Ohm's Law & I-V Characteristics

At a microscopic level, resistance arises from collisions between charge carriers (usually electrons) and the fixed positive ions within the lattice structure of the conductor.

In Ohmic conductors, the drift velocity of electrons increases linearly with the applied electric field, maintaining a constant ratio between $V$ and $I$ as long as the lattice vibrations (temperature) remain stable.

For Non-Ohmic components, the resistance changes as the current changes, often because the energy dissipated as heat increases the temperature of the material, which in turn increases the frequency of electron-ion collisions.

To determine the I-V characteristics of a component, a circuit must be constructed with an ammeter in series to measure current and a voltmeter in parallel across the component to measure potential difference.

A variable power supply or a potentiometer (potential divider) is used to vary the voltage across the component in small, discrete increments.

For each voltage setting, the corresponding current is recorded, and the process is repeated for negative voltages by reversing the connections to the power supply.

Data is plotted on a graph with Voltage ($V$) on the x-axis and Current ($I$) on the y-axis; the static resistance at any point is calculated as $R = \frac{V}{I}$.

Check the Axes: Always verify if the graph is $I$ vs $V$ or $V$ vs $I$. If $I$ is on the y-axis, the gradient is $\frac{1}{R}$ for a linear graph; if $V$ is on the y-axis, the gradient is $R$.

Origin Check: An ohmic conductor must produce a line that passes exactly through the origin $(0,0)$. If it does not, there may be a systematic error or a zero error in the measuring instruments.

Unit Consistency: Ensure all values are converted to standard SI units (Amperes and Volts) before calculating resistance in Ohms. Common traps include $mA$ (milliamps) or $k\Omega$ (kilo-ohms).

Reasonableness Check: If a component heats up (like a lamp), expect the resistance to rise. If your calculation shows resistance decreasing as a lamp gets brighter, re-check your data points.

Misconception: Students often believe that $R = \text{gradient}$ of the I-V graph. This is only true for linear graphs passing through the origin; for non-linear graphs, $R$ must be calculated using the specific $V$ and $I$ values at that point.

Diode Polarity: Forgetting that a diode only conducts in one direction (forward bias) and has effectively infinite resistance in the other (reverse bias) until the breakdown voltage is reached.

Temperature Neglect: Assuming Ohm's Law applies to all conductors at all times. It only applies if temperature is constant; therefore, a filament lamp is strictly non-ohmic because its temperature changes during operation.