The Equivalent Resistor Calculator helps users find the total resistance of two or more resistors connected in either series or parallel. Instead of solving equations manually, this calculator gives quick and accurate results based on the resistor values and their configuration.
This tool is especially useful for students, hobbyists, and engineers working with electrical circuits. Knowing the total resistance helps in designing and analyzing circuits efficiently. Whether it's a simple LED project or a complex amplifier, calculating the correct resistance is essential for safe and effective performance.
Formula of Equivalent Resistor Calculator
1. Series Configuration:
Rₑq = R₁ + R₂ + R₃ + ... + Rₙ
Where:
Rₑq = total equivalent resistance
R₁, R₂, ..., Rₙ = resistances of resistors in series
In a series circuit, the resistors are connected end-to-end. The total resistance is the sum of all resistor values.
2. Parallel Configuration:
1 / Rₑq = (1 / R₁) + (1 / R₂) + (1 / R₃) + ... + (1 / Rₙ)
or
Rₑq = 1 / [(1 / R₁) + (1 / R₂) + (1 / R₃) + ... + (1 / Rₙ)]
Where:
Rₑq = total equivalent resistance
R₁, R₂, ..., Rₙ = resistances of resistors in parallel
In a parallel setup, all resistors are connected to the same voltage source. The reciprocal of the total resistance is the sum of the reciprocals of each resistor.
Helpful Reference Table
This table shows typical values of equivalent resistance in common resistor combinations.
| Configuration | Resistors (Ω) | Equivalent Resistance (Ω) |
|---|---|---|
| Series | 10, 20, 30 | 60 |
| Series | 5, 5, 5, 5 | 20 |
| Parallel | 10, 10 | 5 |
| Parallel | 20, 30 | 12 |
| Parallel | 100, 100, 100 | 33.33 |
Use this table to get quick estimates or double-check your manual calculations. It's helpful when setting up circuits or troubleshooting.
Example of Equivalent Resistor Calculator
Let’s say you have three resistors:
- R₁ = 10 Ω
- R₂ = 20 Ω
- R₃ = 30 Ω
Series Example:
Rₑq = R₁ + R₂ + R₃ = 10 + 20 + 30 = 60 Ω
So, the total resistance in series is 60 ohms.
Parallel Example:
1 / Rₑq = (1 / 10) + (1 / 20) + (1 / 30)
1 / Rₑq = 0.1 + 0.05 + 0.0333 = 0.1833
Rₑq = 1 / 0.1833 ≈ 5.45 Ω
The equivalent resistance in parallel is about 5.45 ohms.
Most Common FAQs
In a series circuit, resistors add directly, increasing total resistance. In a parallel setup, current has multiple paths, which lowers the total resistance.
Yes, complex circuits often use a combination. Calculate each section separately and then combine them step by step.
Always use ohms (Ω) for resistance. The calculator automatically provides the result in ohms.