# 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.

انٹرایکٹو صورت: https://www.calcopenly.com/ur/science/series-parallel-calculator
موضوع: سائنس کے کیلکولیٹر

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.

## اندراجات

- **Components** (اختیارات: Resistors, Capacitors, Inductors)
- **Connected in** (اختیارات: Series, Parallel)
- **Values**: Separate with commas or spaces; 4.7k works for kilo
- **اکائی** (اختیارات: mΩ, Ω, kΩ, MΩ)
- **اکائی** (اختیارات: pF, nF, µF, mF, F)
- **اکائی** (اختیارات: nH, µH, mH, H)

## نتائج

- Equivalent value — بنیادی نتیجہ
- In base units
- Number of components

## فارمولا

$$
\text{Series: } R = \sum R_i,\ L = \sum L_i,\ \tfrac1C = \sum \tfrac1{C_i}\qquad \text{Parallel: } \tfrac1R = \sum \tfrac1{R_i},\ \tfrac1L = \sum \tfrac1{L_i},\ C = \sum C_i
$$

## حل شدہ مثالیں

### 100, 220, 470 Ω in series

- Components: Resistors
- Connected in: Series
- Values: 100, 220, 470
- اکائی: Ω
- **Equivalent value: 790 Ω**
- جانچ کا ماخذ: ⁨Python 3.8 decimal: 100 + 220 + 470⁩

### 100, 220, 470 Ω in parallel

- Components: Resistors
- Connected in: Parallel
- Values: 100, 220, 470
- اکائی: Ω
- **Equivalent value: 59.9768 Ω**
- جانچ کا ماخذ: ⁨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
- اکائی: Ω
- **Equivalent value: 500 Ω**
- جانچ کا ماخذ: ⁨R/n for n equal resistors (OpenStax UP2 §10.2)⁩

### Three 100 nF in parallel

- Components: Capacitors
- Connected in: Parallel
- Values: 100 100 100
- اکائی: nF
- **Equivalent value: 300 nF**
- جانچ کا ماخذ: ⁨Sum: 300 nF⁩

### 10 µF and 22 µF in series

- Components: Capacitors
- Connected in: Series
- Values: 10, 22
- اکائی: µF
- **Equivalent value: 6.875 µF**
- **In base units: 6.875 × 10⁻⁶ F**
- جانچ کا ماخذ: ⁨Python 3.8 fractions: 1/(1/10 + 1/22) = 6.875 µF⁩

### 10 mH and 4.7 mH in series

- Components: Inductors
- Connected in: Series
- Values: 10, 4.7
- اکائی: mH
- **Equivalent value: 14.7 mH**
- **In base units: 1.47 × 10⁻² H**
- جانچ کا ماخذ: ⁨Sum: 14.7 mH (no mutual coupling)⁩

## سوالات

### 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” کتنا درست ہے؟

درستی آپ کی درج کردہ قدروں اور طریقے کے مفروضوں پر منحصر ہے۔ اعشاری حساب 50 بامعنی ہندسے استعمال کرتا ہے، مگر تخمینے، عددی طریقے اور ماخذ کا ڈیٹا کم درست ہو سکتے ہیں؛ دکھائی گئی قدروں کو راؤنڈ کرنے سے یہ حدود ختم نہیں ہوتیں۔ آزاد ذرائع کی حل شدہ مثالوں سے جانچ: 7۔ مثلاً، “⁨100, 220, 470 Ω in series⁩” کو ⁨Python 3.8 decimal: 100 + 220 + 470⁩ سے جانچا جاتا ہے۔

### اس طریقے کا ماخذ کیا ہے؟

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).

## ماخذ

- [OpenStax University Physics Volume 2, §10.2 Resistors in series and parallel; §8.2 Capacitors in series and in parallel](https://openstax.org/books/university-physics-volume-2/pages/10-2-resistors-in-series-and-parallel)
- [HyperPhysics — Inductors in series and parallel (no mutual inductance)](http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indcom.html)