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lesson · 10min · Lesson 14 of 37

Voltage dividers and current dividers

Course syllabusCourse overview
01Atoms, Electrons & Electric Charge
  1. ReadWhat is electricity?: atomic model
  2. ReadElectric charge and the coulomb
  3. ReadConductors, insulators, and semiconductors
  4. ReadConventional current vs electron flow
  5. quizModule quiz
02Voltage, Current & Resistance
  1. ReadPotential difference: the driving force
  2. ReadCurrent: the rate of charge flow
  3. ReadResistance and resistivity
  4. ReadOhm's Law: derivation and examples
  5. exerciseWorked examples: Ohm's Law problems
03Series & Parallel Circuits
  1. ReadSeries circuits: characteristics and rules
  2. ReadParallel circuits: characteristics and rules
  3. ReadCombined series-parallel networks
  4. ReadVoltage dividers and current dividers
  5. exerciseCircuit analysis practice
04Kirchhoff's Laws
  1. ReadKCL: Kirchhoff's Current Law
  2. ReadKVL: Kirchhoff's Voltage Law
  3. ReadMesh and nodal analysis
  4. exerciseKirchhoff's law problems set
05Power & Energy
  1. ReadElectrical power: watts and horsepower
  2. ReadEnergy: kilowatt-hours and joules
  3. ReadEfficiency and power loss in cables
  4. quizPower quiz
06Alternating Current Fundamentals
  1. ReadAC vs DC: why AC won
  2. ReadSinusoidal waveforms: peak, RMS, average
  3. ReadFrequency and period
  4. ReadPhase relationships
  5. ReadAC circuit analysis introduction
07Capacitors & Inductors
  1. ReadCapacitor construction and capacitance
  2. ReadCapacitors in AC circuits: reactance
  3. ReadInductor construction and inductance
  4. ReadInductors in AC circuits: reactance
  5. ReadRC and RL circuits: time constants
08Measurement & Instruments
  1. ReadMultimeters: AC/DC voltage and current
  2. ReadClamp meters and measuring live current
  3. ReadOscilloscopes: reading waveforms
  4. quizFinal assessment
Lesson · 10min
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In this lesson

PurposeCore theoryWorked exampleKnowledge checkSources

In this lesson

PurposeCore theoryWorked exampleKnowledge checkSources
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ElectraCore lesson handout

Voltage dividers and current dividers

Electrical Fundamentals · Lesson 14 · Beginner

BeginnerReview: professional review pending

Purpose

Use unloaded voltage dividers and two-branch current dividers while recognising loading limits.

Before you beginSeries and parallel networks · Ratios · Ohm's law

Learning objectives

  • Calculate divider output voltage
  • Calculate two-branch current division
  • Explain loading error
  • Check limiting cases

Divider rules are shortcuts derived from series and parallel laws; they are valid only when their assumptions match the circuit.

DIVIDER RELATIONSHIPSDIVIDER RELATIONSHIPSR₁R₂Vout = Vin·R₂/(R₁+R₂)

Core theory

For two series resistors, the unloaded output across R₂ is Vin R₂/(R₁+R₂). A connected load sits in parallel with R₂ and changes the ratio.

For two parallel resistors, current through R₁ equals total current times R₂/(R₁+R₂); current favours the lower resistance.

Divider networks dissipate power continuously and often need buffering when driving a load.

Terms, symbols, and units
TermMeaningSymbolUnit
Voltage dividerSeries network producing a fraction of input voltageNot applicableNot applicable
Current dividerParallel network splitting total currentNot applicableNot applicable
LoadingOutput change caused by a connected loadNot applicableNot applicable
Vout = Vin·R₂/(R₁+R₂); I₁ = It·R₂/(R₁+R₂)

The current-divider numerator uses the other branch resistance.

V and A
Worked exampleA 10 kΩ/5 kΩ unloaded divider is connected across 15 V; output is across 5 kΩ.

Assumptions: Output load impedance is effectively infinite.

  1. Ratio: R₂/(R₁+R₂) = 5/(10+5) = 1/3.
  2. Output: Vout = 15 × 1/3 = 5 V.
  3. Check: Series current is 1 mA; drops are 10 V and 5 V.

The unloaded output is 5 V.

Reasonableness check: The lower resistor is one-third of total resistance, so it receives one-third of the voltage.

Common mistakes
  • Ignoring load resistance
  • Using the wrong resistor in the numerator
  • Applying current division to series components

Where this appears in practice

Dividers scale sensor signals, establish reference levels, and estimate branch currents, but precision designs account for tolerance and loading.

SafetyA divider is not protective isolation and must not be used to make hazardous mains safe for touch or low-voltage electronics without approved isolation and protection.
Local code checkThe physical relationships are universal. Installation methods, permitted work, test procedures, and equipment ratings must be checked against current local rules and manufacturer instructions.

Knowledge check

What happens when a finite load is added across the lower divider resistor?

Its effective resistance falls and the output voltage usually falls. The load is parallel with the lower resistor.

Answer: Its effective resistance falls and the output voltage usually falls. The load is parallel with the lower resistor.

Practical exercise

Calculate a 9 V divider using 2 kΩ and 1 kΩ, then repeat with a 1 kΩ load across the lower resistor.

Summary

  • Divider rules come from network laws
  • Loading changes voltage division
  • A divider does not provide isolation

Sources and review

  • The International System of Units (SI Brochure): BIPM; 9th edition, updated 2026; International
  • SI Units: Electric Current: NIST; Current web edition; United States / SI reference
  • University Physics Volume 2: OpenStax; Current web edition; Physics reference

Editorial review date: 2026-08-21. Professional electrical review is pending.

Educational material for learning and preliminary checks. Verify current local requirements and exact equipment instructions. This lesson does not replace competent professional work.

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