Introduction to Potential Dividers

Welcome! In this chapter, we are looking at one of the most useful "building blocks" in electronics: the Potential Divider. Whether you are adjusting the volume on a radio or using a sensor to turn on streetlights at night, you are likely using a potential divider circuit. The name says it all: it is a circuit designed to divide the potential (voltage) from a power source into smaller, specific amounts.

What is a Potential Divider?

A potential divider is a simple circuit consisting of two or more resistors connected in series across a voltage supply. In a series circuit, the total supply voltage (\(V_{in}\)) is shared between the components. The amount of voltage each resistor gets depends on its resistance. The bigger the resistance, the bigger its share of the voltage. Key Takeaway: Potential dividers allow us to get a specific output voltage (\(V_{out}\)) that is just a fraction of the total supply voltage (\(V_{in}\)).

The Potential Divider Formula

To calculate the output voltage across a specific resistor (let’s call it \(R_2\)), we use a standard formula. Imagine two resistors, \(R_1\) and \(R_2\), connected in series with an input voltage \(V_{in}\). We take our output voltage \(V_{out}\) across \(R_2\).

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

Why does this work?

Don't worry if the formula looks intimidating; it's just Ohm's Law in disguise!
1. The total resistance of the circuit is \(R_{total} = R_1 + R_2\).
2. The current in the circuit is \(I = \frac{V_{in}}{R_1 + R_2}\).
3. The voltage across \(R_2\) (which is \(V_{out}\)) is \(V = I \times R_2\).
4. Substitute the current from step 2 into step 3, and you get the formula!

The Ratio Method

If you prefer a simpler way to think about it, remember that the ratio of voltages is the same as the ratio of resistances:

\(\frac{V_1}{V_2} = \frac{R_1}{R_2}\)

Example: If \(R_2\) has twice the resistance of \(R_1\), it will receive twice the voltage.

Using Variable Components

Potential dividers become really powerful when we replace a fixed resistor with a variable resistor, a thermistor, or a Light Dependent Resistor (LDR). This allows the output voltage to change automatically based on the environment.

1. Using a Variable Resistor (Potentiometer)

By manually changing the resistance of a variable resistor in a potential divider, you can move \(V_{out}\) anywhere from \(0\) up to the full \(V_{in}\). This is how manual volume controls or dimmer switches work.

2. Temperature Sensors (NTC Thermistors)

In the AQA syllabus, we focus on Negative Temperature Coefficient (NTC) thermistors.
- Temperature Increases \(\implies\) Resistance of thermistor Decreases.
- Temperature Decreases \(\implies\) Resistance of thermistor Increases. If you place a thermistor in the \(R_2\) position (where \(V_{out}\) is measured):
- When it gets colder, the thermistor's resistance increases, so it takes a larger share of the voltage. \(V_{out}\) rises. This could be used to turn on a heater!

3. Light Sensors (LDRs)

An LDR works similarly but responds to light intensity:
- Light Intensity Increases \(\implies\) Resistance of LDR Decreases.
- Light Intensity Decreases \(\implies\) Resistance of LDR Increases. Did you know? To make a sensor that turns a light on when it gets dark, you would place the LDR in the \(R_2\) position. As it gets darker, the LDR's resistance goes up, and the \(V_{out}\) across it increases until it is high enough to trigger a switch.

Summary of Sensor Behavior

If the sensor (LDR or Thermistor) is \(R_2\) (where we measure \(V_{out}\)):
  • Resistance of sensor increases \(\implies\) \(V_{out}\) increases.
  • Resistance of sensor decreases \(\implies\) \(V_{out}\) decreases.
If the sensor is \(R_1\) (the "other" resistor):
  • Resistance of sensor increases \(\implies\) \(V_{out}\) decreases (because \(R_1\) is "stealing" more of the voltage).
  • Resistance of sensor decreases \(\implies\) \(V_{out}\) increases.

Common Mistakes to Avoid

  • Mixing up \(R_1\) and \(R_2\): Always make sure the resistor you want the voltage for is the one on the top of the fraction in the formula.
  • Ignoring Units: Ensure all resistances are in the same units (e.g., all in \(\Omega\) or all in \(k\Omega\)) before plugging them into the formula.
  • Internal Resistance: Remember that in real-world applications, the supply might have internal resistance (covered in the Emf and Internal Resistance chapter), which would reduce the total \(V_{in}\) available to the divider.

Quick Review

Q: What happens to \(V_{out}\) across an LDR if the room gets brighter?
A: Brightness increases \(\implies\) LDR resistance decreases \(\implies\) LDR takes a smaller share of the voltage \(\implies\) \(V_{out}\) decreases. Key Takeaway: The potential divider is all about ratios. The voltage is distributed according to how much resistance a component has compared to the total resistance of the loop.