I–V Graphs

• Ohm's Law: This principle states that the current through a conductor is directly proportional to the potential difference across it, provided physical conditions like temperature remain constant ($V = IR$).

• Resistance Calculation: At any point on an I–V graph, the resistance $R$ can be calculated using the ratio $R = \frac{V}{I}$.

• Gradient Interpretation: On a standard I–V graph (where $I$ is on the y-axis), the gradient of a straight line represents the reciprocal of the resistance ($\text{Gradient} = \frac{1}{R}$). A steeper line indicates a lower resistance.

Analyzing Ohmic Conductors

• Identification: Look for a straight line that passes through the origin $(0,0)$. This indicates that the resistance is constant and the component obeys Ohm's Law.
• Calculation: Select any point $(V, I)$ on the line and apply $R = \frac{V}{I}$ to find the fixed resistance value.

Analyzing Non-Ohmic Conductors

• Filament Lamp: Observe a curve that gets shallower as voltage increases. This happens because the filament heats up, increasing the vibration of metal ions, which obstructs electron flow and raises resistance.
• Semiconductor Diode: Note that current only flows when the potential difference is positive and exceeds a specific threshold voltage (typically around $0.6$ to $0.7$ V). In reverse bias (negative voltage), the resistance is extremely high, and virtually no current flows.

• Check the Axes: Always verify which variable is on which axis. If $V$ is on the y-axis and $I$ is on the x-axis, the gradient is equal to the resistance $R$, not $\frac{1}{R}$.

• Origin Check: Ensure the graph passes through $(0,0)$. If it doesn't, there may be a systematic error (zero error) in the measurements or a specific threshold behavior like in a diode.

• Resistance at a Point: For curved graphs, do NOT use the gradient of the tangent to find resistance. Instead, use the specific $V$ and $I$ values at that point to calculate $R = \frac{V}{I}$.

• Symmetry: Note that for resistors and filament lamps, the graph is usually symmetrical in the negative quadrant, whereas for diodes, it is highly asymmetrical.

• Temperature Neglect: Students often forget that Ohm's Law only applies if temperature is constant. A resistor can become non-Ohmic if it carries enough current to heat up significantly.

• Gradient Confusion: A common error is assuming a steeper I–V graph means higher resistance. In reality, a steeper I–V graph means more current for the same voltage, which implies a lower resistance.

• Diode Reverse Bias: Many assume diodes have 'infinite' resistance in reverse. While practically true for most circuits, it is more accurate to say the resistance is 'extremely high' until the breakdown voltage is reached.