Physics 10.18 - 10.20 - Component characteristics

Reading current-potential difference characteristics

A current-potential difference characteristic, often shortened to an I-V characteristic, shows how the current through one component changes as the potential difference across that component changes.

• Potential difference, $V$, is plotted on the horizontal axis.
• Current, $I$, is plotted on the vertical axis.
• Positive and negative values show opposite directions of potential difference and current. A negative current is not “less current”; it is current in the opposite direction.

The resistance at a non-zero point on an I-V graph comes from that point's ratio $\frac{V}{I}$. Do not calculate resistance at the origin: $\frac{0}{0}$ is undefined. Also, do not call resistance “the gradient” of any curved I-V graph. With these axes, the gradient of a straight fixed-resistor line is $\frac{I}{V}$, which is $\frac{1}{R}$.

Worked example

A filament lamp has these two readings:

Solution

At $1.0\,\mathrm{V}$:

$R = \frac{V}{I} = 1.0\,\mathrm{V} / 0.25\,\mathrm{A} = 4.0\,\Omega$

At $4.0\,\mathrm{V}$:

$R = \frac{V}{I} = 4.0\,\mathrm{V} / 0.50\,\mathrm{A} = 8.0\,\Omega$

The potential difference is four times larger while the current is only twice as large. The calculated resistance has increased from $4.0\,\Omega$ to $8.0\,\Omega$, which is the expected behaviour of a filament lamp as it becomes hotter.

Three component characteristics

[DIAGRAM: asset_name: Physics 10.18-10.21 - Component characteristics and circuit design - diagram 01; asset_slug: physics_10_18_10_21_component_characteristics_and_circuit_design__diagram_01; recommended_method: matplotlib; description: Three aligned monochrome illustrative I-V plots with potential difference V on each horizontal axis and current I on each vertical axis: a straight fixed-resistor line through the origin, a symmetric filament-lamp curve that becomes less steep as the magnitude of potential difference increases, and a diode curve with approximately zero reverse current and a steep forward rise after a threshold region. Direct panel titles, no numerical scale, no reverse-breakdown branch, and a note that curves are illustrative and not to scale.]

Fixed resistor

For a fixed resistor kept at constant temperature, current is directly proportional to potential difference. Doubling the p.d. doubles the current, so $\frac{V}{I}$ stays constant. Its I-V characteristic is a straight line through the origin. Reversing the p.d. reverses the current, giving the same pattern in the opposite quadrant.

For two straight fixed-resistor I-V lines, the steeper line has the smaller resistance because its gradient is $\frac{I}{V} = \frac{1}{R}$. This shortcut is not valid for a curved component characteristic.