I-V Characteristics

• I-V Characteristics are graphical representations that show how the current through a component changes as the potential difference across it is varied. These graphs are fundamental for identifying the electrical behavior and resistance properties of different circuit elements.

• An Ohmic Conductor is a component that follows Ohm's Law, meaning the current is directly proportional to the potential difference ($I \propto V$) provided physical conditions like temperature remain constant. This results in a straight-line graph passing through the origin.

• Resistance ($R$) is defined as the ratio of potential difference to current ($R = \frac{V}{I}$). On an $I-V$ graph (where $I$ is on the y-axis), the resistance at any point is the reciprocal of the ratio $\frac{I}{V}$.

• To measure I-V characteristics, a circuit is constructed containing the component, an Ammeter in series to measure current, and a Voltmeter in parallel to measure potential difference.

• A Variable Resistor or a potential divider is used to vary the potential difference across the component systematically. This allows for multiple data points to be collected across a wide range of voltages.

• For components like diodes, it is essential to reverse the connections of the power supply to investigate the Reverse Bias region of the graph, where the potential difference and current values are negative.

Comparison of Components

• Ohmic vs. Non-Ohmic: Ohmic components maintain a constant ratio of $V/I$ regardless of the applied voltage, whereas non-Ohmic components have a resistance that changes based on the current or external factors like temperature and light.

• Check the Axes: Always verify if the graph is $I$ vs $V$ or $V$ vs $I$. If the axes are swapped ($V$ on y-axis), the gradient directly represents the resistance $R$, rather than $1/R$.

• Calculating Resistance: To find the resistance of a non-Ohmic component at a specific point, do NOT use the gradient of the tangent. Instead, use the coordinates of that specific point to calculate $R = \frac{V}{I}$.

• Origin Check: Ensure the graph passes through $(0,0)$. If a component requires a minimum voltage to start conducting (like a diode), the graph will stay on the x-axis until that threshold is reached.

• Symmetry: Note that while resistors and filament lamps often show symmetrical behavior in the negative quadrant, diodes are strictly asymmetrical due to their one-way conduction property.

• Gradient Misinterpretation: A common error is assuming the gradient of a curved $I-V$ graph is the resistance. The gradient is $\frac{dI}{dV}$, which is the dynamic conductance; the static resistance is always the total $V$ divided by the total $I$ at that point.

• Temperature Assumptions: Students often forget that Ohm's Law only applies if the temperature is constant. In a filament lamp, the 'non-Ohmic' behavior is a direct result of the temperature change caused by the current itself.

• Diode Reverse Bias: It is a misconception that diodes have zero resistance in forward bias. They have very low resistance only after the threshold voltage is reached; below that, their resistance is very high.