AP Syllabus focus: 'Materials obeying Ohm's law have constant resistance for all currents; an ohmic material has constant resistivity regardless of temperature.'
These notes explain how AP Physics 2 defines ohmic behavior, why constant resistance matters, and how constant resistivity lets a material respond predictably when current and potential difference change.
What It Means to Be Ohmic
When a circuit element obeys Ohm's law, the potential difference across it is directly proportional to the current through it.
Current–voltage (–) characteristic for an ohmic device: the straight line through the origin indicates . Because the slope is constant, the resistance can be treated as constant over the range shown (equivalently, stays the same). Source
That proportional behavior means the element keeps the same resistance as the current changes. In AP Physics 2, this idea is used as a model for conductive materials and resistors whose electrical behavior stays predictable.
Ohmic material: A material whose resistivity remains constant regardless of temperature, so a sample with fixed dimensions can have a constant resistance.
In this course, the term ohmic links a material property to a circuit property. If the material's resistivity stays unchanged and the object's geometry does not change, then the resistance of that object can remain unchanged as different currents pass through it.
Constant resistance in a circuit element
For an element that follows Ohm's law, the ratio of potential difference to current is the same at every current value considered. That is what physicists mean by constant resistance. The current may increase or decrease, but the resistance value does not need to be recalculated each time.
= resistance, measured in ohms
= potential difference across the element, measured in volts
= current through the element, measured in amperes
This equation is especially important for recognizing ohmic behavior. If changes in the same proportion as , then stays constant. For example, doubling the current in an ohmic resistor requires doubling the potential difference. The resistance is not becoming larger or smaller; the element is simply responding proportionally.
A common mistake is to think that constant resistance means constant current. It does not. Current depends on the applied potential difference. An ohmic element can carry many different currents while still keeping one fixed resistance value.
Resistance and Resistivity Are Not the Same
Although the words sound similar, resistance and resistivity describe different things. Resistance belongs to a specific object, such as a wire or resistor. Resistivity belongs to the material the object is made from. Two objects made from the same material can share the same resistivity but still have different resistances.
For this subtopic, the important idea is the connection between the two. If a material is ohmic, its resistivity is treated as constant regardless of temperature. Then, for a sample whose dimensions stay fixed, the resistance can also remain constant. This is why AP Physics 2 can model an ohmic resistor with one resistance value even when the current changes.
Why the temperature statement matters
The syllabus definition goes beyond a single current setting. It says an ohmic material has constant resistivity regardless of temperature.
Resistivity vs. temperature comparison for a metal, a semiconductor, and a superconductor. The different curve shapes emphasize that is often temperature-dependent in real materials (increasing for many metals and decreasing for many semiconductors), which is why AP’s “constant resistivity” wording is an idealization for an ohmic model. Source
In other words, the material's intrinsic opposition to charge flow is treated as unchanged even if temperature varies. That makes the model simpler and keeps the resistance predictable.
This point matters because a resistor could seem to follow Ohm's law at one operating condition but fail to remain truly ohmic if its intrinsic properties changed. The AP model avoids that complication by defining an ohmic material as one with unchanging resistivity.
How to Recognize Ohmic Behavior
An element or material is treated as ohmic when its electrical response stays proportional and consistent.
The ratio stays the same for all currents considered.
A larger current requires a proportionally larger potential difference.
A smaller current requires a proportionally smaller potential difference.
One measured resistance value can be used again as long as the element remains ohmic.
If the ratio changes, the behavior is not ohmic.
One measurement can tell you the resistance at that moment, but it cannot by itself prove that a material is ohmic. Ohmic behavior is about consistency across changing conditions, not just a single numerical calculation.
Why This Matters in AP Physics 2
The ohmic model makes circuit analysis possible without constantly redefining the properties of each resistor. Once a resistor is identified as ohmic, you can treat its resistance as fixed while current and potential difference vary. That lets you focus on the relationship between variables instead of assuming the resistor itself is changing.
This also explains the meaning of the phrase materials obeying Ohm's law have constant resistance for all currents. The phrase does not mean every material is ohmic. It means that when a material is modeled as obeying Ohm's law, its resistance remains the same no matter which current value is being analyzed.
Common Misunderstandings
Ohmic does not mean perfect conductor. An ohmic resistor can still have substantial resistance.
Constant resistance does not mean the element always transfers the same amount of energy each second.
A component can have a calculated resistance at one operating point and still fail to be ohmic overall.
Saying a material is ohmic is stronger than saying a single data pair fits .
FAQ
Real measurements are affected by practical limits, even when the component is intended to be ohmic.
Common causes include:
meter precision and rounding
loose connections
small fluctuations in the power supply
contact resistance at clips or terminals
A resistor can still be modeled as ohmic if the deviations are small enough that the overall pattern remains proportional within experimental uncertainty.
Yes. Many real components act nearly ohmic only over a limited range of currents or potential differences.
At low or moderate currents, the resistance may stay almost constant. At higher currents, heating or internal changes can make the resistance shift enough that the component is no longer well described as ohmic.
In introductory physics, the word ohmic is often used for the idealized range where the proportional model works well.
For an ordinary ohmic resistor, reversing current direction does not change its ohmic nature.
If the resistor is truly ohmic, the magnitude of the potential difference is still proportional to the magnitude of the current. The signs of $V$ and $I$ both reverse together, so the ratio stays consistent.
This symmetry is one reason simple resistors are easier to model than devices whose behavior depends strongly on current direction.
The material being tested may be ohmic, but extra resistance from the setup can distort the results.
Possible issues include:
resistance in connecting wires
poor metal-to-metal contact
oxidation at terminals
heating at the contact points
If those effects are large, the measured $V$ and $I$ may describe the whole setup rather than just the sample. Good experimental design tries to isolate the material itself.
In many basic circuit situations, metals respond in a simpler and more proportional way than semiconductor devices.
Semiconductor devices often depend strongly on internal junction behavior, charge carrier concentration, and direction of bias. That can make the relationship between $V$ and $I$ change noticeably as conditions change.
Metals used in standard resistors are chosen because their behavior is more stable and easier to approximate with constant resistance, which makes them better fits to the ohmic model used in AP Physics 2.
Practice Questions
An ohmic resistor has a potential difference of when the current is . The current is increased to .
State what happens to the resistance, and determine the new potential difference. [2 marks]
1 mark: States that the resistance stays constant.
1 mark: Correctly determines the new potential difference as .
A student tests a wire and records the following data:
At , the potential difference is
At , the potential difference is
At a different temperature, at , the potential difference is
Using the AP Physics 2 definition of an ohmic material, determine whether this wire can be modeled as ohmic. Justify your answer using resistance and resistivity. [5 marks]
1 mark: Calculates or states that
1 mark: Calculates or states that
1 mark: Calculates or states that
1 mark: Concludes that the resistance is constant for all currents tested.
1 mark: Correctly states that, under the AP Physics 2 definition, constant resistance together with unchanged behavior at a different temperature is consistent with an ohmic material having constant resistivity regardless of temperature.
