4.2.3 - Resistance and I-V characteristics

Resistance and Ohm's Law

When a potential difference is applied across a component, charge carriers transfer energy as they move through it. The component's resistance is the ratio of the potential difference across it to the current through it.

Here $R$ is resistance in ohm, $V$ is potential difference in volt, and $I$ is current in ampere. This equation is expected recall for this specification point.

There is a subtle but important distinction:

• $R=V/I$ defines the resistance at one operating point.
• Ohm's law says that the current through a conductor is directly proportional to the potential difference across it, provided physical conditions, especially temperature, remain constant.

So a component can always have a value of $R=V/I$ at a point, but it only obeys Ohm's law if $V/I$ stays constant as $V$ and $I$ change.

Worked example: a resistor has a potential difference of $6.0\ \text{V}$ across it and a current of $0.24\ \text{A}$ through it.

If this resistor is ohmic and stays at the same temperature, doubling the p.d. to $12.0\ \text{V}$ doubles the current to $0.48\ \text{A}$. The resistance is still $25\ \Omega$.

Reading I-V Graphs

An I-V characteristic shows how the current through a component changes as the potential difference across it changes. The usual OCR-style graph has current $I$ on the vertical axis and potential difference $V$ on the horizontal axis.

On that graph:

For a straight line through the origin, this gradient is $I/V$, which is $1/R$. A steeper I-V line means a smaller resistance. This is a common trap: if a resource plots $V$ against $I$ instead, the gradient is $R$, so always check the axes.

In the characteristics image, the dashed forward curve is an LED and the solid forward curve is a diode. The thermistor curve illustrates an NTC device heated by the test current. On a curved I-V graph the resistance at a point is $V/I$ for that point; the tangent gradient $\mathrm{d}I/\mathrm{d}V$ is not generally equal to $I/V$.

A fixed resistor at constant temperature gives a straight line through the origin. The ratio $V/I$ is constant, so the resistor is ohmic.

A filament lamp is non-ohmic. As current increases, the filament heats up. Hotter metal ions vibrate more, so charge carriers collide more often and the resistance increases. On an I-V graph with $I$ on the vertical axis, the curve becomes less steep at larger p.d.

A thermistor is also non-ohmic in typical I-V measurements because its resistance depends on its temperature. If the current changes the component temperature during the measurement, the graph will not have one constant gradient. A self-heating thermistor can therefore show a curved characteristic. At a controlled, constant temperature and sufficiently small measuring current, it can instead be approximately ohmic over a suitable range.

A diode conducts mainly in one direction. In reverse bias the current is very small for normal lab voltages. In forward bias, the current stays small until the p.d. is large enough for the diode to conduct strongly. An LED behaves as a diode but emits light when forward-biased and normally needs a larger forward p.d. than a silicon diode.

These characteristics determine how components can be used. A diode can suppress current in the unwanted direction; an LED transfers some electrical energy to light, but needs a current-limiting component because a small further forward p.d. can produce a large current. Selecting a component therefore requires checking its operating current and p.d., not merely recognising its symbol.

A diode’s rapid forward-current rise is gradual: the turn-on p.d. is an approximate operating value rather than a perfectly sharp threshold. The LED curve is usually displaced to a higher forward p.d. than that of a typical silicon diode; the value depends on the device. Always limit the forward current.

[DIAGRAM: asset_slug: 4_02_3_resistance_ohms_law_and_iv_characteristics__diagram_01; description: Schematic I–V characteristics of a fixed resistor, filament lamp, self-heating NTC thermistor, diode and LED.; caption: Current–voltage characteristics of resistors, a lamp, a thermistor, a diode and an LED.]

Investigating Characteristics

The practical aim is to measure pairs of $V$ and $I$ values for the component under test, then plot the I-V characteristic. The circuit must measure the current through the component and the p.d. across the same component.

A good method is:

1. Connect the component, ammeter, variable resistor, switch and low-voltage d.c. supply in series.
2. Connect the voltmeter in parallel across the component under test.
3. Start with a small p.d. and close the switch only while taking a reading.
4. Adjust the variable resistor to obtain a range of p.d. values. Record $V$ and $I$ each time.
5. Reverse the component or the supply connections to collect negative readings where the component can safely be tested both ways.
6. Use a current-limiting resistor or a suitable variable resistor setting for a diode or LED, because the current can rise very rapidly in forward bias.