Parallel Resistors Calculator | Qucs-S S-parameter Viewer Documentation

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# Parallel Resistors Calculator

## Overview

Calculates the equivalent resistance of any number of parallel resistors, along with the current and power dissipation through each one. Flags resistors that exceed a user-defined maximum power rating.

## Formulas

### Equivalent Resistance

    R_eq = 1 / (1/R₁ + 1/R₂ + ... + 1/Rₙ)

### Per-Resistor Current (shared voltage ΔV)

    Iₙ = ΔV / Rₙ

### Per-Resistor Power Dissipation

    Pₙ = Iₙ² × Rₙ = ΔV² / Rₙ

## Input Parameters

Parameter | Range | Default | Description
--- | --- | --- | ---
ΔV | 0 – 1000 V | 5 V | Voltage across the parallel network
P_max | 0 – 10000 mW | 50 mW | Per-resistor power threshold for warnings
R₁…Rₙ | dynamic | 1k | Resistor values (minimum 1)

## Resistance Parsing

Resistor values are entered as strings and support standard shorthand notation. The prefix letter replaces the decimal point:

Input | Parsed Value
--- | ---
`470` | 470 Ω
`2k2` | 2200 Ω
`0k5` | 500 Ω
`22k` | 22 kΩ
`4.7meg` | 4.7 MΩ
`100m` | 100 mΩ
`1g` | 1 GΩ

Supported prefixes: `m` (10⁻³), `k` (10³), `meg` (10⁶), `g` (10⁹).

## Output

- R_{eq}: Equivalent resistance of the full parallel network

- Per-resistor table: Current and power for each resistor, plus a total row

- Power warning: Any resistor whose dissipation exceeds P_max is highlighted

## Example

Input:

- ΔV: 5 V

- P_max: 50 mW

- R₁ = 1k, R₂ = 2k2, R₃ = 470

Calculation:

    R_eq = 1 / (1/1000 + 1/2200 + 1/470)
         = 1 / (0.001 + 0.000454 + 0.002128)
         = 1 / 0.003583
         ≈ 279.1 Ω

    I₁ = 5 / 1000   = 5 mA       →  P₁ = 5² × 1000    = 25 mW
    I₂ = 5 / 2200   ≈ 2.27 mA    →  P₂ = 2.27² × 2200 ≈ 11.36 mW
    I₃ = 5 / 470    ≈ 10.64 mA   →  P₃ = 10.64² × 470 ≈ 53.19 mW  ⚠️

Output:

Resistor | Current | Power Dissipation
--- | --- | ---
R1 | 5 mA | 25 mW
R2 | 2.273 mA | 11.36 mW
R3 | 10.64 mA | 53.19 mW ⚠️
Total | 17.91 mA | 89.55 mW

R₃ exceeds the maximum dissipation power threshold (50 mW).

## See Also

- Series Capacitors Calculator
- Parallel Inductors Calculator
- RF Engineering Calculators