Resistor Calculator
Calculate the total equivalent resistance for series and parallel circuits.
Series Resistor Circuit
Circuit Diagram
Total Equivalent Resistance (Req)
How It Works?
Series Circuits
In a series circuit, resistors are connected end-to-end. The total resistance is the sum of all individual resistances. The current is the same through all resistors.
Req = R1 + R2 + ... + Rn
Parallel Circuits
In a parallel circuit, resistors are connected across the same two points. The reciprocal of the total resistance is the sum of the reciprocals of individual resistances. The voltage is the same across all resistors.
1/Req = 1/R1 + 1/R2 + ... + 1/Rn
Worked Examples
Example: Series
Calculate the total resistance for three resistors of 100Ω, 220Ω, and 470Ω connected in series.
Req = 100Ω + 220Ω + 470Ω = 790Ω
Example: Parallel
Calculate the total resistance for two resistors of 1kΩ (1000Ω) and 2kΩ (2000Ω) connected in parallel.
Req = 1 / (1/1000 + 1/2000) = 666.67Ω
Frequently Asked Questions
Why is parallel resistance always lower?
Adding resistors in parallel creates more paths for the current to flow. More pathways mean less overall opposition to the current, hence the total equivalent resistance is lower than the smallest individual resistor in the parallel combination.
How do you calculate mixed series-parallel circuits?
You simplify the circuit in steps. First, identify any groups of resistors that are purely in series or purely in parallel. Calculate their equivalent resistance. Replace that group with a single equivalent resistor. Repeat this process until you are left with a single equivalent resistance for the entire circuit.
What are some real-world applications?
Series circuits are used in applications like Christmas lights (the old kind, where if one bulb goes out, they all do) and as voltage dividers. Parallel circuits are much more common; for example, all the outlets and lights in your house are wired in parallel so they all receive the same voltage from the source.