Potential Dividers

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Understand the principle of a potential divider circuit
  2. Recall and use the principle of the potentiometer as a means of comparing potential differences
  3. Understand the use of a galvanometer in null methods
  4. Explain the use of thermistors and light-dependent resistors in potential dividers to provide a potential difference that is dependent on temperature and light intensity

1. The Principle of a Potential Divider Circuit

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What is a Potential Divider?

A potential divider is a circuit that splits (or divides) the voltage from a power source between two or more components. Think of it like sharing a pizza between friends—the total voltage gets divided up among the resistors in the circuit.

When two resistors are connected in series (one after the other), the voltage from the battery is shared between them. The bigger the resistance of a resistor, the bigger the share of voltage it gets.

Why Do We Use Potential Dividers?

Potential dividers have three main purposes:

  1. To provide a variable voltage – You can adjust the output voltage by changing the resistors
  2. To choose a specific voltage – You can select exactly the voltage you need for a component
  3. To split voltage between components – Useful when different parts of a circuit need different voltages

You'll find potential dividers in everyday devices like volume controls on speakers and in sensor circuits that detect light or temperature changes.

The Potential Divider Formula

Here's how the voltage divides between two resistors:

V_out = (R₂ / (R₁ + R₂)) × V_in

Where:

  • V_in = the input voltage (from the battery or power supply)
  • V_out = the output voltage (across the resistor you're interested in)
  • R₁ = resistance of the first resistor
  • R₂ = resistance of the second resistor (the one V_out is measured across)

Important rule: The resistor that you're measuring V_out across always goes in the numerator (top) of the fraction.

How Does It Work?

In a series circuit, the current is the same through all components. Using Ohm's Law (V = IR):

  • The resistor with larger resistance gets a larger share of the voltage
  • The resistor with smaller resistance gets a smaller share of the voltage

The voltage across each resistor is proportional to its resistance. If you double the resistance, you double the voltage across it (assuming the other resistor stays the same).

Worked Example 1: Basic Potential Divider

A potential divider circuit has a 12 V battery connected to two resistors in series: 20 kΩ and 10 kΩ. Calculate the voltage across the 10 kΩ resistor.

Solution:

Step 1: Identify what we know

  • V_in = 12 V
  • R₁ = 20 kΩ (top resistor)
  • R₂ = 10 kΩ (bottom resistor, the one we want V_out across)

Step 2: Use the potential divider formula

V_out = (R₂ / (R₁ + R₂)) × V_in

V_out = (10 / (20 + 10)) × 12

V_out = (10 / 30) × 12

V_out = 4 V

The voltage across the 10 kΩ resistor is 4 V.

Worked Example 2: Finding Input Voltage

A potential divider has two resistors: 12 kΩ and 20 kΩ in series. The voltage across the 20 kΩ resistor is 5.3 V. Calculate the input voltage.

Solution:

Step 1: Identify what we know

  • R₁ = 12 kΩ
  • R₂ = 20 kΩ (the one with V_out across it)
  • V_out = 5.3 V

Step 2: Rearrange the formula to find V_in

V_out = (R₂ / (R₁ + R₂)) × V_in

V_in = V_out × ((R₁ + R₂) / R₂)

V_in = 5.3 × ((12 + 20) / 20)

V_in = 5.3 × (32 / 20)

V_in = 5.3 × 1.6

V_in = 8.5 V

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