Equivalent Resistance
Compute equivalent resistance of resistors in series or parallel; with source voltage also output total current.
Inputs
Formula
Series R = ΣRi; Parallel 1/R = Σ(1/Ri)
Fundamentals
Equivalent resistance reduces a network to a single resistor for whole-circuit Ohm's-law analysis.
Series $R_\text{eq}=\sum R_i$; parallel $1/R_\text{eq}=\sum 1/R_i$, two in parallel $R_\text{eq}=R_1R_2/(R_1+R_2)$.
History
Series-parallel reduction rests on Kirchhoff's laws (1845), the basis of network analysis.
Engineering applications
Used for circuit equivalence, current/voltage division and sensor-bridge design.
Glossary
| Series | End-to-end, same current. |
| Parallel | Common ends, same voltage. |
| Equivalent $R$ | Single value the network presents. |
How to use
- Fill in Connection, Resistor R1, Resistor R2, Resistor R3, Resistor R4, Source U (opt.) in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Equiv. R_eq, Total current I in the results area.
Formula notesSeries R_eq = Σ R_i; parallel 1/R_eq = Σ(1/R_i); two in parallel R_eq = R₁·R₂/(R₁+R₂).
Formula · Worked Example · Knowledge
Formula
Series $R=\sum R_i$; parallel $1/R=\sum(1/R_i)$; with source $I=U/R_{eq}$.
Worked Example
Parallel 100+200+300 Ω → Req=54.5 Ω; U=12 V → I≈0.22 A.
Key Points
- Series: same current, divided voltage.
- Parallel: same voltage, divided current.
- Mixed networks reduce step by step to Req.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Connection | mode | parallel | |
| Resistor R1 (Ω) | R1 | Ω | 100 |
| Resistor R2 (Ω) | R2 | Ω | 200 |
| Resistor R3 (Ω) | R3 | Ω | 300 |
| Resistor R4 (Ω) | R4 | Ω | 0 |
| Source U (opt.) (V) | U | V | 0 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Equiv. R_eq | Req | Ω |
| Total current I | I | A |
Applications
- Common engineering use cases
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: Series R = ΣRi; Parallel 1/R = Σ(1/Ri)
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Common engineering use cases