O-Level Physics I–V Graphs: When Is the Gradient Resistance?

Read the axes before recalling a rule

In the Singapore O-Level Physics practical discussion, students debated whether a graph’s gradient represented resistance or its reciprocal. This is a useful revision problem: the answer depends on what is plotted on each axis, not simply on remembering that the question involves voltage and current.

This guide explains the underlying relationships using invented examples. It does not reconstruct the examination graph, confirm forum calculations or predict how a particular response was marked. SEAB’s 2026 Physics 6091 syllabus includes resistance as potential difference divided by current and interpretation of I–V characteristics.

Write the quantity represented by the gradient

For a straight-line graph, gradient is the change in the vertical-axis quantity divided by the change in the horizontal-axis quantity. Write those quantities and units before substituting values. Follow the actual axis labels, even if a revision sheet casually calls both arrangements an I–V graph.

When potential difference V is vertical and current I is horizontal, the gradient has units V/A. For a metallic conductor at constant temperature with a straight line through the origin, V = RI, so the gradient is R. The through-origin condition and the physical model matter.

Reverse the axes and check the reciprocal

When current is vertical and potential difference is horizontal, the gradient has units A/V. For the same constant-resistance model, I = V/R, so the gradient is 1/R. Take its reciprocal to obtain resistance in ohms; do not label an A/V gradient as an ohmic resistance.

For an invented example, a 3.0-ohm resistor at constant temperature carries 0.20 A at 0.60 V and 0.40 A at 1.20 V. A V-against-I graph has gradient (1.20−0.60)/(0.40−0.20) = 3.0 V/A. Reversing the axes gives approximately 0.33 A/V, whose reciprocal is approximately 3.0 ohms.

Do not apply the straight-line shortcut to every curve

A filament lamp’s characteristic need not be a straight line because its temperature and resistance change. At a specified operating point, the ratio V/I gives the resistance at that point. That ratio is not automatically the same as the gradient of a tangent or a line joining two other points.

Read whether the question asks for a gradient, a resistance at a stated point or a description of a characteristic. These are different tasks. If you are unsure which relationship is intended, write the quantities explicitly before choosing a calculation.

Check units and sensible graph reading

Convert milliamperes to amperes where needed before quoting resistance in ohms. On a straight best-fit line, use two suitably separated points on that line to calculate the gradient, following the task’s instructions. Copy their coordinates carefully rather than choosing two convenient-looking table entries without considering the plotted fit.

A result with an unexpected sign or scale should trigger a check of the axes, subtraction order, units and transcription. During actual practical work, record genuine observations and seek the permitted assistance for apparatus problems; do not invent readings to force an expected graph.

Practise both arrangements together

Use an appropriate question from our Secondary Pure Physics papers. Write the gradient’s units first, then explain why it is R or 1/R in that model. Check older papers against your current syllabus. Being able to explain the relationship is more reliable than memorising an axis-free slogan.

Sources and further reading

Checked on 2 November 2026. The linked question or discussion is real; the practice routines and labelled examples are our original editorial guidance. Forum replies are not official examination answers.

• 6091/03 O Level Physics Practical Megathread 2026 — Thread opened 4 October 2026; relevant graph discussion dated 5 October 2026.
• SEAB O-Level Physics 6091 syllabus, 2026