Circuit Design for Characteristics

When using a variable resistor, the causal chain works like this: adjusting the slider changes the total resistance of the circuit. This changes the current flowing through the circuit ($I = V/R$), which consequently alters the potential difference across the component being tested. To plot negative values for your graph, you must reverse the connections to the power supply. Always switch the circuit off between readings to prevent the components from heating up, which would make the results inaccurate.

I-V Characteristics: Filament Lamps

You can literally feel the energy wasting as heat when you place your hand near an old-fashioned incandescent bulb. A filament lamp is a non-ohmic conductor, meaning its current is not directly proportional to the potential difference.

As the potential difference increases, the current increases, causing the filament's temperature to rise. This thermal energy causes the metal ions in the filament's lattice to vibrate more vigorously. These increased vibrations cause more frequent collisions between the metal ions and the flowing electrons.

Due to these collisions, the resistance increases. On an I-V graph, this creates a non-linear, S-shaped curve that becomes shallower (flattens out) as the potential difference gets higher.

I-V Characteristics: Diodes

Imagine a turnstile that only lets people walk through in one direction—this is exactly how a diode controls electricity. A diode only allows current to flow in one direction, known as forward bias. In the opposite direction, known as reverse bias, the diode has extremely high resistance, and the current remains at $0\text{ A}$.

When testing a diode, you must include a protective fixed resistor (typically $10\ \Omega$) in series to limit the current and prevent the diode from burning out once it begins to conduct. Because the initial forward current is very small, a milliammeter should be used instead of a standard ammeter.

The resulting I-V graph is a flat line at zero for all negative voltages and low positive voltages. Once the potential difference reaches a specific threshold (usually $0.6\text{ V}$ to $0.7\text{ V}$), the graph curves sharply and steeply upwards.

Resistance Variation: Thermistors (NTC)

Why does an electric oven know exactly when to stop heating? It uses an NTC thermistor (Negative Temperature Coefficient), a component whose resistance decreases as temperature increases.

To investigate this variation, place the thermistor in a water bath alongside a digital thermometer. Stir the water bath to ensure a uniform temperature. Record the potential difference and current at various temperature intervals to calculate the resistance using the formula:

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

It is critical to switch off the circuit between readings to prevent self-heating, a phenomenon where the current flowing through the thermistor warms it up independently of the water bath. Graphing resistance against temperature will produce a downward-sloping curve.

Worked Example

During an experiment, a student places a thermistor in a $40^{\circ}\text{C}$ water bath. The voltmeter reads $4.5\text{ V}$ and the ammeter reads $0.15\text{ A}$. Calculate the resistance of the thermistor at this temperature.

Step 1: State the formula.

• $R = \frac{V}{I}$

Step 2: Substitute the known values.

• $V = 4.5\text{ V}$
• $I = 0.15\text{ A}$
• $R = \frac{4.5}{0.15}$

Step 3: Calculate the final answer with units.

• $R = 30\ \Omega$

Resistance Variation: Light Dependent Resistors (LDR)

A solar-powered garden light turns on automatically at dusk without any human input. It detects the darkness using an LDR, a component whose resistance decreases as light intensity increases.

To investigate an LDR, conduct the experiment in a dark room to control background light. You can vary the light intensity by moving a lamp to different fixed distances, using a dimmer switch, or placing black cards with different-sized holes over the LDR.

Always wait a few seconds after changing the light level before taking a reading to allow the LDR to fully react. Its resistance can range from millions of ohms (megohms) in total darkness down to a few hundred ohms in bright light. Plotting resistance against light intensity produces a steep downward-sloping curve.