Potential Dividers

A potential divider is a simple circuit that allows you to obtain a specific voltage from a larger voltage source. It is constructed using two resistors connected in series.

Circuit Diagram

The Potential Divider Equation

The voltage across each resistor in a potential divider is proportional to its resistance. The equation for the voltage across the first resistor (V₁) and the second resistor (V₂) is:

$ \frac{V_1}{R_1} = \frac{V_2}{R_2} $

Where:

• $V_1$ is the voltage across resistor R₁
• $R_1$ is the resistance of resistor R₁
• $V_2$ is the voltage across resistor R₂
• $R_2$ is the resistance of resistor R₂

This equation can be rearranged to find the voltage across either resistor:

$ V_1 = \frac{V_{total} \times R_1}{R_1 + R_2} $

$ V_2 = \frac{V_{total} \times R_2}{R_1 + R_2} $

$ V_{total}$ is the total voltage of the source.

How it Works

When current flows through the series circuit, the voltage source provides a potential difference across the entire series combination of the two resistors. Because the resistors are in series, the same current flows through both. The voltage drop across each resistor is proportional to its resistance. Therefore, the voltage at the junction between the resistors (V₁) is a fraction of the total voltage, determined by the ratio of the resistors.

Example Calculation

Consider a potential divider with a 12V source, R₁ = 100Ω, and R₂ = 200Ω. Calculate the voltage across R₁ (V₁).

Quantity	Value
$V_{total}$	12V
$R_1$	100Ω
$R_2$	200Ω
$V_1 = \frac{V_{total} \times R_1}{R_1 + R_2}$	$V_1 = \frac{12 \times 100}{100 + 200} = \frac{1200}{300} = 4V$

Therefore, the voltage across R₁ is 4V.

Applications

Potential dividers are used in a variety of applications, including:

• Voltage sensing in electronic circuits
• Creating adjustable voltage references
• Signal attenuation (reducing the amplitude of a signal)
• Creating voltage scales in meters and other measuring instruments