Voltage Dividers

Part of Electrical Theory

Using resistor networks to produce specific voltages from a higher supply — design, calculation, loading effects, and practical applications.

Why This Matters

Voltage dividers are among the most frequently used circuits in electronics. They appear everywhere: setting reference voltages, creating bias points for amplifiers, scaling sensor signals for measurement, providing feedback in regulators. They’re simple to build and require nothing more than resistors.

In rebuilding contexts, voltage dividers help you interface different pieces of salvaged equipment, build simple voltage meters, create adjustable voltage references for battery charging circuits, and provide the bias points needed for transistor amplifier stages. The key is understanding not just the ideal divider formula, but also the critical concept of loading — how connecting a device to a divider changes its output.

The Basic Voltage Divider

Two resistors in series from supply to ground, with the output taken from the junction between them:

V_in ---[R1]---+---[R2]--- GND
               |
             V_out

Divider equation: V_out = V_in × R2 / (R1 + R2)

The output voltage is the supply times the fraction of total resistance that R2 represents.

Examples:

V_in	R1	R2	V_out
12V	1kΩ	1kΩ	6V
12V	3kΩ	1kΩ	3V
12V	2kΩ	10kΩ	10V
5V	1kΩ	4kΩ	4V

Design procedure:

1. Choose V_out / V_in ratio = R2 / (R1 + R2)
2. Choose a total resistance R1+R2 (see loading section for guidance)
3. R2 = (V_out/V_in) × (R1+R2)
4. R1 = (R1+R2) - R2

Example: Produce 5V from 12V supply.

• Ratio = 5/12 = 0.417
• Choose total R = 10kΩ
• R2 = 0.417 × 10,000 = 4,170Ω → use 4.7kΩ
• R1 = 10,000 - 4,170 = 5,830Ω → use 5.6kΩ
• Actual V_out = 12 × 4700/(4700+5600) = 12 × 0.456 = 5.47V

Not exactly 5V due to choosing standard values — adjust R2 up or R1 down to fine-tune, or add a trimmer potentiometer for precise adjustment.

Loading Effect: The Critical Concept

An ideal voltage divider produces exactly V_in × R2/(R1+R2). A real voltage divider feeds a load — and the load changes the output voltage.

Why: When you connect a load resistor R_L to the output, R_L is in parallel with R2. This parallel combination is less than R2, so the divider ratio changes — V_out drops.

Loaded divider equation: R2_eff = R2 × R_L / (R2 + R_L) V_out_loaded = V_in × R2_eff / (R1 + R2_eff)

Example: Divider with R1=5kΩ, R2=5kΩ from 12V supply. Unloaded: V_out = 12 × 5/10 = 6.0V

Load R_L = 10kΩ connected: R2_eff = 5000×10000/(5000+10000) = 3,333Ω V_out = 12 × 3333/(5000+3333) = 12 × 0.4 = 4.8V

The load drew V_out down from 6.0V to 4.8V — a 20% change.

Rule of thumb for acceptable loading: R_L should be at least 10× R2 for less than 10% voltage change. At R_L = 10×R2 = 50kΩ: R2_eff = 5000×50000/55000 = 4545Ω V_out = 12 × 4545/9545 = 5.71V (5% drop from 6V — acceptable for most purposes)

Consequence for design: Choose low-value resistors (stiff divider) when the load may be heavy or variable. Use high-value resistors only when load is known and light.

Adjustable Voltage Dividers: Potentiometers

A potentiometer (pot) is a continuously adjustable voltage divider — a resistive track with a sliding contact (wiper) that taps off any fraction of the voltage across it.

Types:

• Rotary pot: Wiper moves in a circular arc; 270° of adjustment range typical
• Slide pot: Wiper moves linearly along a track
• Trimmer pot: Small, for single adjustment; not meant for repeated use

Connecting as a divider:

• Top terminal to V_in
• Bottom terminal to GND
• Wiper = V_out
• Rotating fully clockwise: V_out = V_in
• Rotating fully counterclockwise: V_out = 0V
• Middle position: V_out = V_in/2

Loading still applies: The pot’s total resistance acts as R1+R2. The wiper’s position determines R2/total ratio, but connecting a low-impedance load still causes output voltage shift.

Building a rudimentary potentiometer (improvised):

• Resistance wire (nichrome or steel) stretched taut
• Sliding contact: a piece of copper or brass pressing against the wire
• Scale marks along the wire
• Total resistance = wire resistivity × length / cross-section
• Adjust by sliding contact along wire

Voltage Reference Divider for Battery Monitoring

A practical application — monitoring battery voltage with a lower-voltage meter:

Problem: 24V battery bank, voltmeter reads only 0–15V. Need to scale 24V range down to 15V range.

Scaling factor: 15/24 = 0.625 R2/(R1+R2) = 0.625

If voltmeter input resistance R_meter = 10kΩ: For 10% loading effect maximum: R2 ≤ R_meter/10 = 1kΩ Choose R2 = 1kΩ, then R1 = (1/0.625 - 1) × R2 = 0.6 × 1000 = 600Ω → use 620Ω

At 24V battery: V_meter = 24 × 1000/1620 = 14.8V ≈ full scale ✓

When battery is at 20V: V_meter = 20 × 1000/1620 = 12.3V — readable on scale.

Calibration: After building, apply a known voltage (measured independently) and mark the meter scale accordingly.

Wheatstone Bridge: Two Dividers in Comparison

A Wheatstone bridge consists of two voltage dividers sharing the same supply, with a meter between their mid-points:

     V_in
      |
  +---+---+
 [R1]   [R3]
  +---G---+
 [R2]   [R4]
  +---+---+
     GND

When R1/R2 = R3/R4, both dividers produce the same V_out — galvanometer G reads zero (balanced bridge).

If one resistor changes (e.g., R4 becomes R4+δR due to temperature, strain, or chemical change), the bridge unbalances, and G shows a deflection proportional to the change.

Applications:

• Measuring unknown resistance: replace R4 with unknown; adjust R3 (variable resistor) until balanced; then R4 = R3 × R2/R1
• Strain gauge sensors, thermistor temperature sensors — small resistance changes precisely detected
• Any precision resistance measurement

Sensitivity advantage: The bridge can detect tiny resistance changes that would be undetectable with direct measurement, because you’re measuring the difference between two nearly equal values.

Resistive Sensor Dividers

Many sensors change resistance with physical quantities (temperature, light, humidity, strain). Combining a sensor in a divider converts resistance changes to voltage changes for measurement:

Thermistor temperature sensing:

• Thermistor resistance decreases with temperature (NTC type)
• Connect thermistor as R2 (bottom of divider), fixed resistor as R1 (top)
• As temperature rises, R2 decreases, V_out decreases
• Calibrate: measure V_out at known temperatures, plot calibration curve

LDR (light-dependent resistor) as light sensor:

• LDR resistance decreases in bright light
• Connect LDR as R1 (top), fixed resistor as R2
• In bright light: LDR resistance low → V_out high
• In darkness: LDR resistance high → V_out low
• Threshold: choose R2 = LDR resistance at the desired switching light level

Voltage dividers are the connective tissue of electronics — simple, reliable, calculable, and ubiquitous. Mastering their design and loading behavior gives you a powerful tool that appears in virtually every practical circuit you’ll build or repair.