Resistors in Parallel

Calculator and formulas for calculating parallel connected resistors

Parallel Resistance Calculator

Input Format

Enter the resistance values separated by semicolons.

Example: 100; 220; 470

Enter all values in the same unit (Ω, kΩ, MΩ)
Result
Total resistance:

Parallel Circuit

Parallel connection of resistors

Parallel connection of resistors

Properties
  • Same voltage across all resistors
  • Total current is the sum of partial currents
  • Total resistance is always smaller than the smallest individual resistor
Basic Formula
\[\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}\]
Conductances are added
Special Cases
Two resistors: Rtotal = (R₁ × R₂) / (R₁ + R₂)
n equal resistors: Rtotal = R / n

Formulas for Parallel Circuits

General Formula

For n resistors:

\[\frac{1}{R_{total}} = \sum_{i=1}^n \frac{1}{R_i}\]
Add conductances
Product Formula (2 resistors)

Simplified formula for two resistors:

\[R_{total} = \frac{R_1 \cdot R_2}{R_1 + R_2}\]
Frequently used
Equal Resistors

When all n resistors are equal:

\[R_{total} = \frac{R}{n}\]
Simplest form

Practical Examples

Example 1: Three different resistors

Given: R₁ = 4Ω, R₂ = 6Ω, R₃ = 12Ω

\[\frac{1}{R_{total}} = \frac{1}{4} + \frac{1}{6} + \frac{1}{12} = 0.5\]
Rtotal = 2Ω

✓ Check: 2Ω < 4Ω (smallest resistor)

Example 2: Two equal resistors

Given: Two 100Ω resistors in parallel

\[R_{total} = \frac{100 \times 100}{100 + 100} = 50Ω\]
or: Rtotal = 100/2 = 50Ω

For equal resistors: Rtotal = R/n

Example 3: Practical application - Reduce resistance

Task: A 470Ω resistor should be reduced to about 150Ω. What resistor must be connected in parallel?

Rearranging the product formula:
\[R_2 = \frac{R_1 \times R_{total}}{R_1 - R_{total}} = \frac{470 \times 150}{470 - 150} = 220Ω\]
Answer: 220Ω parallel to 470Ω gives 150Ω

Current Distribution and Applications

Current Distribution in Parallel Circuits

In a parallel circuit, the total current divides inversely proportional to the resistance values. Current flows preferentially through the smaller resistance.

Current Distribution Formula
\[I_{total} = I_1 + I_2 + I_3 + ... + I_n\]
\[I_i = \frac{U}{R_i}\]
Common Applications
  • Electrical lighting: Lamps in house installations
  • Electronics: Voltage dividers and bias circuits
  • Measurement technology: Shunt resistors for current measurement
  • Power matching: Reduction of total resistance
Important Note

When connecting resistors in parallel, the total power increases because more current flows.

Consider: Load capacity of the voltage source and thermal stress on components!

Memory Rules
  • Rtotal is always smaller than the smallest individual resistor
  • More current flows through small resistors
  • All resistors have the same voltage
  • Total power is the sum of individual powers

Input Guidelines for the Calculator

Correct Input
  • Format: Separate values with semicolons (e.g. 100; 220; 470)
  • Units: Enter all values in the same unit
  • Decimal separator: Use comma (,) or period (.)
  • Exponents: Not allowed - use 1000 instead of 1E3
  • Result: Displayed in the same unit as the input


Circuits with resistors

Ohms Law  •  Total resistance of a resistor in parallel  •  Parallel- total resistance of 2 resistors  •  Series resistance for a voltmeter  •  Parallel resistance for an ampere meter  •  Voltage divider  •  Loaded voltage divider  •  Pi Attenuator  •  T Attenuator  •