IMAT Physics · Electricity

Current, Ohm's Law and Resistivity

Current is the rate of flow of charge; resistance is how hard a component makes that flow, and for a wire it depends on the material, the length and the cross-section.

All Electricity notes

Why this matters

The 2018 paper asked for the resistance of a wire from its resistivity, length and diameter. The 2025 ministry paper asked which particles move, and which way, in a metal wire carrying a current.

Concept 1 of 3: Electric current: charge per second, and which way it flows

A current is charge on the move, and its size is how many coulombs pass a point each second. Long before electrons were discovered, current was defined as flowing from the positive terminal to the negative. In a metal it is actually electrons that move, and they go the other way.

Definition

Current is the rate of flow of charge: $I = Q/t$ , in amperes ( $1\ \text{A} = 1\ \text{C/s}$ ).

Conventional current flows from the positive terminal, round the circuit, to the negative terminal.
In a metal the moving charges are electrons, drifting opposite to the conventional current. The positive ions stay in place; protons never move along a wire.
In an electrolyte both kinds of ion move: positive ions with the conventional current, negative ions against it.
The current is the same at every point of a single loop: charge is not used up, only its energy is.

Current

I = \frac{Q}{t}

$I$ current, in A
$Q$ charge passing a point, in C
$t$ time, in s

Worked example

A lamp carries a steady current of 0.40 A for 5.0 minutes. How much charge passes through it, and how many electrons is that?

Practice this conceptself-check · 3 quick reps

Electrons move against the conventional current

The arrow on a circuit diagram shows conventional current, from + to −. In a metal wire the charges actually moving are electrons, going the opposite way. Protons do not move along a wire at all, so any option with moving protons in a metal is wrong.

Concept 2 of 3: Resistance and Ohm's law

A voltage pushes charge round a circuit; resistance holds it back. For a metal wire at a steady temperature, double the push and you double the flow: the current is proportional to the voltage. That straight-line rule is Ohm's law, and the slope tells you the resistance.

Definition

Resistance is the p.d. across a component divided by the current through it: $R = V/I$ , in ohms ( $1\ \Omega = 1\ \text{V/A}$ ).

Ohm's law: for a metal conductor at constant temperature, $I$ is proportional to $V$ , so $R$ is constant. Such a component is ohmic.
A filament lamp is not ohmic: as it heats up its resistance rises, so its current-voltage graph curves towards the voltage axis.
The resistance of a metal rises with temperature; that of a semiconductor (a thermistor) falls.
A superconductor below its critical temperature has zero resistance (mercury below 4.2 K is the classic example).

Ohm's law

V = I R

$V$ p.d. across the component, in V
$I$ current through it, in A
$R$ resistance, in Ω

Worked example

A heater connected to 230 V draws a current of 5.0 A. Find its resistance. If its resistance stayed the same, what current would it draw from 115 V?

Practice this conceptself-check · 3 quick reps

Ohm's law needs a constant resistance

R = V/I

defines resistance for any component at any moment, but Ohm's law (current proportional to voltage) holds only when the resistance is constant, as for a metal at steady temperature. A filament lamp does not obey it, so doubling its voltage less than doubles its current.

Concept 3 of 3: Resistivity: how a wire's length and thickness set its resistance

A longer wire is like a longer corridor: the charges have further to push through, so the resistance grows in proportion to the length. A thicker wire is like a wider corridor: more paths side by side, so the resistance falls as the cross-section area grows. The material itself sets the starting value, its resistivity.

Definition

The resistance of a uniform wire is $R = \rho L/A$ .

$\rho$ is the resistivity, a property of the material and its temperature, in $\Omega\,\text{m}$ . It does not depend on the wire's shape.
Good conductors have tiny resistivities (copper about $1.7 \times 10^{-8}\ \Omega\,\text{m}$ ); insulators have enormous ones.
For a round wire, $A = \pi r^2 = \pi d^2/4$ . Doubling the diameter makes the area four times larger and the resistance four times smaller.

Resistance of a wire

R = \frac{\rho L}{A} \qquad A = \frac{\pi d^2}{4}

$\rho$ resistivity of the material, in Ω m
$L$ length, in m
$A$ cross-section area, in m²
$d$ diameter of the wire, in m

Worked example

A copper wire (

\rho = 1.7 \times 10^{-8}\ \Omega\,\text{m}

) is 10 m long with a diameter of 1.0 mm. Find its resistance.

Practice this conceptself-check · 3 quick reps

Diameter is squared in the area

The area of a round wire is

\pi d^2/4

. Doubling the diameter quarters the resistance, it does not halve it. Forgetting the 4 in

\pi d^2/4

, or using the diameter as the radius, gives an answer four times off.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Electric current: charge per second, and which way it flows
Current
$I = \frac{Q}{t}$
Resistance and Ohm's law
Ohm's law
$V = I R$
Resistivity: how a wire's length and thickness set its resistance
Resistance of a wire
$R = \frac{\rho L}{A} \qquad A = \frac{\pi d^2}{4}$

Watch out for (3)

Electrons move against the conventional current
→ Electric current: charge per second, and which way it flows
Ohm's law needs a constant resistance
→ Resistance and Ohm's law
Diameter is squared in the area
→ Resistivity: how a wire's length and thickness set its resistance

Drill the past-year questions on this topic

Open the bank with this topic pre-filtered.

Open in the bank