Introduction: Taking Control of Voltage

In our study of circuits so far, we’ve looked at how batteries provide energy and how resistors limit current. But what if you have a 9V battery and you only want to power a tiny 2V LED? Or what if you want a circuit that automatically turns on a fan when it gets too hot?

This is where potential dividers come in. They are simple but brilliant circuits that allow us to "tap off" a specific fraction of the total voltage. By using components like thermistors and LDRs, we can even make these circuits respond to the world around them. Let's dive in!

1. What is a Potential Divider?

At its simplest, a potential divider is just two or more resistors connected in series across a voltage source (like a battery). Because they are in series, they share the total potential difference (p.d.) provided by the source.

The Golden Rule: In a series circuit, the component with the largest resistance takes the largest share of the voltage.

Imagine two resistors, \(R_1\) and \(R_2\), connected to an input voltage \(V_{in}\). If we measure the voltage across just one of them (\(R_2\)), we call that our output voltage, \(V_{out}\).

The Potential Divider Equation

You don't need to memorize this if you understand ratios, but it’s very helpful for the exam:

\(V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2}\)

Why does this work?
Since the resistors are in series, the same current \(I\) flows through both.
1. The total resistance is \(R_{total} = R_1 + R_2\).
2. The current is \(I = \frac{V_{in}}{R_1 + R_2}\).
3. The voltage across \(R_2\) is \(V_{out} = I \times R_2\).
Substituting the current into the third equation gives us the formula above!

Quick Tip: If \(R_1 = R_2\), the voltage is split exactly in half. If \(R_2\) is much, much bigger than \(R_1\), then \(V_{out}\) will be almost equal to \(V_{in}\).

2. Potentiometers: The Sliding Potential Divider

Sometimes we want to change the output voltage manually—like turning the volume up on a radio. For this, we use a potentiometer.

A potentiometer is a single long strip of resistive material with a sliding contact (called a "wiper"). As you move the wiper along the wire:

  • The length of the wire on either side of the wiper changes.
  • Since resistance is proportional to length (\(R \propto l\)), the ratio of resistances changes.
  • This allows you to vary \(V_{out}\) smoothly from \(0\text{V}\) all the way up to \(V_{in}\).

Key Takeaway: For a uniform current-carrying wire, the potential varies linearly with the length of the wire. If you are halfway along the wire, you have "tapped off" half the total potential.

3. Sensory Resistors: LDRs and Thermistors

To make a circuit "smart," we replace one of the fixed resistors with a component that changes its resistance based on the environment.

A. Light Dependent Resistors (LDRs)

An LDR is a component whose resistance changes depending on the illumination (light intensity) hitting it.

  • In the dark: Resistance is very high (millions of ohms).
  • In the light: Resistance is very low (hundreds of ohms).

Memory Trick: "LURD" — Light Up, Resistance Down.

B. Thermistors (NTC)

In this syllabus, we focus on Negative Temperature Coefficient (NTC) thermistors.

  • When cold: Resistance is high.
  • When hot: Resistance is low.

Memory Trick: "TURD" — Temperature Up, Resistance Down.

Why does the resistance change?

This is a favorite exam question! You need to know the difference between metals and these semiconductors:

  • In Metals: When they get hotter, the metal ions vibrate more (lattice vibrations). This makes it harder for electrons to flow, so resistance increases.
  • In NTC Thermistors/LDRs: These are semiconductors. When you add energy (heat or light), it frees up more conduction electrons (charge carriers). Even though the lattice vibrates more, the huge increase in the number of charge carriers (\(n\) in the equation \(I = nqvA\)) wins, and the resistance decreases.

4. Designing Sensor Circuits

By putting an LDR or a Thermistor into a potential divider, we can create a circuit that gives a voltage signal when conditions change.

Example: A Heat-Sensing Fan

Imagine a circuit where \(V_{in} = 6\text{V}\). We have a fixed resistor \(R_1\) on top and an NTC thermistor \(R_2\) on the bottom. We connect a fan across \(R_2\).

  1. The temperature rises.
  2. The resistance of the thermistor (\(R_2\)) decreases.
  3. Because \(R_2\) is now a smaller share of the total resistance, it takes a smaller share of the voltage.
  4. \(V_{out}\) drops, and the fan slows down.

Wait! What if we want the fan to turn ON when it's hot?
Simple! We swap the components. If we put the thermistor at the top (\(R_1\)) and the fixed resistor at the bottom (\(R_2\)):

  1. Temperature rises \(\implies\) Thermistor resistance (\(R_1\)) drops.
  2. The fixed resistor (\(R_2\)) now represents a larger share of the total resistance.
  3. \(V_{out}\) (across \(R_2\)) increases.
  4. The fan turns on!

Don't worry if this seems tricky at first! Just remember: whoever has the highest resistance gets the most "attention" (voltage). If the sensor's resistance goes down, the other resistor gets more voltage.

Quick Review: Common Mistakes to Avoid

  • Mixing up the share: Always check which resistor \(V_{out}\) is measured across. Is it the variable one or the fixed one?
  • Units: Ensure your resistances are both in \(\Omega\) or both in \(k\Omega\) before using the ratio formula.
  • NTC vs Metals: Remember that for NTC thermistors, temperature and resistance move in opposite directions. For metals, they move in the same direction.
  • Significant Figures: In Unit 2 and Unit 3 papers, always provide your final answer to a consistent number of significant figures (usually 2 or 3, matching the data given in the question).

Key Takeaways Summary

1. Potential Divider: A way to split voltage using resistors in series.

2. The Equation: \(V_{out} = V_{in} \times \frac{R_{target}}{R_{total}}\).

3. LDRs: Light intensity up \(\implies\) Resistance down.

4. Thermistors (NTC): Temperature up \(\implies\) Resistance down (due to more charge carriers being released).

5. Uniform Wires: Potential drops steadily along the length of a wire, acting as a continuous divider.