Sensing Circuits and Voltage Dividers
From Sensor to Signal
A resistive sensor on its own produces a change in resistance, not a change in voltage. To turn a varying resistance into a varying voltage that a comparator or logic gate can read, you use a voltage divider. This is the most common input circuit in electronics and it appears on virtually every exam paper.
How a Voltage Divider Works
Two resistors, R1 and R2, are placed in series across a supply voltage \(V_{in}\). The output voltage \(V_{out}\) is taken from the junction between them and is given by:
$$V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2}$$
If R2 is much larger than R1, most of the supply voltage appears across R2, so \(V_{out}\) is high. If R2 is much smaller than R1, most of the voltage is dropped across R1 and \(V_{out}\) is low. Replacing one of the resistors with a sensor (LDR, thermistor, etc.) makes \(V_{out}\) change with the physical quantity being sensed.
Voltage divider: \(V_{out} = V_{in} \times \dfrac{R_2}{R_1 + R_2}\). \(V_{out}\) is taken across R2. If R2 increases relative to R1, \(V_{out}\) increases. If R2 decreases, \(V_{out}\) decreases.
LDR Sensing Circuit — Light Level Detection
A light-dependent resistor (LDR) has a high resistance in the dark (hundreds of kilohms) and a low resistance in bright light (hundreds of ohms). In a voltage divider with the LDR as R1 and a fixed resistor as R2:
- In the dark: LDR (R1) is large ⇒ most voltage drops across R1 ⇒ \(V_{out}\) is LOW.
- In bright light: LDR (R1) falls ⇒ less voltage drops across R1 ⇒ \(V_{out}\) rises towards \(V_{in}\).
Swapping the positions of the LDR and the fixed resistor (putting the LDR as R2 instead of R1) reverses the behaviour: \(V_{out}\) is HIGH in the dark and LOW in the light. This is a common error — always identify which resistor is connected to 0 V to determine what happens to \(V_{out}\).
NTC Thermistor Sensing Circuit — Temperature Detection
An NTC thermistor works on the same principle. Its resistance falls as temperature rises. In a divider with the thermistor as R1:
- Cold: thermistor resistance is high ⇒ large voltage drop across thermistor ⇒ \(V_{out}\) is LOW.
- Hot: thermistor resistance falls ⇒ smaller voltage drop across thermistor ⇒ \(V_{out}\) rises.
If the circuit needs to trigger when it gets cold (e.g. a frost alarm), place the thermistor as R2 so \(V_{out}\) rises as temperature falls. This “orientation” decision is the main skill tested on exam questions about sensing circuits.
Sensor orientation determines output behaviour. Sensor as R1 (top): \(V_{out}\) rises when sensor resistance falls (e.g. hotter, brighter). Sensor as R2 (bottom): \(V_{out}\) falls when sensor resistance falls. Getting this wrong produces the opposite output to what is wanted.
Other Sensing Types
The same voltage-divider principle applies to all resistive sensors in the specification:
- Pressure sensor (force-sensitive resistor): resistance decreases under applied force. Used in electronic door mats and scales.
- Moisture sensor: two copper tracks on a PCB; resistance falls when water bridges the gap between them. Used in plant-watering monitors.
- Sound sensor (electret microphone + amplifier): produces a small AC voltage proportional to sound level. The signal is amplified before being fed into a comparator.
- Potentiometer (variable resistor): a manually-adjusted voltage divider. The wiper provides a continuously variable \(V_{out}\) between 0 V and \(V_{in}\).
Pulse Generator as an Input Sub-System
A pulse generator produces a regular square wave. It is used as a timing input — for example, providing the clock pulses that advance a counter. The output of the pulse generator feeds the clock input of a processing circuit; it is never placed in the sensor position of a voltage divider.
Pull-up and pull-down resistors are used with switches and other two-state inputs to ensure the logic level is well-defined when the switch is open. A pull-up resistor (connected between the input pin and the positive supply) holds the logic level HIGH when the switch is open; the switch itself pulls it LOW when closed. A pull-down resistor does the reverse.
Sizing the LED Current-Limiting Resistor
When an LED is included in a sensing circuit output, a series resistor limits the current to a safe value. The LED has a typical forward voltage (given in the exam data: approximately 2 V for a red LED, 3 V for blue or white). The resistor takes the remaining voltage:
$$R = \frac{V_{supply} - V_{LED}}{I_{LED}}$$
For a 9 V supply, a 2 V red LED and a target current of 10 mA: \(R = (9 - 2)/0.010 = 700 \text{ }\Omega\). The nearest E24 value above 700 Ω is 750 Ω — always round up to keep current at or below the target.
Problem: A 9 V supply, a 10 kΩ fixed resistor (R1, top) and an LDR (R2, bottom). In daylight, the LDR resistance is 1 kΩ. Calculate \(V_{out}\).
\(V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2} = 9 \times \frac{1000}{10000 + 1000} = 9 \times \frac{1000}{11000} = 9 \times 0.0909 = 0.82 \text{ V}\)
This LOW output voltage would not trigger a HIGH logic level. If the circuit is supposed to activate in daylight, the positions of R1 and R2 should be swapped.
The most common mistake in sensing circuit questions is drawing the resistor and sensor in the wrong order. A question might ask for a circuit that triggers when it is warm. If you place the thermistor as R1 (top) and the fixed resistor as R2 (bottom), \(V_{out}\) rises when the thermistor gets hot — that’s correct. If you accidentally swap them, \(V_{out}\) falls when it gets hot, which is the opposite of what is required.
Always write a one-line logic check before drawing: “Hot ⇒ thermistor resistance falls ⇒ if thermistor is R1, \(V_{out}\) rises ⇒ correct for triggering on warmth.” This takes five seconds and prevents the most common error in sensing circuit questions.