Current and Circuits ⚡

students, electricity is one of the clearest places where the particulate nature of matter shows up in everyday life. When you switch on a lamp, charge a phone, or power a fan, tiny charged particles move through a material and transfer energy. In this lesson, you will learn how current works, how circuits control that current, and why these ideas matter in IB Physics HL.

What you will learn

By the end of this lesson, students, you should be able to:

explain the meaning of electric current, potential difference, resistance, and electromotive force;
describe how charges move in simple circuits;
apply key circuit equations correctly;
connect current and circuits to energy transfer and thermal effects;
use experimental evidence to analyze circuit behaviour.

A useful idea to keep in mind is this: in a circuit, electrons do not “use up” electricity. Instead, they transfer energy as they move through components such as resistors, lamps, and motors. That energy transfer is central to how matter behaves at the microscopic level 🔋.

Electric current: moving charge

Electric current is the rate of flow of charge. The definition is

$$I=\frac{Q}{t}$$

where $I$ is current, $Q$ is charge, and $t$ is time.

The unit of current is the ampere, $\text{A}$, where $1\,\text{A}=1\,\text{C s}^{-1}$. This means a current of $2\,\text{A}$ corresponds to $2\,\text{C}$ of charge passing a point each second.

In metal wires, the moving charge carriers are usually electrons. Even though electrons move, the direction of conventional current is defined as the direction positive charge would move. So conventional current is opposite to electron flow in metals.

Real-world example: when you plug in a phone charger, charges in the wire begin to drift, and energy is transferred to the phone battery and to the surroundings. The wire itself does not store all that energy; it acts as part of the pathway for the transfer.

A common misunderstanding is that current is “used up” in a circuit. That is not correct. In a series circuit, the current is the same at every point because charge is conserved. What changes around the circuit is the energy transferred per unit charge.

Potential difference, energy, and resistance

Potential difference, often called voltage, tells you how much energy is transferred per unit charge between two points:

$$V=\frac{W}{Q}$$

where $V$ is potential difference and $W$ is energy transferred.

The unit is the volt, $\text{V}$, where $1\,\text{V}=1\,\text{J C}^{-1}$. If a component has a potential difference of $3\,\text{V}$, then each coulomb of charge transfers $3\,\text{J}$ of energy as it passes through that component.

Resistance measures how strongly a component opposes current:

$$R=\frac{V}{I}$$

where $R$ is resistance in ohms $\Omega$.

For example, if a resistor has $V=6\,\text{V}$ and $I=2\,\text{A}$, then

$$R=\frac{6}{2}=3\,\Omega$$

Resistance matters because different materials and components allow charge to move more or less easily. A thin filament in a lamp has much higher resistance than a thick copper wire, so it heats up more and emits light.

This is where the particulate nature of matter becomes important. In a metal, electrons move through a lattice of positive ions. When the electrons collide with the ions, energy is transferred to the lattice, increasing internal energy and often causing heating. This is why a resistor gets warm when current flows through it 🌡️.

Ohm’s law and I–V characteristics

A conductor is ohmic if its resistance stays constant when temperature is constant. For an ohmic conductor,

$$V\propto I$$

so the graph of $V$ against $I$ is a straight line through the origin.

Ohm’s law is often written as

$$V=IR$$

This equation is extremely useful, but students, remember it applies only when resistance is constant. Many components do not behave ohmically.

Examples of non-ohmic components include:

a filament lamp, whose resistance increases as it heats up;
a diode, which allows current mainly in one direction;
thermistors, whose resistance changes with temperature.

A filament lamp’s $I$–$V$ graph is curved because as the current increases, the filament gets hotter, the ions vibrate more strongly, and electrons collide more often. That increases resistance.

A diode has a very small current in reverse bias and a significant current in forward bias only after a threshold potential difference is reached. This makes it useful in electronics, such as converting alternating current to direct current.

Series circuits and parallel circuits

Circuits are arranged in two main ways: series and parallel.

In a series circuit:

the current is the same everywhere: $I_1=I_2=I_3$;
the potential differences across components add up to the supply potential difference;
the total resistance increases when more components are added.

For two resistors in series,

$$R_{\text{total}}=R_1+R_2$$

If a $4\,\Omega$ resistor and a $6\,\Omega$ resistor are in series, the total resistance is

$$R_{\text{total}}=4+6=10\,\Omega$$

This means that for a fixed supply voltage, the current will be smaller than with either resistor alone.

In a parallel circuit:

the potential difference across each branch is the same;
the current splits between branches;
the total resistance decreases as more branches are added.

For resistors in parallel,

$$\frac{1}{R_{\text{total}}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots$$

If $R_1=4\,\Omega$ and $R_2=6\,\Omega$, then

$$\frac{1}{R_{\text{total}}}=\frac{1}{4}+\frac{1}{6}=\frac{5}{12}$$

$$R_{\text{total}}=\frac{12}{5}=2.4\,\Omega$$

This is smaller than either individual resistor. A common real-life example is household wiring: appliances are connected in parallel so each one receives the same potential difference and can operate independently 🏠.

Electromotive force and internal resistance

The electromotive force, or emf, is not a force in the everyday sense. It is the energy supplied per unit charge by a source such as a battery:

$$\varepsilon=\frac{E}{Q}$$

where $\varepsilon$ is the emf.

An ideal source would supply all its energy without any loss, but real sources have internal resistance. This means some energy is transferred inside the battery itself, so the terminal potential difference is less than the emf when current flows.

The relation is

$$\varepsilon=V+Ir$$

where $r$ is the internal resistance and $V$ is the terminal potential difference.

If a battery has $\varepsilon=12\,\text{V}$, internal resistance $r=1\,\Omega$, and current $I=3\,\text{A}$, then

$$V=\varepsilon-Ir=12-3(1)=9\,\text{V}$$

This helps explain why batteries “sag” under heavy load. The larger the current, the bigger the lost voltage inside the source.

Energy transfer and power in circuits

Electric circuits are really energy transfer systems. The power supplied to or dissipated by a component is the rate of energy transfer:

$$P=\frac{W}{t}$$

Useful circuit forms include

$$P=IV$$

and, using $V=IR$,

$$P=I^2R$$

$$P=\frac{V^2}{R}$$

These formulas help explain why high current can cause wires to heat up. For a resistor, greater current means greater power dissipation. That is why toaster elements, electric heaters, and kettle coils are designed with relatively high resistance.

Example: if a device operates at $V=9\,\text{V}$ and carries $I=2\,\text{A}$, then its power is

$$P=IV=18\,\text{W}$$

So it transfers $18\,\text{J}$ of energy each second.

Practical skills and evidence in IB Physics HL

You should also be able to interpret circuit data from experiments. Common practical tasks include measuring $I$ and $V$ with an ammeter and voltmeter, then plotting an $I$–$V$ graph.

Key measurement ideas:

an ammeter is connected in series so it measures the current through a component;
a voltmeter is connected in parallel so it measures the potential difference across a component;
a variable resistor can change the current safely during an investigation.

If you collect data for a resistor and the graph is linear, you can determine resistance from the slope. Since

$$V=IR$$

a graph of $V$ against $I$ has slope $R$.

If you investigate a filament lamp, the curve is not straight, so the resistance changes with current and temperature. This is strong evidence that microscopic particle motion and collisions affect electrical behaviour.

students, in HL Physics, you may be asked to reason from graphs, compare different circuit components, or explain why real sources and wires are not ideal. These skills rely on both equations and physical understanding.

Conclusion

Current and circuits are a powerful example of the particulate nature of matter. Electric current is the motion of charge carriers, usually electrons in metals, and circuit components control how charge moves and how energy is transferred. Potential difference describes energy transfer per charge, resistance shows opposition to current, and real sources have internal resistance. By studying $I$–$V$ graphs, series and parallel rules, and power equations, you can explain everyday electrical devices with accurate physics. These ideas connect microscopic particle motion to macroscopic effects like heating, lighting, and powering electronics ⚡.

Study Notes

$I=\frac{Q}{t}$ defines current as charge flow rate.
Conventional current goes from positive to negative; electrons move the opposite way in metals.
$V=\frac{W}{Q}$ means potential difference is energy transferred per unit charge.
$R=\frac{V}{I}$ defines resistance.
Ohmic conductors obey $V=IR$ when temperature is constant.
In series, current is the same and resistances add: $R_{\text{total}}=R_1+R_2+\cdots$.
In parallel, potential difference is the same and total resistance decreases.
Emf is energy supplied per unit charge: $\varepsilon=\frac{E}{Q}$.
Real cells have internal resistance, so $\varepsilon=V+Ir$.
Power in circuits can be found using $P=IV$, $P=I^2R$, or $P=\frac{V^2}{R}$.
Heating in circuits happens because moving electrons collide with ions in the material, transferring energy to the lattice.
Ammeter in series, voltmeter in parallel.
A straight-line $V$–$I$ graph for a resistor indicates constant resistance.