Define electric current, potential difference and resistance, and apply Ohm's law ($V = IR$) to simple resistive circuits

What this dot point is asking

QCAA wants you to define the three fundamental electrical quantities (current, potential difference, resistance), apply Ohm's law $V = IR$, and distinguish ohmic from non-ohmic conductors.

The three quantities

Electric current ($I$). The rate of flow of electric charge:

SI unit: ampere (A). One ampere is one coulomb per second. By convention, current direction is the direction of positive charge flow (opposite to electron flow in a metal).

Potential difference ($V$). The work done per unit charge moved between two points:

SI unit: volt (V). One volt is one joule per coulomb. Potential difference is the cause of current flow in a circuit; it drives charge through resistors.

Resistance ($R$). The opposition to current flow:

SI unit: ohm ($\Omega$). One ohm is one volt per ampere. Resistance depends on the material, geometry and temperature of the conductor.

Ohm's law

For an ohmic conductor (most metals at constant temperature), resistance is constant and current is directly proportional to applied voltage:

A current-voltage graph for an ohmic conductor is a straight line through the origin. For a non-ohmic conductor (a filament lamp, a diode, a thermistor), the line is curved or zero in some regions, and $R$ depends on the operating point.

Ohmic and non-ohmic examples

• Ohmic: copper wire at constant temperature, carbon resistors.
• Non-ohmic: filament lamp (resistance rises with temperature so the I-V curve flattens at high $V$), semiconductor diode (zero current below the threshold, near-vertical above), thermistor (resistance falls with temperature).

For non-ohmic conductors, $R = V/I$ still gives the instantaneous resistance at the operating point, but $R$ is not constant.

How this appears in IA1 and EA

IA1

Often an ohm-meter reading or an unseen I-V graph asking for the resistance at a stated point and whether the device is ohmic.

EA Paper 1

Multiple choice on the units, the formula, and identifying ohmic from non-ohmic shapes.

EA Paper 2

Combined with the power-and-energy and series-and-parallel dot points to find unknown resistors or currents in a small circuit.

Examples in context

Example 1. A Townsville workshop $48 \text{ V}$ welder uses a copper lead with $R = 0.020 \text{ ohms}$ at $200 \text{ A}$. Voltage drop along the lead is $V = IR = 4.0 \text{ V}$, dissipating $I^2 R = 800 \text{ W}$ as heat. Switching to twice the cross-section halves $R$ and quarters the dissipation. The same Ohm's-law accounting tells the apprentice why old or undersized leads scorch; QCAA Unit 1 EA Paper 1 typically sets the same sums on a smaller domestic appliance.

Example 2. A Bundaberg cane farmer pumps water through a $4.0 \text{ kW}$ submersible motor connected by $80 \text{ m}$ of $4 \text{ mm}^2$ copper cable ($R \approx 0.36 \text{ ohms}$). At rated current $I = P/V = 17 \text{ A}$ on $230 \text{ V}$, cable voltage drop is $V = IR = 6.1 \text{ V}$ ($2.7$ per cent of supply). Doubling cable length doubles the drop and quadruples the $I^2 R$ heat. Australian Standard AS/NZS$3000$ caps voltage drop at $5$ per cent, so the farmer must upsize cable if a second pump is added.

Try this

Q1. Define electric current and potential difference, and state Ohm's law. [3 marks]

• Cue. $I = Q/t$; $V = W/Q$; $V = IR$ for an ohmic conductor.

Q2. A $230 \text{ V}$ kettle draws $9.0 \text{ A}$. Calculate the resistance of the heating element and the charge through it in $4.0 \text{ minutes}$. [3 marks]

• Cue. $R = V/I = 25.6 \text{ ohms}$; $Q = It = 2160 \text{ C}$.

Q3. A student measures $V$ across a filament lamp at six currents and finds $V$ vs $I$ curves upward. (a) Define an ohmic conductor. (b) Explain why the lamp is non-ohmic. (c) Calculate the resistance at the operating point $V = 240 \text{ V}$, $I = 0.42 \text{ A}$ and compare with the cold value $R_c = 50 \text{ ohms}$. [2+3+3 marks; ISMG: Knowledge and conceptual understanding, Analysis and interpretation]

• Cue. (a) Constant $R$ at fixed $T$; (b) heating raises filament $R$; (c) $R = 571 \text{ ohms}$, factor about eleven above cold.