What Ohm's law actually asserts
For an ohmic conductor the current $I$ through it is directly proportional to the potential difference $V$ across it, provided the physical conditions (chiefly temperature) remain unchanged. The content of the law is that the ratio $V/I$ — which we call the resistance $R$ — is a constant, independent of $V$. Equivalently, the plot of $I$ against $V$ is a straight line passing through the origin.
The deeper microscopic statement, following from $E = \rho\, j$, is that a material obeys Ohm's law when its resistivity $\rho$ does not depend on the magnitude or direction of the applied electric field. The moment $R$ (or $\rho$) starts to change as $V$ changes, the material has stepped outside the law. As NCERT stresses, Ohm's law is obeyed by many substances but it is not a fundamental law of nature; deviations are the rule rather than the exception once we widen the class of materials beyond ordinary metals.
An ohmic conductor must be linear AND symmetric AND single-valued
A device is ohmic only if its V–I graph is a straight line through the origin in both quadrants — equal $V$ of either sign gives equal-and-opposite $I$, and each $V$ gives exactly one $I$. Failing any one of the three conditions (linearity, sign-symmetry, single-valuedness) makes the device non-ohmic.
Linear · Symmetric · Single-valued — all three, or it is non-ohmic.
The three types of deviation
NCERT Section 3.6 classifies departures from $V \propto I$ into three broad types. They are best remembered by the shape and behaviour of the V–I characteristic curve, summarised below.
| Type | Deviation | V–I signature | Example device / material |
|---|---|---|---|
| 1 | $V$ ceases to be proportional to $I$ | Curve bends away from the straight line; $R$ varies with $V$ | Good conductor at high current; filament lamp |
| 2 | V–I relation depends on the sign of $V$ | Reversing $V$ does not give equal-and-opposite $I$ (asymmetric) | Semiconductor diode, vacuum diode |
| 3 | V–I relation is not unique | More than one value of $I$ (or $V$) for the same $V$ (or $I$) | Gallium arsenide (GaAs) |
Type 1 — The V–I curve is non-linear
In the first kind of deviation $V$ simply ceases to be proportional to $I$. The characteristic is still a single curve in the first quadrant and still single-valued, but it is no longer straight. NCERT Fig. 3.5 shows exactly this: the dashed line is the ideal linear Ohm's-law response, while the solid line is the actual $V$ versus $I$ curve for a good conductor, which curls away from the dashed line at higher currents. The physical cause is that large currents heat the conductor, raising its resistance, so $R = V/I$ grows as $V$ grows.
Type 2 — The relation depends on the sign of V (diode)
In the second kind of deviation the V–I relation depends on the direction of the applied voltage. If a current $I$ flows for a certain $V$, then reversing the direction of $V$ while keeping its magnitude the same does not produce a current of the same magnitude in the opposite direction. The characteristic is asymmetric about the origin. The standard example is the semiconductor diode, studied in detail in the Semiconductors chapter: it conducts strongly in forward bias and almost not at all in reverse bias.
These deviations only make sense against the baseline. Revise Ohm's Law — its statement, the meaning of resistance, and the linear V–I graph — before reading the curves below.
Type 3 — The relation is not unique (GaAs)
The third deviation is the most striking: the V–I relation is not unique, so there is more than one value of current for the same voltage. The characteristic curve doubles back on itself, producing a region of negative differential resistance where the current falls even as the voltage rises. NCERT cites gallium arsenide (GaAs) as a material that behaves this way. Because the curve is multi-valued, you cannot assign a single $R$ to a given $V$ at all.
"Negative resistance" is not negative R
In the falling part of the GaAs curve, an increase in $V$ accompanies a decrease in $I$, so the slope $\dfrac{dV}{dI}$ (the differential resistance) is negative. The static resistance $R = V/I$ remains positive throughout. Examiners exploit the confusion between $V/I$ and the slope $dV/dI$.
Static $R = V/I > 0$; differential resistance $dV/dI$ can be negative.
Non-ohmic devices in practice
Resistors that obey Ohm's law are called ohmic; those that do not are non-ohmic. Most metals are ohmic and give a linear V–I relation. The NIOS module lists vacuum diodes, semiconductor diodes and transistors among devices that show non-ohmic character, noting that for a semiconductor diode Ohm's law fails even at low voltages. Electrolytes are an interesting middle case: a copper-sulphate cell can behave as an ohmic resistor (a straight line through the origin), but its resistivity depends on the electrode area, plate separation and concentration, and at high fields the behaviour departs from linearity.
NCERT adds an important caveat that applies to every material: even homogeneous conductors like silver, and pure or doped germanium, obey Ohm's law only within a limited range of electric field. If the field becomes too strong, there are departures from Ohm's law in all cases. Ohmic behaviour is therefore an approximation valid over a working range, not an absolute property.
| Device / material | Behaviour | Why it departs |
|---|---|---|
| Metallic resistor (Cu, Ag) | Ohmic over a working range | Departs only at very high fields / heating |
| Semiconductor diode | Non-ohmic (Types 1 & 2) | Non-linear and sign-dependent — conducts only one way |
| Vacuum diode (tube) | Non-ohmic | One-way conduction; non-linear characteristic |
| Thermistor | Non-ohmic (Type 1) | $R$ changes sharply as temperature/current changes |
| Electrolyte (CuSO$_4$) | Ohmic over a range | $\rho$ depends on area, separation, concentration; fails at high field |
| Gallium arsenide (GaAs) | Non-ohmic (Type 3) | Multi-valued curve; negative differential resistance region |
Does V = IR fail for non-ohmic devices?
A frequent misconception is that $V = IR$ "breaks down" for a diode. It does not. The relation $V = IR$ merely defines resistance as the ratio $V/I$, and it can be applied to any conducting device, ohmic or not — at any operating point a diode has a perfectly well-defined value of $V/I$. What fails for the diode is Ohm's law, which is the separate assertion that this ratio $R$ is constant, i.e. that the I–V plot is a straight line with $R$ independent of $V$. For a diode $R = V/I$ changes from point to point along the curve, so $R$ exists but is not constant.
"V = IR is Ohm's law" — false
The statement that "$V = IR$ is a statement of Ohm's law" is not true. That equation defines resistance and applies to all conductors. Ohm's law is the stronger claim that the I–V plot is linear, i.e. $R$ is independent of $V$. Resistance can be defined for a diode at every point; it just is not constant.
$R = V/I$ always defined · Ohm's law = $R$ constant (linear graph).
Limitations of Ohm's law in one screen
- Ohm's law asserts $I \propto V$, i.e. $R = V/I$ is constant and the I–V graph is a straight line through the origin. It is not a fundamental law of nature.
- Type 1: $V$ ceases to be proportional to $I$ — the V–I curve is non-linear (good conductor at high current).
- Type 2: the relation depends on the sign of $V$ — reversing $V$ does not give equal-and-opposite $I$ (semiconductor diode, vacuum diode).
- Type 3: the relation is not unique — more than one $I$ for the same $V$ (GaAs, with a negative differential resistance region).
- Non-ohmic devices: semiconductor diode, vacuum tube, transistor, thermistor, GaAs; electrolytes are ohmic only over a range.
- $V = IR$ only defines resistance; it holds for any conductor. Ohm's law is the stronger statement that $R$ is constant.