Resistance, Resistivity, and Ohm’s Law
Resistance measures how strongly an object opposes charge motion, while resistivity is a material property. For a uniform conductor, resistance depends on resistivity, length, and cross-sectional area; ohmic behavior is identified by a linear current–potential-difference relationship under fixed conditions.
Resistance, Resistivity, and Ohm’s Law: quick answer
Resistance measures how strongly an object opposes charge motion, while resistivity is a material property. For a uniform conductor, resistance depends on resistivity, length, and cross-sectional area; ohmic behavior is identified by a linear current–potential-difference relationship under fixed conditions. Resistance belongs to an object; resistivity belongs to a material. Geometry converts the material property into an object resistance, while an I–V or V–I graph tests whether resistance remains constant under the conditions of the measurement.
Do not assume every component is ohmic or that resistance stays constant while temperature changes. When using a graph, state which variable is on each axis before interpreting the slope.
What you should be able to explain and do
Use these as closed-note retrieval prompts before looking at worked examples.
Use R=ρL/A and predict factor changes from geometry.
Distinguish resistance from resistivity.
Identify ohmic versus nonohmic behavior from current–potential-difference data.
Interpret resistance from a graph only after checking which quantity is on each axis.
Key terms you need for this lesson
Definitions stay beside the circuit model so unfamiliar terminology does not break the reasoning chain.
resistance
resistance is a measure of how strongly an object opposes the motion of electric charge.
resistivity
resistivity is an intrinsic material property quantifying opposition to charge motion.
ohmic element
ohmic element is an element whose resistance remains constant over the conditions being considered so current and potential difference are proportional.
nonohmic element
nonohmic element is an element whose current–potential-difference relation is not proportional under the conditions being considered.
cross-sectional area
cross-sectional area is the area perpendicular to current flow in a conductor.
current–voltage graph
current–voltage graph is an experimental graph used to test proportionality and infer resistance or conductance from its slope, depending on axis choice.
Know what each relationship means and when it applies
The relationship, variables, topology condition, and physical anchor belong together.
| Relationship / model | Variables & units | When to use it | Physical anchor |
|---|---|---|---|
R = ρL/A | R resistance (Ω); ρ resistivity (Ω·m); L length (m); A cross-sectional area (m²) | uniform conductor | doubling length doubles resistance; doubling area halves resistance |
ΔV = IR | ΔV potential difference (V); I current (A); R resistance (Ω) | ohmic element under fixed physical conditions | a 4 Ω resistor carrying 2 A has 8 V across it |
slope depends on axes | for ΔV vs I, slope = R; for I vs ΔV, slope = 1/R | interpreting experimental current-voltage graphs | always read axis labels before converting graph slope into resistance |
What a strong circuit diagram or graph must show
Translate the same physical model among topology, arrows, graphs, equations, and energy/charge reasoning.
Geometry diagram
length is measured along current flow and area perpendicular to it.
ΔV-versus-I graph
straight line through the origin for an ideal ohmic element; slope equals R.
I-versus-ΔV graph
straight line through the origin for an ideal ohmic element; slope equals 1/R.
Temperature comparison
changing temperature can change resistivity and therefore resistance.
Change one circuit condition and inspect what responds
Make a prediction before moving a control, then explain the output using topology, conservation, or the governing relationship.
Two examples with the model choice shown
The solution exposes the circuit reasoning pathway rather than only the arithmetic.
Wire geometry factor
Situation: A uniform wire is replaced by one of the same material with twice the length and half the cross-sectional area.
Reasoning: R=ρL/A, so the length factor is 2 and the area factor contributes another 2.
The new resistance is 4 times the original.
Graph-axis check
Situation: An I-versus-ΔV graph for a resistor has slope 0.25 A/V.
Reasoning: Because current is vertical and potential difference is horizontal, slope=I/ΔV=1/R.
R=1/0.25=4.0 Ω.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 11.3?
Use resistance/resistivity reasoning when voltage-current behavior, material choice, length, area, or ohmic versus non-ohmic response is central.
How this idea fits the course
This topic provides the element model used in 11.4 power and 11.5–11.7 multi-element circuit analysis.
Scope check before solving
Do not assume every component is ohmic or that resistance stays constant while temperature changes. When using a graph, state which variable is on each axis before interpreting the slope.
Turn this topic into measurable evidence
Choose variables and meters that test the intended relationship without accidentally changing the circuit model.
Investigation target
Measure V–I data for a resistor and lamp; use graph shape to classify ohmic versus nonohmic behavior.
Reasoning errors to eliminate
Repair the circuit model before doing more arithmetic.
Six things you should be able to do before moving on
Use these as closed-note transfer prompts.
- I can identify the circuit topology before applying series/parallel formulas.
- I can define every electrical quantity and give its SI unit.
- I can distinguish charge conservation at junctions from energy conservation around loops.
- I can interpret current, potential, resistance, and power from a graph or schematic.
- I can place ideal meters correctly and predict qualitative loading effects of nonideal meters.
- I can design or critique a circuit experiment and justify a claim from measured evidence.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 11.3 FAQs
What is the difference between resistance and resistivity?
Resistance describes a specific object; resistivity characterizes the material from which it is made.
How does length affect resistance?
For fixed material and cross-sectional area, resistance is directly proportional to length.
How does area affect resistance?
For fixed material and length, resistance is inversely proportional to cross-sectional area.
What graph indicates ohmic behavior?
A linear current–potential-difference relation through the origin under fixed conditions.
How do I get resistance from an I-versus-V graph?
Take the reciprocal of the slope because slope=I/V=1/R.
Can a resistor heat up and change resistance?
Yes. Thermal energy transfer can change temperature and therefore resistivity for many materials.