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Series and parallel resistor calculator

Series and parallel resistor calculator: total resistance of any number of resistors, plus capacitors or inductors in series or parallel.

업데이트 검증한 예제: 7

Separate with commas or spaces; 4.7k works for kilo
시도하기
Equivalent value
Ω
Equivalent value: 59.9768 Ω
유효 자릿수: 6; 가장 가까운 값, 중간값은 0에서 먼 쪽으로
Number of components
3

3 resistors in parallel act like one of 59.9768 Ω — always smaller than the smallest single part.

3 resistors in parallel: 59.9768 Ω

AB100 Ω220 Ω470 Ω
계산 방법 S

  1. Resistors in parallel

    1Req=1100+1220+1470  ⇒  Req=59.9768 Ω\frac{1}{R_{\text{eq}}} = \frac{1}{100} + \frac{1}{220} + \frac{1}{470} \;\Rightarrow\; R_{\text{eq}} = 59.9768\ \mathrm{\Omega}

    Reciprocals add.

Series and parallel resistor calculator 소개

Resistors add in series, R = R₁ + R₂ + …, while in parallel their reciprocals add, 1/R = 1/R₁ + 1/R₂ + … . Inductors follow the same two rules when their magnetic fields do not interact. Capacitors do the opposite: they add in parallel and combine by reciprocals in series. Enter any number of values in one unit; 4.7k is read as 4,700.

The default, 100 Ω, 220 Ω and 470 Ω in parallel, gives 59.98 Ω, below the smallest part as every parallel network must be; the same three in series give 790 Ω. Combining parts is how a value outside the E-series is built, such as 500 Ω from two 1 kΩ resistors in parallel.

The parts are treated as ideal: no lead or contact resistance, no capacitor leakage and no mutual inductance between coils.

계산 예제

100, 220, 470 Ω in series

Components
Resistors
Connected in
Series
Values
100, 220, 470
단위
Ω
Equivalent value
790 Ω

검증 출처: Python 3.8 decimal: 100 + 220 + 470

100, 220, 470 Ω in parallel

Components
Resistors
Connected in
Parallel
Values
100, 220, 470
단위
Ω
Equivalent value
59.9768 Ω

검증 출처: Python 3.8 fractions: 1/(1/100 + 1/220 + 1/470) = 25850/431 = 59.976798…

Two equal 1 kΩ in parallel

Components
Resistors
Connected in
Parallel
Values
1k 1k
단위
Ω
Equivalent value
500 Ω

검증 출처: R/n for n equal resistors (OpenStax UP2 §10.2)

Three 100 nF in parallel

Components
Capacitors
Connected in
Parallel
Values
100 100 100
단위
nF
Equivalent value
300 nF

검증 출처: Sum: 300 nF

자주 묻는 질문

How do you calculate resistors in parallel?

Add the reciprocals and invert: 1/R = 1/R₁ + 1/R₂ + … . For two resistors this reduces to product over sum, R = R₁R₂/(R₁ + R₂), so 100 Ω and 220 Ω in parallel give 22,000/320 = 68.75 Ω. The total is always smaller than the smallest resistor, because each extra path carries more current.

What is the resistance of equal resistors in parallel?

Divide one resistor's value by the number of resistors: n equal resistors R in parallel give R/n. Two 1 kΩ resistors give 500 Ω and four 100 Ω resistors give 25 Ω. They share the current equally, so the power ratings add too: four ¼ W resistors in parallel can dissipate 1 W between them.

How do you add capacitors in series and in parallel?

In parallel, capacitances add directly: three 100 nF capacitors give 300 nF. In series, the reciprocals add, 1/C = 1/C₁ + 1/C₂, so 10 µF and 22 µF give 6.875 µF, less than the smaller part. Series capacitors carry the same charge, so the smaller capacitor takes the larger share of the voltage.

Do inductors add like resistors?

Yes, when their magnetic fields do not couple: L = L₁ + L₂ in series and 1/L = 1/L₁ + 1/L₂ in parallel, so 10 mH and 4.7 mH in series give 14.7 mH. Coils that share flux add or subtract a mutual-inductance term of 2M in series, depending on winding direction, which this calculator does not model.

“Series and parallel resistor calculator”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 7. 예를 들어 “100, 220, 470 Ω in series”은 Python 3.8 decimal: 100 + 220 + 470와 대조해 확인합니다.

이 계산 방법의 출처는 무엇인가요?

OpenStax University Physics Volume 2, §10.2 Resistors in series and parallel; §8.2 Capacitors in series and in parallel; HyperPhysics — Inductors in series and parallel (no mutual inductance).

이 계산기 소개

Series: R=∑Ri, L=∑Li, 1C=∑1CiParallel: 1R=∑1Ri, 1L=∑1Li, C=∑Ci\text{Series: } R = \sum R_i,\ L = \sum L_i,\ \tfrac1C = \sum \tfrac1{C_i}\qquad \text{Parallel: } \tfrac1R = \sum \tfrac1{R_i},\ \tfrac1L = \sum \tfrac1{L_i},\ C = \sum C_i

출처

  1. OpenStax University Physics Volume 2, §10.2 Resistors in series and parallel; §8.2 Capacitors in series and in parallel
  2. HyperPhysics — Inductors in series and parallel (no mutual inductance)

출처와 대조하여 검증

이 계산기에는 독립적인 출처에서 답을 얻은 계산 예제가 7개 있습니다. 테스트 모음에서 실행되며 여기에서도 실행할 수 있습니다.

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