Potential Dividers

A potential divider is one of the most useful and commonly tested circuits at A-Level. It allows you to obtain any output voltage between zero and the supply voltage by choosing appropriate resistor values.

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How a Potential Divider Works

A potential divider consists of two (or more) resistors connected in series across a voltage supply. The output voltage is taken from the point between the resistors.

Consider two resistors, R₁ and R₂, connected in series across a supply voltage V_in. The output voltage V_out is taken across R₂.

Since the same current flows through both resistors (series circuit):

I = V_in / (R₁ + R₂)

The voltage across R₂ is:

V_out = V_in × R₂ / (R₁ + R₂)

This is the potential divider equation. Notice that the output voltage is simply the fraction R₂/(R₁ + R₂) of the input voltage.

Equivalently, the ratio of the two output voltages is:

V₁ / V₂ = R₁ / R₂

The voltage divides in the same ratio as the resistances.

Worked Example 1

A 12 V supply is connected across two resistors: R₁ = 4.0 kΩ and R₂ = 8.0 kΩ. Calculate the output voltage across R₂.