Read resistance from a specified current–voltage operating point
Use the line from the origin to a chosen non-zero I–V point and avoid confusing its ratio with a curved graph's tangent.
Section P4.1 · Electrical quantities
Cross-referenced to the 2028–2029 0653 section using original teaching from the related single-science courses. A 0653-specific objective-by-objective and Core/Supplement review is in progress. Written practice is self-checked and does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Explain resistor, lamp and diode I–V patterns.
- Use R = V/I.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What unit belongs to an I–V graph's vertical current axis?
What you will learn
- Calculate V/I for supplied graph points.
- Distinguish origin ratios, local tangent slopes and uncalibrated sketches.
Read coordinate values first
On I-vertical, V-horizontal axes, choose a non-zero operating point and read its actual coordinate values from the labelled scales. The operating resistance is V/I, the reciprocal of the origin-to-point ratio I/V. For a supplied point (6 V, 0.75 A), R = 8 Ω.
A curved graph's local tangent describes a small-change slope near that point, not automatically the same ratio V/I from the origin. The basic operating resistance calculation still uses the stated point's voltage and current rather than measuring an arbitrary curve angle on the page.
Retain sign and calibration conditions
For an ordinary resistor or filament lamp under reversal, a non-zero point such as (−6 V, −0.75 A) gives positive V/I = 8 Ω because both signs reverse. That does not mean the current itself is positive on the chosen reference.
An uncalibrated curve cannot provide an exact numeric resistance from ink dimensions alone. At a zero-origin point the quotient is 0/0 and is indeterminate. Read supplied scales or data, and do not infer that a diode's near-zero reverse current provides a finite accurately measured resistance without sensitivity information.
Sources for this lesson
Pause and explain
A supplied point is (−6 V, −0.75 A). What V/I follows?
Worked example
A supplied lamp point is (6 V, 0.75 A). Calculate operating resistance without using a tangent slope.
Show the worked solution
- Read the point's V and I coordinates.
- R = V/I = 6/0.75.
- R = 8 Ω at this state.
Answer 8 Ω at the specified point.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find operating resistance at (6 V, 0.75 A).
Give me a hint
Use the labelled coordinate values rather than the curve's page angle.
Compare my reasoning
- V = 6 V and I = 0.75 A.
- R = V/I.
- 6/0.75 = 8 Ω.
8 Ω.
Look for these in your work
- Use the point coordinates.
- State the operating state.
Find V/I at (−6 V, −0.75 A) and at (2 V, 0.40 A).
Give me a hint
Retain both signs and calculate each state independently.
Compare my reasoning
- (−6)/(−0.75) = 8 Ω.
- 2/0.40 = 5 Ω.
- The two states do not have the same operating resistance.
8 Ω; 5 Ω.
Look for these in your work
- Keep both signs.
- Do not force one constant R across different states.
A qualitative lamp curve has no calibrated scales. A learner claims 8 Ω from its tangent angle. Assess the result.
Give me a hint
Check both calibration and whether the chosen slope represents V/I.
Compare my reasoning
- No coordinate calibration is supplied.
- A local tangent is not generally the origin ratio.
- An exact operating resistance is not established.
No exact 8 Ω result follows from an uncalibrated tangent angle.
Look for these in your work
- Name both limitations.
- Require supplied non-zero V and I values.
Common mistakes
- Read labelled coordinates, not drawing angles.
- A tangent differs from an origin ratio on a curved graph.
- The origin's 0/0 is not zero resistance.
What can you explain now?
Which ratio gives operating resistance at a non-zero point?
Compare with the explanation
V/I.
It uses the actual point coordinates, not an arbitrary local tangent slope.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
Calculate operating-point V/I with labelled coordinates and avoid tangent, origin and uncalibrated-ink errors.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.