Exceptions of Ohm's Law : Non-Linear V-I Characteristics

The minimum potential difference required before a measurable current starts flowing through certain devices.

• As current flows, the conductor heats up (Joule heating), increasing its resistance.
• The V–I graph starts linear at low current but curves upward (bends towards the V-axis) at higher current as resistance increases with temperature.
• Example: Torch bulb filament (tungsten) — resistance increases significantly as it glows.

Think of a busy road — as more "current" (traffic) flows, "friction" (resistance) increases, slowing the proportional relationship, just like a filament heats up and resists more current flow.

• In devices like a water voltameter (electrolytic cell), no measurable current flows until the applied voltage crosses a minimum value called the threshold voltage V₀.
• Beyond V₀, current may increase linearly, but the graph does not pass through the origin, violating Ohm's Law.

Similar to a car needing a minimum push to overcome static friction before it starts rolling — no motion (current) below that "threshold force."

Devices whose V–I graph is non-linear and often non-symmetric for forward/reverse voltage:

A diode behaves like a one-way valve in a pipe — it lets "water" (current) flow easily in one direction but blocks it in the other.

Since resistance is not constant for non-ohmic devices, we define a local/dynamic resistance at any point on the curve:

• Calculated using the slope of the tangent at a point on a non-linear V–I graph, using two nearby points.
• Differs from static resistance R = V/I, which uses total values from the origin.