By Kim Lewis
Updated Mar 24, 2022

Resistors are not only current limiters; they also serve as voltage reducers in many circuits. When arranged in series, they form a voltage divider, breaking an input voltage into proportional outputs that match the resistors’ values.

How Voltage Dividers Work

A resistor obeys Ohm’s Law, V = I R, where V is voltage, I is current, and R is resistance. In a series connection, the same current flows through each resistor, but the voltage drops across each component are proportional to its resistance. This property lets us tailor the output voltage for a downstream stage.

The Voltage Divider Formula

For two resistors in series (R1 and R2) connected to an input voltage V_in, the total resistance is R_total = R1 + R2. The current is I = V_in / R_total. The output voltage across R2 is therefore:

V_out = V_in · R2 / (R1 + R2)

Example 1: Practical Calculation

Given a 1.5 V battery and resistors R1 = 10 Ω, R2 = 100 Ω, the output voltage is:

V_out = 1.5 V × 100 Ω / (10 Ω + 100 Ω) ≈ 1.30 V.

Verify this by building the circuit and measuring with a multimeter.

Example 2: Targeting a Specific Output

With a 9 V supply and a desired 6 V output, choose R1 = 330 Ω. Solve for R2:

R2 = (V_out / (V_in – V_out)) × R1 ≈ 825 Ω.

If a precise 825 Ω resistor isn’t available, use a value within 10–20 % tolerance or combine standard values.

Practical Tips

• Use an online resistance calculator to determine resistor values quickly.

• When experimenting, wire multiple resistors in series and measure the voltage drop across each to confirm the theory.

• Remember that voltage dividers should be used where the load impedance is much higher than the divider resistors; otherwise, the output voltage will shift.