Parallel Resistor Calculator
Easily calculate the equivalent resistance of up to ten resistors in parallel with our Parallel Resistor Calculator.
Key Characteristics
- Equal Voltage: All resistors share the same voltage
- Current Division: Total current splits according to branch resistance
- Lower Total Resistance: Equivalent resistance is always less than the smallest individual resistor
- Branch Independence: Each branch can be disconnected without affecting others
Circuit Diagram
Mathematical Derivation
Starting with Ohm's Law and Kirchhoff's Current Law:
\[R_{eq} = \frac{V}{I_{total}} = \frac{V}{\left(\frac{V}{R_1} + \frac{V}{R_2} + \frac{V}{R_3} + \cdots + \frac{V}{R_n}\right)}\]After voltage cancellation (V is equal across all branches):
\[R_{eq} = \frac{1}{\left(\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots + \frac{1}{R_n}\right)}\]The standard conductance form (G = 1/R):
\[\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots + \frac{1}{R_n}\]Special case for two resistors (product over sum):
\[R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2}\]Engineering Applications
- Current Shunts: Precise current measurement in high-current circuits
- Power Distribution: Multiple loads sharing a common voltage source
- Precision Resistance: Achieving non-standard resistance values
- Redundancy: Fault-tolerant circuit design
Design Considerations
- Power Rating: Each resistor must handle its branch current
- Tolerance: Component variations affect current distribution
- Temperature Effects: Consider thermal coefficients for precision applications
- Contact Resistance: Connection quality affects overall accuracy
Common Examples
- Two 100Ω resistors in parallel = 50Ω (doubles current capacity)
- 100Ω || 100Ω || 100Ω = 33.33Ω (triples current capacity)
- 1kΩ || 1kΩ = 500Ω (common LED current limiting configuration)
- 10kΩ || 90kΩ = 9kΩ (precision voltage divider alternative)