Circuit Design for Characteristics

What the circuit must discover

The resistance of a component can depend on its operating conditions. A filament lamp changes temperature as its current changes; a diode behaves differently when connected in opposite directions; a thermistor responds to temperature; and an LDR responds to light intensity. A suitable circuit must let us change the relevant condition, make the necessary electrical measurements and compare the resistance at different points.

For any operating point,

$R=\frac{V}{I}$

where $R$ is resistance in ohms (Ω), $V$ is the potential difference across the component in volts (V), and $I$ is the current through it in amperes (A).

Measuring potential difference and current

Connect the component under test in series with a low-voltage d.c. supply, an ammeter and a variable resistor. The ammeter measures the current passing through the component, so it must be in series. Connect a voltmeter in parallel across the component because it measures the potential difference between the component's two ends.

The variable resistor limits the current and allows a range of readings to be taken. Start with it set to a high resistance, close the switch and adjust it gradually. At each setting, record $V$ and $I$, then calculate $R=V/I$. An adjustable low-voltage power supply may instead be used to vary the potential difference, but the current must still be limited to protect the component.

A table should include the quantities that were deliberately changed and measured, with their units. Repeated readings can reveal anomalies and allow a mean to be calculated where appropriate. Use enough different settings to show a pattern rather than relying on only two points.

Exploring a filament lamp

Use the measurement circuit to obtain pairs of current and potential-difference readings for the lamp. Plot current on the vertical axis against potential difference on the horizontal axis. The graph is curved rather than a straight line, showing that the lamp does not have a constant resistance.

At low current the filament is relatively cool. Increasing the potential difference produces a greater current and heats the filament. The hotter filament has a greater resistance, so the current then increases less rapidly for each further increase in potential difference. Calculating $V/I$ at successive operating points makes this rise in resistance visible.

Temperature is part of the lamp's behaviour, so readings should be taken consistently. Allowing the lamp to heat for very different lengths of time at different settings could make comparisons less reliable. Do not exceed its rating, and switch off between sets of readings if it becomes excessively hot.

Exploring a diode

Place the diode in the same type of circuit, using a variable resistor to limit the current. In its forward direction, very little current flows at small potential differences; after the potential difference becomes large enough, the current rises steeply. Its calculated resistance therefore changes greatly across its characteristic.

To investigate the other direction, switch off the supply and reverse the diode. Record the readings using the opposite sign convention for potential difference and current. In this reverse direction, the current is extremely small under ordinary school-circuit conditions, so the resistance is very high. Plotting both sets of results on the same axes displays the diode's directional behaviour. The current-limiting resistor is particularly important once the forward current begins to rise rapidly.

Exploring an NTC thermistor

For the negative temperature coefficient thermistor required here, resistance falls as temperature rises. Its resistance can be measured directly with an ohmmeter, with the thermistor disconnected from any powered circuit. Alternatively, keep a small potential difference constant, measure the current and calculate $R=V/I$.

Place the thermistor in a water bath and measure the water temperature with a thermometer. Change the temperature in stages, stir the water so that its temperature is more uniform, and wait for the thermistor and thermometer readings to settle before recording them. Keep the supply potential difference and the immersion position constant. Plot resistance against temperature; the downward trend shows the thermistor's response.

Exploring an LDR

An LDR's resistance decreases as the light intensity falling on it increases. Its resistance may be read directly using an ohmmeter or found from current and potential-difference measurements at a constant supply setting.

Illuminate the LDR with a lamp and alter the illumination in measured stages. Moving the lamp to different measured distances provides a simple way to produce different illumination levels; a light meter can measure the actual light intensity if available. Keep the lamp's brightness, its angle to the LDR and the surrounding light as constant as possible. Shielding the arrangement from changing room light improves the validity of the comparison. Plot resistance against light intensity, or against the chosen controlled measure of illumination, and look for the decrease in resistance as illumination increases.

Choosing and interpreting the graph

For a filament lamp or diode, the most informative result is an $I$–$V$ characteristic because the investigation changes the electrical operating point directly. For a thermistor, plot resistance against temperature. For an LDR, plot resistance against light intensity or a clearly identified proxy such as lamp distance.

A straight line through the origin on an $I$–$V$ graph would indicate constant resistance. Curvature shows that $V/I$ changes. For non-linear components, resistance belongs to a particular operating point: quoting one resistance for the whole curve would hide the behaviour the circuit was designed to explore.

Core measurement circuit

• Ammeter: in series with the test component.
• Voltmeter: in parallel across the test component.
• Variable resistor: varies and limits the current.
• Use a low-voltage d.c. supply.
• For every operating point, calculate

$R=\frac{V}{I}$

What to vary and plot

Valid results

Take several readings, repeat where appropriate and control all variables other than the one being investigated. Limit the current, remain within component ratings and let temperature readings settle. A curved $I$–$V$ graph means resistance varies; use $V/I$ at the specified operating point.