Ohmic vs Non-Ohmic Conductors
Ohm's Law states that the current through a conductor is directly proportional to the voltage across it, provided physical conditions such as temperature remain constant. Not all conductors obey this relationship. An ohmic conductor is one that maintains a constant resistance regardless of the applied voltage, producing a perfectly straight line on a current–voltage (I–V) graph. Common examples include metal resistors at constant temperature, such as a coil of nichrome wire or a standard carbon resistor used in school laboratories. A non-ohmic conductor is one whose resistance changes as the voltage or current changes. The I–V graph for such a device is curved or asymmetric, revealing that the ratio V/I is not constant. Examples include filament light bulbs (where resistance rises sharply with temperature), semiconductor diodes (which only allow current in one direction), and thermistors (whose resistance falls dramatically as temperature increases). Understanding why some materials obey Ohm's Law and others do not requires looking at how charge carriers behave under different physical conditions. The distinction between ohmic and non-ohmic behaviour is fundamental in circuit design. Engineers must know whether a component will maintain predictable resistance or whether its resistance will shift under operating conditions. A simple fuse wire is deliberately non-ohmic — its resistance rises catastrophically when current becomes dangerously large, causing it to melt and break the circuit. Recognising the shape of an I–V characteristic curve is therefore an essential experimental and analytical skill in physics.
- What Makes a Conductor Ohmic?
- Temperature: The Key Variable
- Semiconductors and Diodes
- Identifying Behaviour from I–V Graphs
What Makes a Conductor Ohmic?
A conductor is ohmic when its resistance R = V/I remains constant over a wide range of voltages and currents. At the microscopic level, this happens when the drift velocity of electrons is low enough that collisions with lattice ions occur at a steady, predictable rate. In a metal at constant temperature, the lattice structure is fixed and the mean free path of electrons stays roughly the same, so resistance does not change. On an I–V graph, an ohmic conductor produces a straight line through the origin with gradient 1/R.
Temperature: The Key Variable
Ohm's Law holds only when temperature is constant. In a metal, resistance arises because conduction electrons collide with vibrating lattice ions. As current increases, electrical energy heats the wire, causing ions to vibrate more vigorously. This increases the frequency of collisions and raises the resistance. A tungsten filament bulb is the classic example: at room temperature its resistance is about 20 Ω, but at operating temperature (~2500 °C) it exceeds 500 Ω. The I–V graph curves because resistance is continuously changing with temperature.
Semiconductors and Diodes
In semiconductors, the mechanism is the opposite: as temperature rises, more electrons gain enough energy to escape their atoms and become conduction electrons, so resistance falls. A thermistor exploits this — it is used in temperature sensors and self-resetting fuses. A p-n junction diode has an I–V graph that is strongly asymmetric: in the forward-biased direction current rises exponentially with voltage (following the Shockley diode equation, not a linear relationship), while in the reverse-biased direction almost no current flows until a breakdown voltage is reached.
Identifying Behaviour from I–V Graphs
The I–V graph is the definitive test. For an ohmic resistor: a straight line through the origin, symmetric for both positive and negative voltages. For a filament bulb: an S-shaped curve that flattens as voltage increases, symmetric but non-linear, because resistance grows with temperature. For a diode: almost no current for negative (reverse) voltages, then a sharp exponential rise once forward voltage exceeds roughly 0.6 V for silicon. For a thermistor: a curve steeper than a straight line because resistance decreases as current heats the device, making it conduct more easily at higher voltages.
The Key Equation
- R — Resistance (Ohm (Ω)): The ratio V/I; constant for ohmic conductors, variable for non-ohmic ones.
- V — Potential difference (voltage) (Volt (V)): The electrical potential energy per unit charge across the component.
- I — Current (Ampere (A)): The rate of flow of electric charge through the conductor.
- R(T) — Temperature-dependent resistance (Ohm (Ω)): Indicates that resistance is a function of temperature T, causing non-ohmic behaviour.
Worked Example
Problem. A student measures the current through two components at several voltages. Component A gives readings: 2V→0.4A, 4V→0.8A, 6V→1.2A. Component B gives: 2V→0.2A, 4V→0.5A, 6V→1.0A. Calculate the resistance of each component at each voltage and determine which is ohmic.
Answer. Component A is ohmic with R = 5 Ω. Component B is non-ohmic; its resistance decreases from 10 Ω to 6 Ω as voltage increases.
Origins · 1 minGeorg Simon Ohm and how this was discovered
Georg Ohm published his fundamental law of electrical circuits in 1827 in his work 'Die galvanische Kette, mathematisch bearbeitet' (The Galvanic Circuit Investigated Mathematically). Using homemade equipment — he crafted his own wires to ensure consistent cross-sections — he demonstrated that current through a metallic conductor is directly proportional to the voltage and inversely proportional to resistance. His work established the mathematical foundation for all circuit analysis. The SI unit of resistance, the ohm (Ω), is named in his honour. Ohm's 1827 paper was initially dismissed and even ridiculed by leading German scientists of the day, who considered it too mathematical and abstract. He lost his teaching position as a result. It took nearly a decade and recognition from British scientists before his work gained the respect it deserved — he was finally awarded the Copley Medal by the Royal Society of London in 1841.
Related Concepts
- Ohm's Law (Macroscopic) — Ohmic vs non-ohmic behaviour is a direct extension of Ohm's Law — understanding when the law holds requires first knowing what the law states.
- Electric Current and Charge — Current is one of the two quantities in the I–V graph; understanding charge flow helps explain why resistance changes in non-ohmic devices.
- Resistivity and Resistance — Resistivity is the material property underlying resistance; it changes with temperature, explaining why filament bulbs and thermistors are non-ohmic.
- Series and Parallel Circuits — Circuit calculations depend on whether components are ohmic; non-ohmic components complicate standard series/parallel resistance rules.