Introduction to Potential Dividers
Welcome! In this chapter, we are going to look at one of the most useful circuits in electronics: the potential divider. If you’ve ever adjusted the brightness of a screen or used a heater that turns itself off when it gets too warm, you’ve used the principles of a potential divider.
Simply put, a potential divider is a simple circuit that "splits" the total voltage (potential difference) from a power supply between two or more components. By the end of these notes, you will understand how to calculate these voltages and how sensors like LDRs and thermistors make these circuits "smart."
Note: This chapter builds on your knowledge of series circuits and Ohm's Law (\(V = IR\)). If you need a refresher, check out the "Basics of Electricity" chapter!
1. The Basic Potential Divider
A potential divider consists of two or more resistors connected in series across a voltage supply. Because they are in series, the same current (\(I\)) flows through both, but the total voltage (\(V_{in}\)) is shared between them.
How the Voltage is Shared
The rule is simple: The bigger the resistance, the bigger the share of the voltage it takes.
Imagine two resistors, \(R_1\) and \(R_2\), connected to a battery with voltage \(V_{in}\). If we want to find the output voltage (\(V_{out}\)) across \(R_2\), we use the potential divider formula:
\(V_{out} = V_{in} \cdot \frac{R_2}{R_1 + R_2}\)
Breakdown of the formula:
- \(V_{in}\): The total voltage supplied to the circuit.
- \(R_2\): The resistance you are measuring the voltage across.
- \(R_1 + R_2\): The total resistance of the circuit.
- \(V_{out}\): The voltage "output" across resistor \(R_2\).
An Everyday Analogy
Think of the voltage like a giant chocolate bar. If two people (\(R_1\) and \(R_2\)) are sharing it, the person who is "bigger" (has more resistance) gets a larger piece of the chocolate. If the two resistors are equal, they split the voltage exactly in half!
Quick Review:
- If \(R_1 = R_2\), then \(V_{out} = \frac{1}{2} V_{in}\).
- If \(R_2\) becomes much larger than \(R_1\), \(V_{out}\) will get closer and closer to the value of \(V_{in}\).
2. Variable Potential Dividers
Sometimes we don't want a constant voltage; we want one we can change. We can do this by using a variable resistor (sometimes called a rheostat or a potentiometer used as a divider).
By turning a knob or sliding a contact, you change the resistance of one part of the circuit. This changes the ratio of \(R_1\) to \(R_2\), which in turn changes \(V_{out}\). This is exactly how a traditional volume control on a radio works!
3. Using Sensors: LDRs and Thermistors
This is where potential dividers get really clever. We can replace one of the fixed resistors with a component whose resistance changes based on the environment. The AQA syllabus focuses on two main types:
Light Dependent Resistors (LDRs)
The resistance of an LDR changes depending on the light intensity hitting it.
The Rule: As light intensity increases, the resistance of the LDR decreases.
Mnemonic: LURD — Light Up, Resistance Down!
Thermistors (NTC Type)
In this course, we focus on Negative Temperature Coefficient (NTC) thermistors.
The Rule: As the temperature increases, the resistance of the thermistor decreases.
Mnemonic: TURD — Temperature Up, Resistance Down!
Example: A Night-Sensing Light
Imagine a circuit where \(R_1\) is a fixed resistor and \(R_2\) is an LDR. We measure \(V_{out}\) across the LDR (\(R_2\)).
- When it gets dark, the LDR's resistance increases.
- Because its resistance is now a bigger share of the total, it takes a bigger share of the voltage.
- \(V_{out}\) increases. This high voltage can be used to trigger a switch to turn on a streetlamp.
Common Mistake: Students often forget which resistor \(V_{out}\) is measured across. Always look closely at the circuit diagram! If \(V_{out}\) is measured across the component whose resistance is dropping, then \(V_{out}\) will also drop.
4. Why use a Potential Divider instead of a Variable Resistor in series?
You might wonder why we don't just put a single variable resistor in series with a bulb. The advantage of a potential divider is its range. A potential divider allows you to vary the output voltage all the way from 0V to the maximum supply voltage. A simple series resistor can often only dim a bulb slightly, but cannot necessarily bring the voltage all the way down to zero effectively for all applications.
Summary Table for Sensors
Use this table to quickly check how a sensor in the \(R_2\) position (where \(V_{out}\) is measured) affects the circuit:
| Sensor | Condition Change | Resistance Change | \(V_{out}\) (across sensor) |
|---|---|---|---|
| LDR | Brighter Light | Decreases | Decreases |
| LDR | Darker | Increases | Increases |
| NTC Thermistor | Hotter | Decreases | Decreases |
| NTC Thermistor | Colder | Increases | Increases |
Key Takeaways
1. Logic: Voltage is split in the same ratio as the resistances. \(V \propto R\).
2. Equation: \(V_{out} = V_{in} \cdot \frac{R_2}{R_{total}}\).
3. Sensors: Both LDRs and NTC Thermistors have resistance that drops when the "input" (light or heat) increases.
4. Application: These circuits are used to provide variable voltages or to create sensors that respond to the environment.
Quick Tip for the Exam: If a question asks you to "explain" how a light-sensing circuit works, always follow these three steps: 1. State how the resistance of the sensor changes. 2. State how the total resistance of the circuit changes. 3. Explain how the ratio of resistances changes the share of the voltage.