RobustPCBWhere Robust Design Starts
CalculatorsالعربيةUpgradeSign inSign up

What's new

Full changelogEngine 1.18.3

Series / Parallel Network

Fundamentals

Equivalent resistance of any number of resistors, with the power in each.

Inputs

V
RefValue (Ω)
1 kΩ
2.2 kΩ
4.7 kΩ

Results

Series equivalent Req

Not judged: an equivalent resistance has no target to meet. Check the power in each part, in the table below.
7.9kΩ
Total current I
1.519mA
Total dissipation P
18.23mW
All results (1)
Nearest E24 value

one part instead
8.2kΩ

In series the current is the same in every part, so the largest resistor dissipates the most.

Each resistor
RefRV acrossI throughPshare
R11 kΩ1.519 V1.519 mA2.307 mW12.7 %
R22.2 kΩ3.342 V1.519 mA5.076 mW27.8 %
R34.7 kΩ7.139 V1.519 mA10.84 mW59.5 %

Parameter sweep

Vary one input over a range and see the answer and verdict at each step, as a table and a curve.Pro

Worst-case corners

Put a tolerance on each input and get the worst-case band around the answer.Pro

Circuit

The principle

Series resistances add; parallel conductances add. In practice, what matters is where the power lands and how the tolerances combine.

Series
Req=R1+R2+⋯+RnR_{eq} = R_1 + R_2 + \cdots + R_n
Same current in every element; voltages add.
Parallel
1Req=1R1+1R2+⋯+1Rn\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}
Same voltage across every element; currents add. For two parts:
Two in parallel
Req=R1R2R1+R2R_{eq} = \frac{R_1 R_2}{R_1 + R_2}
Power in element i
Pi=ViIi=I2Ri  (series)=V2Ri  (parallel)P_i = V_i I_i = I^{2} R_i \;\t{(series)} = \frac{V^{2}}{R_i} \;\t{(parallel)}
  • ReqR_{eq}equivalent resistance seen by the source
  • ViV_ivoltage across element i
  • PiP_ipower dissipated in element i
More detail

Design notes

  • Tolerance. The worst case keeps the parts' percentage tolerance, but the statistical (RSS) spread of n equal parts falls as 1/√n. Four 1 % parts spread about half as much as one.
  • Sharing. Nominally equal parts in parallel never share exactly: tolerance and self-heating tip the balance. Size each part for the worst case.
  • Series for voltage, parallel for power. A series string keeps each part within its working-voltage limit. Two 2 Ω 1 W parts in parallel make 1 Ω 2 W and spread the heat.
See also: the Preferred-Value Synthesiser, to hit an exact value from stock parts.

Engine version ⁨1.18.3⁩