What's new

Full changelogEngine 1.26.4

Series / Parallel Network

Fundamentals

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

Inputs

V
RefValue (Ω)Remove row
1 kΩ
2.2 kΩ
4.7 kΩ

Results

Series equivalent Req
7.9kΩ
Total current I
1.519mA
Total dissipation P
18.23mW
All results (1)
Nearest E24 value
8.2kΩ
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 ⁨1.26.4⁩