Sensing Components: Lamps, Diodes, Thermistors and LDRs

Worked Example: Calculating Resistance from an I-V Graph

You cannot find resistance just by looking at the steepness of the curve; you must calculate it using coordinates from the graph. Find the resistance of a filament lamp when the potential difference across it is $12\text{ V}$ and the current is $3\text{ A}$.

Step 1: Write the formula for resistance.

• $R = \frac{V}{I}$

Step 2: Substitute the known values.

• $R = \frac{12\text{ V}}{3\text{ A}}$

Step 3: Calculate the final answer with units.

• $R = 4\text{ }\Omega$

I-V Characteristics of Diodes

• What if you needed to force electricity to travel down a one-way street?
• A diode is a semiconductor component that allows current to flow in one direction only, known as the forward bias.
• In the reverse direction (reverse bias), the diode has a very high resistance, which completely prevents current from flowing.
• On an I-V graph, reverse bias is shown as a completely horizontal line along the x-axis ($I = 0$).
• In forward bias, resistance is initially very high until the potential difference reaches a specific threshold voltage (approximately $0.6\text{ V}$ to $0.7\text{ V}$ for silicon diodes).
• Above this threshold voltage, resistance decreases rapidly, and current increases sharply, curving steeply upwards on the graph.
• In practical circuits, a fixed resistor is often placed in series with a diode to limit the current and prevent the diode from overheating once it starts conducting.

Resistance of Thermistors and LDRs

• Some components actually become better conductors the more extreme their environment gets.
• A thermistor is a temperature-dependent resistor. In a standard NTC (Negative Temperature Coefficient) thermistor, resistance decreases as temperature increases.
• An LDR (Light Dependent Resistor) changes its resistance depending on light intensity. Its resistance decreases as light intensity increases.
• In physical terms, incident photons of light release more charge carriers (electrons) in the semiconductor material of the LDR, making it easier for current to flow.
• An LDR has a very high resistance in total darkness (in the $M\Omega$ range) and a very low resistance in bright light (tens of $\Omega$).
• Both components are non-ohmic conductors. On a graph of Resistance against Temperature/Light, the line forms a non-linear downward curve that does NOT touch the x-axis, because resistance never truly reaches zero.

Sensing Circuits and Potential Dividers

• Every time your mobile phone screen automatically brightens in the sun, a smart circuit is doing the work behind the scenes.
• A potential divider is a series circuit that shares the total supply potential difference ($V_{supply}$) between components in proportion to their resistance.
• The golden rule of a potential divider is that the component with the higher resistance takes a larger share of the total potential difference.
• A sensing circuit uses a potential divider (typically containing a fixed resistor and a sensor like an LDR or thermistor) to monitor environmental changes and trigger an electrical response.
• For example, in a heating system, as the room gets colder, the thermistor's resistance increases.
• This causes the thermistor to take a larger share of the potential difference. If a heater is connected in parallel with the thermistor, this increased voltage will trigger the heater to turn on.
• Similarly, in an automatic street light circuit, as the surroundings get darker, the LDR's resistance increases.
• This causes the LDR to take a larger share of the potential difference. If a street lamp is connected in parallel with the LDR, this increased voltage will trigger the lamp to turn on.

Worked Example: Sensing Circuit Voltages (Higher Tier)

A $12\text{ V}$ battery is connected to a $200\text{ }\Omega$ fixed resistor and a thermistor in series. At $50^\circ\text{C}$, the thermistor has a resistance of $100\text{ }\Omega$. Calculate the potential difference across the fixed resistor.

Step 1: Write down the formula for voltage sharing.

• $V_{out} = V_{in} \times \left(\frac{R_{out}}{R_{total}}\right)$

Step 2: Calculate the total resistance of the circuit.

• $R_{total} = 200\text{ }\Omega + 100\text{ }\Omega = 300\text{ }\Omega$

Step 3: Substitute the values for the fixed resistor.

• $V_{out} = 12\text{ V} \times \left(\frac{200\text{ }\Omega}{300\text{ }\Omega}\right)$

Step 4: Calculate the final answer.

• $V_{out} = 12 \times 0.667 = 8\text{ V}$