Question

Answer the following giving reason :
The assertion that V = IR is a statement of Ohm's law is not true. Why ?

Hint:

To safely avoid losing marks in conceptual questions, always precisely articulate that Ohm's law strictly demands a linear $V-I$ graph passing through the origin. If the graph curves even slightly, Ohm's law is completely broken, but $V=IR$ still perfectly calculates the resistance at any single point on that curve!

Answer 1

Concept:
• Electrical resistance is fundamentally defined for any component as the mathematical ratio of voltage to current at any given instant.
• Ohm's Law is a highly specific physical statement about the strict linearity of certain conducting materials under constant environmental conditions.
• A definition is universally true, while a physical law has specific strict boundaries and limitations.

Step 1: Define the equation $V = IR$
The mathematical equation $V = IR$, or strictly rearranged as $R = \frac{V}{I}$, is universally accepted as the fundamental macroscopic definition of electrical resistance.
This specific equation allows us to mathematically calculate the instantaneous resistance $R$ of absolutely any electrical device, at any specific moment, regardless of how that device fundamentally operates.
It flawlessly applies to a simple copper wire, a complex semiconductor diode, a glowing vacuum tube, or a heated tungsten filament.

Step 2: Define strict Ohm's Law
Ohm's Law, as originally formulated by Georg Simon Ohm, is a much stricter, narrower physical postulate.
It explicitly asserts that the current $I$ flowing through a specific conductor is directly and linearly proportional to the potential difference $V$ firmly applied across its ends ($V \propto I$), strictly provided that all physical conditions (most notably temperature and mechanical strain) remain completely constant.
This strict proportionality implies that the resistance $R$ must remain an absolutely constant value, completely independent of the varying applied voltage or current.

Step 3: Highlight the logical contradiction
There are thousands of commonly used electrical components (such as p-n junction diodes, thermistors, and transistors) known as non-ohmic devices.
For these non-ohmic devices, if you forcefully change the voltage $V$, the resulting current $I$ does not change linearly. Their resistance $R$ actively fluctuates depending on the applied voltage.
These devices violently disobey Ohm's Law.
However, even when a diode is flagrantly violating Ohm's Law, you can still perfectly calculate its instantaneous resistance at any given exact voltage point using the formula $R = \frac{V}{I}$.

Step 4: Conclusion
Because the equation $V = IR$ remains universally valid and actively true even for devices where Ohm's Law completely and utterly fails, it is logically impossible for $V = IR$ to be the actual statement of Ohm's Law itself.
It is merely the mathematical definition of resistance, whereas Ohm's Law is the specific strict physical statement that $R$ must remain constant.