QCE Physics - Unit 1 - Electrical circuits

Resistance, Ohm's law and current-voltage data

Learn resistance and i-v data for QCE Physics Unit 1 with worked reasoning, equations, original diagrams and checked practice.

Part of the free QCE Physics notes library for Unit 1: Electrical circuits.

Updated 2026-08-09 - 7 min read

Relate resistance to $V$-$I$ data and distinguish ohmic from non-ohmic behaviour. This note is designed for active learning: predict the physical outcome before calculating, state the system and assumptions, and then use an equation or diagram to make the reasoning testable. Physics becomes reliable when words, signs, graphs, units and energy or momentum ledgers all tell the same story.

The physical model

Resistance quantifies how much potential difference is required per unit current at an operating point. An ohmic component has constant resistance under constant physical conditions; a non-ohmic component has a changing $V/I$ ratio.

A useful physics model deliberately leaves some features out. Before using it, name the system boundary, the time interval and the conditions that make the relationship appropriate. For a thermal problem this may mean negligible energy loss; for a circuit it may mean ideal wires and meters; for motion it may mean one dimension or constant acceleration; for a wave it may mean a uniform medium. An assumption is not a weakness when it is visible and justified. It becomes a problem only when the conclusion is extended beyond the model's conditions.

Physics explanations should form a causal chain: identify the interaction or energy transfer, state the relevant change, connect it to the mathematical relationship, then describe the observable consequence. Avoid replacing that chain with a label such as "because of inertia", "because heat rises" or "because waves bend". The label names the topic; the chain explains it.

Governing relationships

$ V=IR $

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

Write the relationship before substituting numbers. Define the sign convention and translate every value into SI units unless the equation or data book clearly permits another unit. A negative answer can represent direction or a decrease; it is not automatically an arithmetic error. A positive magnitude without a stated direction can still be incomplete.

Check dimensions before accepting an answer. Joules, watts, volts, newtons and pascals are compact descriptions of base-unit relationships, not decorative labels. If the units do not reduce to the requested quantity, the calculation cannot be correct even when the calculator work is flawless.

Build the concept connections

1. Interpret the model

For a graph of $V$ vertically against $I$ horizontally, gradient is resistance. If the axes are reversed, the gradient is conductance $1/R$.

2. Connect the evidence

A filament lamp is non-ohmic because rising temperature changes lattice vibration and therefore resistance. A curved graph is evidence of changing resistance, not a failure of charge conservation.

3. Protect the boundary conditions

Power dissipated in a resistor represents the rate at which electrical energy is transferred, commonly to internal energy and the surroundings.

The diagram above is a reasoning tool rather than decoration. Recreate it from memory and annotate the invariant quantities, the quantities that change and the boundary conditions. If the context changes, ask which arrows, graph regions or force labels must change. That comparison is often the fastest route through an unfamiliar question.

A repeatable method

1. Read the graph axes and units before interpreting a gradient.
2. For an ohmic region, calculate $\Delta V/\Delta I$ using well-separated points on the best-fit line.
3. For a non-ohmic component, use $V/I$ at the stated operating point and describe how it changes.
4. Select the power relationship that matches the known variables and check watts.

This sequence is a scaffold, not a sentence template. A short numerical response may compress several decisions into one line, while an investigation or explanation must keep the evidence visible. Do not substitute until the system, direction and model have been chosen. Preserve unrounded intermediate values and round only the final result to precision supported by the supplied data.

Worked example

Cover the steps and reproduce the solution from the problem statement. Then change one condition: reverse a direction, double a quantity, introduce a loss, change the boundary or swap a series connection for a parallel one. Predict the effect before recalculating. This counterfactual check exposes whether the method is understood or merely copied.

Experimental and graphical reasoning

Physics data are measurements with uncertainty, not exact copies of equations. Start by reading both axes, units and scale. Decide whether the useful information is a point value, intercept, gradient, area or curve shape. Quote processed evidence when it supports a claim, but always explain the physical meaning of that evidence.

A gradient should be found from well-separated points on a best-fit line rather than two convenient raw points. Where minimum and maximum plausible lines are available, compare their gradients to estimate uncertainty. An area must include the graph's units and sign. A straight line through the origin can support proportionality only when the uncertainty and physical model make a non-zero intercept implausible.

Repeated trials reveal random variation and allow averaging, but they do not remove a systematic offset, energy leak, miscalibrated sensor or consistently wrong zero. Improve validity by changing the method so the dependent variable genuinely measures the stated construct and the relevant confounding variables are controlled. Improve reliability through repeatable procedures and sufficient measurements.

When evaluating evidence, separate the observed pattern from the inference. State a limitation by explaining its likely direction and consequence: for example, energy transferred to the surroundings makes an ideal calorimetry value too low, or uncorrected background count makes a decay reading too high. "Human error" is rarely specific enough to guide an improvement.

Common mistake and repair

The repair matters because an answer can contain a familiar formula and still use the wrong physical model. Before moving on, audit direction, conservation, units and limiting behaviour. Ask what should happen if a key quantity becomes zero, doubles or grows very large. A result that violates that prediction needs investigation.

Practice and verification

Now attempt the second check without returning to the worked example:

• Why is a filament lamp usually non-ohmic?

Then attempt this unfamiliar transfer:

• At fixed potential difference, a resistor's resistance doubles. What happens to power?

For each answer, add one verification sentence. Suitable checks include a reverse substitution, a conservation ledger, graph-area units, an independent equation, a limiting case or a qualitative prediction of direction and scale.

Assessment transfer

Use changing curve steepness to explain device behaviour at a stated operating point rather than assigning one universal resistance.

In a QCAA-style response, match the cognitive verb. Describe the relevant features accurately. Explain the causal relationship. Analyse patterns, relationships and uncertainty in supplied evidence. Evaluate a claim or process against explicit criteria and evidence. Solve with a visible model choice, substitutions, units, appropriate precision and a physical interpretation.

Use diagrams deliberately. Force arrows should begin on the isolated object and name real interactions. Ray angles should be measured from a normal. Circuit diagrams should use standard symbols and unambiguous nodes. Graphs should label variables and units. A clear figure can earn its place by preventing an assumption from remaining hidden.

Before submitting, use this checklist:

• The system and positive direction are stated where relevant.
• The equation's conditions match the context.
• Every substituted value has compatible units.
• Conservation of charge, energy or momentum has been checked where applicable.
• The final result includes direction, sign and appropriate precision.
• The conclusion distinguishes measured evidence from inference.
• A limitation explains how confidence or the result is affected.

Sources

• QCAA Physics subject page
• QCAA Physics 2025 v1.3 syllabus
• QCAA Physics formula and data book
• OpenStax University Physics

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