Define electric current, potential difference and resistance, and apply Ohm's law ($V = IR$) to ohmic and non-ohmic conductors, including filament lamps and diodes

What this dot point is asking

VCAA wants you to define current, voltage and resistance, apply Ohm's law to ohmic devices, and distinguish non-ohmic devices (filament lamps, diodes, thermistors) where resistance varies with operating conditions.

Electric current

The rate of flow of charge:

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

Potential difference

Work done per unit charge:

SI unit: volt (V) = joule per coulomb. Drives current through circuit elements.

Resistance

Opposition to current:

SI unit: ohm ($\Omega$) = volt per ampere. Depends on material, geometry and temperature.

Ohm's law

For an ohmic conductor (constant temperature, most metals at low currents):

with $R$ constant. The I-V graph is a straight line through the origin.

For non-ohmic devices, $R = V/I$ still gives the instantaneous resistance at the operating point, but $R$ varies with $V$ or $I$.

Non-ohmic devices

Filament lamp

As current flows, the filament heats up and its resistance rises. I-V graph curves so that the slope decreases at higher $V$.

Semiconductor diode

Zero current below the threshold voltage (about $0.7$ V for silicon). Near-vertical above. Strongly direction-dependent (only conducts one way).

Thermistor

A semiconductor whose resistance falls steeply with temperature. Used in temperature sensors. The I-V curve is concave up.

VCAA exam style

Year 11 SAC tasks typically include:

• Calculating $R$ at two operating points and identifying whether the device is ohmic.
• Reading an I-V graph to find $R$ at a stated voltage.
• Distinguishing ohmic and non-ohmic shapes.

Common traps

Calling drift velocity "current"

Electron drift velocity in a wire is typically fractions of a millimetre per second. Current is the rate of charge flow.

Treating $R = V/I$ as a definition that proves Ohm's law

$R = V/I$ defines instantaneous resistance for any device. Ohm's law is the additional claim that $R$ is constant for ohmic devices.

Forgetting direction in diodes

A diode conducts only in one direction. Reversing the voltage usually drops the current to near zero.

Mixing units of charge and current

Ampere-second is coulomb; ampere-hour is $3600$ C.

In one sentence

Electric current ($I = Q/t$) is the rate of charge flow in amperes, potential difference ($V = W/Q$) is the energy delivered per coulomb in volts, resistance ($R = V/I$) is the opposition to current flow in ohms, and ohmic conductors obey $V = IR$ with constant $R$, while non-ohmic devices (lamps, diodes, thermistors) have $R$ that varies with the operating point.

Examples in context

Example 1. AGL Hornsdale battery cell characterisation. Each lithium-iron-phosphate cell in the Hornsdale Power Reserve has a nominal terminal potential difference of $3.2$ V. When delivering $130$ A during a frequency-control event, internal resistance of approximately $0.0005$ $\Omega$ causes a voltage drop $\Delta V = IR = 130 \times 0.0005 = 0.065$ V, so the terminal voltage falls to $3.135$ V. This is ohmic behaviour: voltage scales linearly with current. The cell heats at rate $P = I^2 R = 130^2 \times 0.0005 = 8.5$ W, which the liquid cooling loop must remove to keep the cell below $45^\circ$C and prolong life.

Example 2. Filament lamp non-ohmic behaviour in heritage Melbourne street lights. Some Carlton heritage lamps still use $150$ W tungsten filaments. At room temperature ($20^\circ$C), the cold filament resistance is about $30$ $\Omega$; at operating temperature ($2500^\circ$C), it rises to roughly $360$ $\Omega$, a factor of $12$. Switching the lamp on, the inrush current is $I = 230/30 \approx 7.7$ A, but steady-state current is only $I = 230/360 \approx 0.64$ A. A $V$-$I$ plot is therefore strongly non-linear: doubling the voltage less than doubles the current because the filament heats. This is why filament lamps are classed as non-ohmic, in contrast to nichrome heating elements.

Try this

Q1. Define electric current and state its SI unit. [2 marks]

• Cue. Rate of flow of charge, $I = Q/t$, measured in amperes ($1$ A = $1$ C s$^{-1}$).

Q2. A $12$ V battery delivers a current of $1.5$ A through an unknown resistor for $5$ minutes. Calculate (a) the resistance, and (b) the total charge that has flowed. [2+2 marks]

• Cue. (a) $R = V/I = 8$ $\Omega$. (b) $Q = It = 1.5 \times 300 = 450$ C.

Q3. A filament lamp shows a non-linear voltage-current graph. (a) Define an ohmic conductor. (b) Explain why a tungsten lamp behaves non-ohmically. (c) Sketch the $V$ versus $I$ graph and indicate the region where the lamp behaves approximately ohmically. [2+2+2 marks]

• Cue. (a) Constant ratio $V/I$ at fixed temperature. (b) Filament resistance rises with temperature. (c) Curve concave to the $V$ axis; near origin (cold) the slope is roughly constant.