Calculate equivalent resistance for resistors connected in parallel. Free online electrical circuit calculator with support for multiple resistors using 1/R_total = 1/R₁ + 1/R₂ + ...
Calculate equivalent resistance for resistors in parallel
Formula:
1/R_total = 1/R₁ + 1/R₂ + ... + 1/Rₙ
For two resistors: R_total = (R₁ × R₂) / (R₁ + R₂)
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Parallel resistor circuits are fundamental in electrical engineering and electronics. When resistors are connected in parallel, they share the same voltage but divide the current. Understanding how to calculate equivalent parallel resistance is essential for circuit design, analysis, and troubleshooting. Our Parallel Resistor Calculator makes it easy to determine the total resistance of any number of resistors connected in parallel.
The key principle of parallel resistors is that the equivalent resistance is always less than the smallest individual resistor. This is because parallel connections provide multiple paths for current flow, effectively reducing the overall resistance of the circuit.
Our Parallel Resistor Calculator is designed for simplicity and accuracy. Follow these steps:
The calculator uses the fundamental parallel resistance formula: 1/R_total = 1/R₁ + 1/R₂ + ... + 1/Rₙ
The equivalent resistance of resistors in parallel is calculated using:
1/R_total = 1/R₁ + 1/R₂ + ... + 1/Rₙ
Where: R_total = equivalent resistance, R₁, R₂, ..., Rₙ = individual resistor values
For two resistors, the formula simplifies to:
R_total = (R₁ × R₂) / (R₁ + R₂)
This is often called the "product over sum" formula
Parallel resistor calculations are used in countless electrical and electronic applications:
What is the equivalent resistance of two 100Ω resistors in parallel?
R_total = (R₁ × R₂) / (R₁ + R₂) = (100 × 100) / (100 + 100) = 10,000 / 200 = 50 Ω
Note: Two equal resistors in parallel = half the individual resistance
What is the equivalent resistance of 10Ω and 20Ω resistors in parallel?
R_total = (10 × 20) / (10 + 20) = 200 / 30 = 6.67 Ω
What is the equivalent resistance of 10Ω, 20Ω, and 30Ω resistors in parallel?
1/R_total = 1/10 + 1/20 + 1/30 = 0.1 + 0.05 + 0.0333 = 0.1833 Ω⁻¹
R_total = 1 / 0.1833 = 5.45 Ω
What is the equivalent resistance of four 100Ω resistors in parallel?
1/R_total = 1/100 + 1/100 + 1/100 + 1/100 = 4/100 = 0.04 Ω⁻¹
R_total = 1 / 0.04 = 25 Ω
Note: N equal resistors in parallel = R / N
Understanding the difference between parallel and series connections is crucial:
In parallel circuits, current divides among the branches according to:
Iₙ = I_total × (R_total / Rₙ)
Where: Iₙ = current through resistor n, I_total = total current, R_total = equivalent resistance, Rₙ = resistance of branch n
The branch with the smallest resistance carries the most current, and vice versa. This is the inverse relationship: lower resistance = higher current.
The formula for parallel resistors is: 1/R_total = 1/R₁ + 1/R₂ + ... + 1/Rₙ. For two resistors, this simplifies to: R_total = (R₁ × R₂) / (R₁ + R₂), which is often called the 'product over sum' formula.
Parallel resistance is always less than the smallest resistor because parallel connections provide multiple paths for current flow. More paths mean less overall resistance. It's like having multiple lanes on a highway - more lanes allow more traffic to flow, reducing overall 'resistance' to traffic.
Adding more resistors in parallel decreases the total equivalent resistance. Each additional parallel path provides another route for current, further reducing the overall resistance. The equivalent resistance approaches zero as more parallel resistors are added.
Yes, absolutely! Resistors with different values can be connected in parallel. The equivalent resistance will be less than the smallest individual resistor. The calculator handles any combination of resistor values.
Two equal resistors (R) in parallel have an equivalent resistance of R/2. For example, two 100Ω resistors in parallel equal 50Ω. This is because 1/R_total = 1/R + 1/R = 2/R, so R_total = R/2.
In parallel circuits, all resistors have the same voltage. Use Ohm's law: I = V / R for each branch. The current through each resistor is: Iₙ = V / Rₙ, where V is the voltage across the parallel combination and Rₙ is the resistance of that branch.
Understanding parallel resistor circuits is fundamental to electrical engineering and electronics. Our Parallel Resistor Calculator simplifies these calculations, making it easy to determine equivalent resistance for any number of parallel resistors.
Ready to explore more electrical concepts? Check out our other calculators like the Watt Calculator for power calculations, or the Wire Size Calculator for electrical wiring calculations that often complement circuit analysis.
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