Comparisons
electricalComparison

Series vs Parallel

Series vs parallel circuits: voltage distribution, current flow, resistance calculations, power sharing, and practical applications in electrical systems.

Enginist Team
Published: December 3, 2025
Updated: December 4, 2025

Table of Contents

Series vs Parallel Circuits: Complete Comparison Guide

Quick AnswerWhat is the difference between series and parallel circuits?
Series circuits have one current path—same current through all components, voltage divides. Parallel circuits have multiple paths—same voltage across all components, current divides. Series resistance adds directly; parallel resistance combines as reciprocals. Parallel provides redundancy; series fails if one component opens.

Quick Verdict

The series vs parallel distinction is the most fundamental concept in circuit analysis. Understanding how voltage, current, and resistance behave in each configuration is essential for all electrical work.

Bottom Line: Use series for voltage division, current limiting, and sequential control. Use parallel for voltage consistency, redundancy, and independent operation. Most practical circuits combine both configurations strategically.

At-a-Glance Comparison Table

FeatureSeriesParallelWinner
Current FlowSame through allDivides among paths—
VoltageDivides among componentsSame across all—
ResistanceRtotal=R1+R2R_{total} = R_1 + R_21Rtotal=1R1+1R2\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}—
Failure ModeTotal circuit failsRemaining paths workParallel
Voltage DivisionNaturally dividesNeeds resistorsSeries
RedundancyNoneBuilt-inParallel
Wiring ComplexitySimplerMore connectionsSeries
Home WiringNot usedStandardParallel

Series Circuit Fundamentals

In a series circuit, components connect end-to-end forming a single path for current flow.

Series Circuit Rules

Itotal=I1=I2=I3(same current everywhere)I_{total} = I_1 = I_2 = I_3 \quad \text{(same current everywhere)} Vtotal=V1+V2+V3(voltages add)V_{total} = V_1 + V_2 + V_3 \quad \text{(voltages add)} Rtotal=R1+R2+R3(resistances add)R_{total} = R_1 + R_2 + R_3 \quad \text{(resistances add)}

Series Circuit Characteristics

PropertyBehavior
CurrentIdentical through all components
VoltageProportional to resistance (V = IR)
Total ResistanceAlways greater than largest individual
Component FailureOpens entire circuit
Power DistributionP ∝ R (higher R = more power)

Voltage Divider Formula

For resistors in series:

V1=Vtotal×R1R1+R2V_1 = V_{total} \times \frac{R_1}{R_1 + R_2}

Example: 12V supply with 4kΩ and 8kΩ in series.

  • V4kΩ=12V×4kΩ4kΩ+8kΩ=12V×13=4VV_{4kΩ} = 12V \times \frac{4kΩ}{4kΩ + 8kΩ} = 12V \times \frac{1}{3} = 4V
  • V8kΩ=12V×8kΩ12kΩ=8VV_{8kΩ} = 12V \times \frac{8kΩ}{12kΩ} = 8V
  • Check: 4V + 8V = 12V ✔

Parallel Circuit Fundamentals

In a parallel circuit, components connect across the same two points, providing multiple current paths.

Parallel Circuit Rules

Vtotal=V1=V2=V3(same voltage everywhere)V_{total} = V_1 = V_2 = V_3 \quad \text{(same voltage everywhere)} Itotal=I1+I2+I3(currents add)I_{total} = I_1 + I_2 + I_3 \quad \text{(currents add)} 1Rtotal=1R1+1R2+1R3(reciprocal sum)\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \quad \text{(reciprocal sum)}

Parallel Circuit Characteristics

PropertyBehavior
VoltageIdentical across all components
CurrentInversely proportional to resistance
Total ResistanceAlways less than smallest individual
Component FailureOther paths continue working
Power DistributionP ∝ 1/R (lower R = more power)

Two-Resistor Shortcut

For exactly two resistors in parallel:

Rtotal=R1×R2R1+R2R_{total} = \frac{R_1 \times R_2}{R_1 + R_2}

Example: 10Ω and 15Ω in parallel.

Rtotal=10×1510+15=15025=6ΩR_{total} = \frac{10 \times 15}{10 + 15} = \frac{150}{25} = 6Ω

Note: Result (6Ω) is less than smaller resistor (10Ω).

Equal Resistors Shortcut

For n equal resistors in parallel:

Rtotal=RnR_{total} = \frac{R}{n}

Example: Four 100Ω resistors in parallel.

Rtotal=100Ω4=25ΩR_{total} = \frac{100Ω}{4} = 25Ω

Current and Voltage Distribution

Series: Voltage Divides by Resistance

ComponentResistanceVoltage Drop
R1100ΩV1=I×100ΩV_1 = I \times 100Ω
R2200ΩV2=I×200ΩV_2 = I \times 200Ω (2× R1)
R3300ΩV3=I×300ΩV_3 = I \times 300Ω (3× R1)

Higher resistance = larger voltage drop (same current through all).

Parallel: Current Divides Inversely

BranchResistanceCurrent
R1100ΩI1=V/100ΩI_1 = V/100Ω
R2200ΩI2=V/200ΩI_2 = V/200Ω (half of I1)
R3300ΩI3=V/300ΩI_3 = V/300Ω (third of I1)

Lower resistance = more current (same voltage across all).

Current Divider Formula

For two resistors in parallel:

I1=Itotal×R2R1+R2I_1 = I_{total} \times \frac{R_2}{R_1 + R_2}

Note: Uses the other resistor in numerator (inverse relationship).

Power Distribution

Series Circuit Power

Since current is the same:

P=I2RP = I^2 R

Higher resistance dissipates more power.

Example: 1A through 10Ω and 20Ω in series.

  • P10Ω=12×10=10WP_{10Ω} = 1^2 \times 10 = 10W
  • P20Ω=12×20=20WP_{20Ω} = 1^2 \times 20 = 20W
  • Ptotal=30WP_{total} = 30W

Parallel Circuit Power

Since voltage is the same:

P=V2RP = \frac{V^2}{R}

Lower resistance dissipates more power.

Example: 12V across 4Ω and 6Ω in parallel.

  • P4Ω=122/4=36WP_{4Ω} = 12^2/4 = 36W
  • P6Ω=122/6=24WP_{6Ω} = 12^2/6 = 24W
  • Ptotal=60WP_{total} = 60W

Practical Applications

When to Use Series

ApplicationReason
LED current limitingSeries resistor limits current
Voltage divisionCreate reference voltages
Battery voltage increase2× 12V cells = 24V
Christmas lights (old)One bulb fails = all fail
Fuses/breakersMust be in series to protect

When to Use Parallel

ApplicationReason
Home wiringEach outlet gets full voltage
Battery capacity increase2× 100Ah = 200Ah
LED arraysIndependent brightness
Computer power railsRedundant supplies
Speaker systemsMaintain impedance

Battery Configurations

Batteries in Series

Vtotal=V1+V2+V3V_{total} = V_1 + V_2 + V_3 Capacitytotal=CapacitysingleCapacity_{total} = Capacity_{single}
ConfigurationVoltageCapacity
Single 12V 100Ah12V100Ah
2S (series)24V100Ah
3S (series)36V100Ah

Use case: Higher voltage for motors, inverters.

Batteries in Parallel

Vtotal=VsingleV_{total} = V_{single} Capacitytotal=C1+C2+C3Capacity_{total} = C_1 + C_2 + C_3
ConfigurationVoltageCapacity
Single 12V 100Ah12V100Ah
2P (parallel)12V200Ah
3P (parallel)12V300Ah

Use case: Longer runtime, higher current capability.

Series-Parallel Combinations

2S2P Example: Four 12V 100Ah batteries

  • 2 in series → 24V, 100Ah
  • 2 series strings in parallel → 24V, 200Ah

Capacitors: Opposite Rules

Capacitors in Parallel (Add)

Ctotal=C1+C2+C3C_{total} = C_1 + C_2 + C_3

Like resistors in series—they add directly.

Capacitors in Series (Reciprocal)

1Ctotal=1C1+1C2+1C3\frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}

Like resistors in parallel—reciprocal sum.

Configuration10µF + 20µF Result
Parallel30µF
Series6.67µF

Inductors: Same as Resistors

Inductors follow the same rules as resistors:

ConfigurationFormula
SeriesLtotal=L1+L2L_{total} = L_1 + L_2
Parallel1Ltotal=1L1+1L2\frac{1}{L_{total}} = \frac{1}{L_1} + \frac{1}{L_2}

Analyzing Mixed Circuits

Step-by-Step Method

  1. Identify pure series and parallel sections
  2. Simplify parallel groups to single equivalent
  3. Combine series elements
  4. Repeat until single equivalent remains
  5. Calculate total current from source
  6. Work backward to find individual values

Example: R1=10Ω in series with (R2=20Ω parallel R3=30Ω)

Step 1: Parallel combination R2∣∣3=20×3020+30=12ΩR_{2||3} = \frac{20 \times 30}{20 + 30} = 12Ω

Step 2: Series combination Rtotal=10+12=22ΩR_{total} = 10 + 12 = 22Ω

Step 3: With 22V supply I=22V/22Ω=1AI = 22V / 22Ω = 1A

Step 4: Voltage across R1 V1=1A×10Ω=10VV_1 = 1A \times 10Ω = 10V

Step 5: Voltage across parallel section V2∣∣3=22V−10V=12VV_{2||3} = 22V - 10V = 12V

Step 6: Individual currents I2=12V/20Ω=0.6AI_2 = 12V / 20Ω = 0.6A I3=12V/30Ω=0.4AI_3 = 12V / 30Ω = 0.4A Check: 0.6A + 0.4A = 1A ✔

Failure Modes

Series Circuit Failure

EventResult
Open circuitEntire circuit dead
Short circuitBypasses that component
DiagnosisEasy (circuit works or doesn't)

Parallel Circuit Failure

EventResult
Open branchOther branches continue
Short circuitTotal circuit shorts
DiagnosisHarder (partial function)

Related Tools

Key Takeaways

  • Series: Same current, voltage divides, resistances add
  • Parallel: Same voltage, current divides, resistances combine reciprocally
  • Total series R always exceeds any individual R
  • Total parallel R always less than smallest individual R
  • Capacitors follow opposite rules (parallel adds, series reciprocal)
  • Most circuits combine both for optimal design

Further Reading

References & Standards

  • IEC 60038: Standard voltages
  • IEEE 315: Graphic symbols for electrical diagrams
  • NEC Article 210: Branch circuits
  • Kirchhoff's Laws: Current and voltage conservation

Frequently Asked Questions