Read an I–V graph before calculating
You will be able to: Distinguish ohmic behavior from a nonlinear I–V relation and identify graph slope units.
Which graph slope tells you resistance?
Measure 1 A at 2 V, then 2 A at 4 V. The ratio V/I stays 2 Ω. Put voltage on the horizontal axis and current on the vertical axis: the straight-line slope is 0.50 A/V, the reciprocal of resistance.
A useful starting point: Material and geometry set resistance →
Words and symbols before equations
- Ohmic model
- Constant resistance: current is proportional to applied voltage.
- Slope
- Vertical change divided by horizontal change; read axis labels first.
- Conductance
- Reciprocal of resistance, measured in A/V, also called siemens.
- Nonohmic
- An element whose I–V relation is not a constant-resistance straight line through the origin.
What this picture assumes
Ohmic line R=5 Ω. Curved teaching relation I=V/(5+0.5V), for V≥0, chosen to show a changing V/I ratio. Synthetic comparison, not measured filament or temperature data.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Ohmic model (blue): I=0.8 A at 4 V. Operating V/I=5 Ω. Ohmic-line slope=0.20 A/V.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
V=IR lets you infer resistance from voltage and current. For an ohmic element with constant R, an I-versus-V graph is a straight line through the origin with slope 1/R. If the axes are reversed, the V-versus-I slope is R.
A filament can warm as current rises, changing its resistance. A curved graph means a single constant R cannot describe all points. At a chosen point V/I is the operating resistance; the local tangent slope dI/dV is a different quantity and is not needed for these algebra-based calculations.
A useful experiment places an ammeter in series and a voltmeter across the element, varies the supply over several settings and plots measured I against V. Control temperature when testing the constant-R model. The curved Explore comparison is a constructed teaching relation, not measured lamp data.
A worked example, step by step
An I–V line includes (2 V,0.40 A) and (6 V,1.20 A). Find R.
- Read the axes: I is vertical and V horizontal.
- Slope=(1.20−0.40)/(6−2)=0.20 A/V.
- R=1/slope=5.0 Ω.
- Check at one point: 6 V / 1.20 A=5.0 Ω.
Do not call every graph slope R: the I–V slope is 1/R.
Does one measured V/I ratio prove an element is ohmic?
Compare with an explanation
No. You need multiple operating points showing the same ratio under controlled conditions.
Predict. Change one thing. Explain.
Compare a constant-R line with the curved teaching model. Move the operating voltage and compare V/I at different points. The comparison is qualitative; it is not a temperature simulation.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Ohmic model (blue): I=0.8 A at 4 V. Operating V/I=5 Ω. Ohmic-line slope=0.20 A/V.
Ohmic line R=5 Ω. Curved teaching relation I=V/(5+0.5V), for V≥0, chosen to show a changing V/I ratio. Synthetic comparison, not measured filament or temperature data.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant current, voltage or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionYou measure (1 V,0.20 A), (3 V,0.60 A), (5 V,1.00 A). (a) Choose graph axes. (b) Determine slope. (c) Infer R. (d) Name an experimental condition to control.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: V horizontal in volts, I vertical in amperes.
- 1 point: Slope 0.20 A/V, approximately through origin.
- 1 point: R=5 Ω.
- 1 point: Keep temperature stable; also describe correct series/parallel meter placement.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What does a straight I–V line through the origin suggest?
Ohmic behavior over the measured range.
RECALL 2What is the unit of I–V slope?
A/V, equivalent to 1/Ω.
RECALL 3Why control temperature?
Heating can change resistance and obscure the model being tested.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Read an I–V graph before calculating
- Ohmic: V=IR with R constant.
- Slope of I versus V = 1/R.
- Slope of V versus I = R.
Remember: Do not call every graph slope R: the I–V slope is 1/R.
Conditions: Ohmic line R=5 Ω. Curved teaching relation I=V/(5+0.5V), for V≥0, chosen to show a changing V/I ratio. Synthetic comparison, not measured filament or temperature data.
Refresh Kid · AP Physics 2 Unit 3 (official Unit 11) · Objectives 11.3.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 11.3, objectives 11.3.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Refresh Kid calls this the third AP Physics 2 unit; College Board numbers it Unit 11; the first unit in this course is official Unit 9. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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