Parallel Resistor Calculator
Calculate equivalent resistance for resistors connected in parallel using 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
Resistor Configuration
Equivalent Resistance Results
Formula: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ... (for parallel resistors)
Example Calculation
LED Current Limiting Example
Circuit: Three current limiting resistors in parallel for LED array
R₁: 220 Ω (for red LED)
R₂: 330 Ω (for green LED)
R₃: 470 Ω (for blue LED)
Calculation
1/R_total = 1/R₁ + 1/R₂ + 1/R₃
1/R_total = 1/220 + 1/330 + 1/470
1/R_total = 0.00454 + 0.00303 + 0.00213 = 0.0097
R_total = 1/0.0097 = 103.1 Ω
Parallel vs Series
Parallel Resistors
1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
Total resistance decreases
Series Resistors
R_total = R₁ + R₂ + R₃ + ...
Total resistance increases
Resistance Units
Parallel Resistor Tips
Parallel resistors follow the reciprocal sum formula
All resistors have the same voltage across them
Total current is the sum of individual currents
Parallel connection decreases total resistance
Lower resistance resistors carry more current
Used for current division and redundancy
Understanding Parallel Resistors
What are Parallel Resistors?
Parallel resistors are resistors connected side by side in a circuit, where each resistor has the same voltage across its terminals. The equivalent resistance is calculated using the reciprocal formula: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
Key Characteristics
- •Same voltage across all resistors (V₁ = V₂ = V₃ = V_source)
- •Total current is sum of individual currents (I_total = I₁ + I₂ + I₃)
- •Equivalent resistance is always less than the smallest resistor
- •Current divides inversely proportional to resistance
Mathematical Derivation
V = I₁ × R₁ = I₂ × R₂ = I₃ × R₃
I₁ = V/R₁, I₂ = V/R₂, I₃ = V/R₃
I_total = I₁ + I₂ + I₃
I_total = V/R₁ + V/R₂ + V/R₃
I_total = V × (1/R₁ + 1/R₂ + 1/R₃)
V/R_total = V × (1/R₁ + 1/R₂ + 1/R₃)
1/R_total = 1/R₁ + 1/R₂ + 1/R₃
Common Applications
- •Current divider circuits
- •LED current limiting (multiple paths)
- •Shunt resistors for current measurement
- •Heating elements with multiple zones
- •Redundant circuit paths for reliability