross-sectional area $A$ gives drifting charge more room to pass, and the material itself sets an intrinsic property known as resistivity $\rho$ :

\rho = \frac{R A}{l}

with the unit ohm metre ( $\Omega\text{ m}$ ).

Temperature dependence

In metallic conductors, rising temperature causes positive lattice ions to vibrate with greater amplitude, increasing collision frequency with drifting electrons, which raises resistance.
In semiconductors and thermistors, rising temperature supplies enough thermal energy to liberate extra valence electrons, generating new electron–hole pairs. Because the charge carrier density multiplies rapidly, the overall resistance drops sharply.

Heating, Magnetic, and Chemical Effects of Current

Electric current produces three distinct phenomena:

Heating effect: dissipated power turns into thermal energy across every current-carrying conductor with resistance. This brings us to Joule's law, and it is the constant resistance condition that students often lose marks on: the rate of heat production in a conductor is proportional to the square of the current flowing through it, provided its resistance remains constant ( $P \propto I^2$ ). Domestic distribution safeguards use this effect: a fuse contains a short thin wire wired into the live lead that melts to isolate a circuit if current exceeds its rated threshold. You can reset a miniature circuit breaker (MCB) with a flick of a switch once an electromagnet trips it under high current. Residual current devices (RCDs) protect people instead of just wires by tripping whenever live and neutral currents differ, catching dangerous leaks to ground. Meanwhile, the earth wire bonds metal appliance casings to ground so any insulation fault safely trips the supply rather than shocking whoever touches it.
Magnetic effect: electric current flowing through any conductor sets up a magnetic field around it. You can see this in the lab with a simple plotting compass beside the wire: switch the circuit on, and the needle instantly deflects from north.
Chemical effect: passing current through an electrolyte drives chemical separation, termed electrolysis. With aqueous copper sulfate and copper electrodes, copper oxidises away from the anode and plates onto the cathode.

Direct Current, Alternating Current, and Electrical Power

Direct current flows in one direction only, whether steady or varying in magnitude. Alternating current periodically reverses direction, operating at $50\text{ Hz}$ across the national grid.

Because alternating voltage oscillates sinusoidally, its heating ability is quantified by its root mean square value. The rms value of an alternating current is the steady direct current that would produce the same heating effect in a given resistor. For sinusoidal mains:

I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \quad \text{and} \quad V_{\text{rms}} = \frac{V_0}{\sqrt{2}}

Irish domestic mains supplies $V_{\text{rms}} = 230\text{ V}$ , giving a peak voltage $V_0 = 230 \times \sqrt{2} \approx 325\text{ V}$ . Meter displays routinely quote rms values.

Electrical power $P$ dissipated across a resistive element is calculated using $P = V I = I^2 R = \frac{V^2}{R}$ , measured in watts ( $\text{W}$ ). The electrical energy converted over time $t$ is $W = P t = V I t = I^2 R t$ , in joules ( $\text{J}$ ). For domestic billing, electrical energy is measured in kilowatt-hours ( $\text{kWh}$ ), where $1\text{ kWh} = 1000\text{ W} \times 3600\text{ s} = 3.6 \times 10^6\text{ J}$ .

Mandatory Experiments

Investigating the variation of current with potential difference

Purpose: To plot the characteristic $I\text{--}V$ behaviour across various electrical components.
Apparatus: Low-voltage d.c. power supply, rheostat, ammeter, voltmeter, connecting leads, and test components (metal wire, filament lamp, copper sulfate solution with copper electrodes, semiconductor diode).
Diagram and setup: A variable d.c. supply or rheostat feeds current through an ammeter in series with the test component, while a voltmeter is wired in parallel across the component.
Method: Adjust the rheostat across at least six distinct settings, reading current $I$ and potential difference $V$ at each stage. Switch the supply off between readings for the metal conductor to prevent resistance changes from resistive heating.
Results: A metallic conductor held at constant temperature and a copper sulfate electrolyte both yield straight lines passing through the origin, confirming Ohm's law. A filament bulb yields an $S$ -shaped curve whose slope $\frac{V}{I}$ increases because temperature climbs with higher current. A forward-biased semiconductor diode conducts almost zero current until roughly $0.6\text{--}0.7\text{ V}$ , after which current climbs steeply; in reverse bias, current remains negligible.
Precautions and sources of error: Keep currents low to avoid heating effects in the metallic conductor; inspect analogue meters for zero errors.

Verifying Joule's law

Purpose: To verify that temperature rise $\Delta\theta$ in a liquid is proportional to $I^2$ .
Apparatus: Calorimeter with lagging and lid, heating coil, liquid (water), thermometer reading to $0.1\text{ }^\circ\text{C}$ , low-voltage d.c. supply, rheostat, ammeter, stopwatch, stirrer.
Diagram and setup: The heating coil rests fully immersed in a known mass of water inside a lagged calorimeter. The power supply, rheostat, ammeter, and coil form a series loop.
Method: Pass a chosen current $I$ through the coil for a fixed duration (such as 4 minutes), stirring continually. Record the initial and highest temperatures reached to obtain $\Delta\theta$ . Repeat the procedure with at least five other current values using the same liquid mass and identical heating time $t$ .
Results: Plotting $\Delta\theta$ on the y-axis against $I^2$ on the x-axis yields a straight line through the origin, verifying that $\Delta\theta \propto I^2$ , and therefore verifying Joule's law.
Analysis: Because electrical energy supplies thermal energy ( $I^2 R t = m c \Delta\theta$ ), the graph slope equals $\frac{R t}{m c}$ . Coil resistance is extracted using $R = \frac{\text{slope} \times m c}{t}$ .
Precautions and sources of error: Lag the calorimeter and fit a lid to minimise heat loss to the room; stir before reading temperatures; adjust the rheostat to hold current constant throughout each timed run.

Measuring the resistivity of the material of a wire

Purpose: To determine $\rho$ for a wire sample.
Apparatus: Metre stick, micrometer, sample wire, ohmmeter (or ammeter, voltmeter, and d.c. supply).
Method: Measure the length $l$ of a stretched section of wire using a metre stick. Use a micrometer to measure the wire diameter $d$ at multiple positions along its length, turning the micrometer between readings to detect oval cross-sections, and find the mean diameter. Compute $A = \frac{\pi d^2}{4}$ . Measure resistance $R$ directly with an ohmmeter.
Analysis: Calculate resistivity using $\rho = \frac{R A}{l}$ .
Precautions and sources of error: Check the micrometer for zero error before measurement; avoid kinking the wire; verify that the wire remains taut against the metre stick.

Key terms

Electric Current: The rate of flow of electric charge, expressed mathematically as I = Q / t.
Coulomb: The quantity of electric charge transported by a steady current of one ampere in one second (1 C = 1 A s).
Ampere: The constant current which, flowing in two infinitely long straight parallel conductors of negligible circular cross-section placed 1 metre apart in a vacuum, produces a force of 2 x 10^-7 newtons per metre of length between them.
Potential Difference: The work done in transferring unit charge from one point to another in an electric circuit (V = W / Q).
Volt: The potential difference between two points when one joule of work is done transferring one coulomb of charge from one point to the other (1 V = 1 J C^-1).
Resistance: The ratio of the potential difference across a conductor to the current flowing through it (R = V / I).
Ohm: The resistance of a conductor when a potential difference of one volt across it produces a current of one ampere through it.
Ohm's Law: The principle stating that the current flowing through a conductor is directly proportional to the potential difference across it, provided temperature and other physical conditions remain constant.
Joule's Law: The principle stating that the rate at which heat is produced in a conductor is directly proportional to the square of the current flowing through it, provided its resistance remains constant (P proportional to I^2).
Resistivity: The resistance of a conductor of unit length and unit cross-sectional area, given by rho = R A / l.
Kirchhoff's Current Law: The principle stating that the sum of the currents entering any circuit junction equals the sum of the currents leaving that junction.
Semiconductor: A material whose resistivity lies between that of a conductor and an insulator, and whose resistance decreases as its temperature increases.

Check yourself

A student measures the current through a filament lamp across several voltages and finds that the graph of V against I is a curve. Does this component obey Ohm's law? Justify your answer.
No. The graph is not a straight line through the origin, which proves that potential difference is not directly proportional to current.
Explain, in terms of charge carriers, why the resistance of a thermistor falls as its temperature rises.
As temperature increases, additional thermal energy frees electrons from parent atoms, creating extra electron-hole pairs. This increase in charge carriers lowers the resistance.
Why is time kept constant when verifying Joule's law experimentally?
Time is held constant as a controlled variable so that the heat energy produced, and therefore the temperature rise, depends solely on the current squared.
State the relationship between peak voltage and rms voltage for a sinusoidal alternating supply.
V_rms = V_0 / sqrt(2), meaning the peak voltage V_0 equals V_rms multiplied by the square root of 2.
What fundamental physical conservation law provides the basis for Kirchhoff's current law?
The conservation of electric charge.

Current & Charge