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Resistor Network Calculator

Series & parallel resistance calculator

Enter values separated by commas or spaces (up to 10 resistors)

Result
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Formulas

SeriesR = R₁ + R₂ + R₃ + ...
Parallel1/R = 1/R₁ + 1/R₂ + ...
2 ParallelR = (R₁×R₂)/(R₁+R₂)

Quick Tips

Series:
• Current same through all
• Voltage divides
• R_total > any R

Parallel:
• Voltage same across all
• Current divides
• R_total < smallest R

Related

Ohm's LawCurrent DividerVoltage Divider

Understanding Resistor Networks

Resistors can be connected in series, parallel, or combinations of both. Understanding how to calculate equivalent resistance is fundamental to circuit analysis and design.

Series Resistors

In a series circuit, resistors are connected end-to-end, creating a single path for current flow. The total resistance is the sum of all individual resistances. Key characteristics:

  • Current is identical through each resistor
  • Voltage divides proportionally to resistance
  • Total resistance is always greater than any single resistor
  • If one resistor fails open, the entire circuit stops

Parallel Resistors

In a parallel circuit, resistors share the same two connection points. Each resistor provides an additional path for current. Key characteristics:

  • Voltage is identical across each resistor
  • Current divides inversely to resistance
  • Total resistance is always less than the smallest resistor
  • If one resistor fails open, others continue working

Practical Applications

Series: Used in voltage dividers, LED current limiting, and sensor circuits where you need to add resistance.

Parallel: Used when you need lower resistance than available, to increase power handling, or for redundancy in critical circuits.

Frequently Asked Questions

For series resistors, simply add all values: R_total = R1 + R2 + R3 + ... For example, 100Ω + 220Ω + 470Ω = 790Ω. The total is always greater than any individual resistor because current must flow through each one sequentially.

For parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3... For two resistors, use: R_total = (R1 × R2) / (R1 + R2). Example: 100Ω and 200Ω in parallel = (100 × 200) / (100 + 200) = 66.67Ω. Result is always less than the smallest resistor.

Each parallel resistor provides an additional path for current. More paths = less total opposition to current flow. Think of it like adding lanes to a highway - traffic (current) flows more easily even though each lane (resistor) has the same capacity.

Series: Current is the same through all resistors (only one path). Voltage divides proportionally. Parallel: Voltage is the same across all resistors. Current divides - more current flows through lower resistance paths (I = V/R).

For n equal resistors in parallel: R_total = R / n. Two 100Ω resistors in parallel = 100/2 = 50Ω. Three 100Ω in parallel = 100/3 = 33.3Ω. This is a quick shortcut when all resistors have the same value.

Use series when: You need more resistance, want to divide voltage, or limit current (like LED circuits). Use parallel when: You need less resistance than available, want to increase power handling capacity, or need redundancy if one resistor fails.

Series: Higher resistance dissipates more power (P = I²R, same current). Parallel: Lower resistance dissipates more power (P = V²/R, same voltage). Parallel configurations can handle more total power as it's distributed across multiple components.

Yes! For complex networks, simplify step by step. First, identify and combine all purely series or purely parallel groups. Then treat each combined group as a single resistor and repeat until you have one equivalent resistance. Work from inside out.