Parallel Circuit Calculator – Equivalent Resistance
Calculate equivalent resistance for resistors in parallel
Table of Contents
How to Use
- Enter resistance values for at least 2 resistors (up to 4)
- Leave unused resistor fields empty
- Click calculate to see the equivalent resistance
- The formula used is: 1/R_eq = 1/R1 + 1/R2 + 1/R3 + ...
What is a Parallel Circuit?
In a parallel circuit, components are connected across each other, forming multiple paths for current flow. Each component receives the same voltage, but the current divides among the branches.
Parallel circuits are commonly used in electrical systems because they allow individual components to operate independently. If one component fails, the others continue to function.
Equivalent Resistance Calculation
For resistors in parallel, the equivalent resistance is always less than the smallest individual resistance. The formula is:
- 1/R_eq = 1/R1 + 1/R2 + 1/R3 + ...
- R_eq = 1 / (1/R1 + 1/R2 + 1/R3 + ...)
For two resistors: R_eq = (R1 × R2) / (R1 + R2)
For equal resistors: If n resistors of value R are in parallel, R_eq = R / n
Parallel Circuit Characteristics
Key properties of parallel circuits:
- Voltage is the same across all branches
- Current divides among branches
- Total current equals sum of branch currents
- Equivalent resistance is less than smallest resistance
- Adding more resistors decreases total resistance
Applications
Parallel circuits are used in:
- Household electrical wiring
- Power distribution systems
- LED lighting circuits
- Battery connections
- Audio speaker systems
- Computer power supplies
Frequently Asked Questions
- Why is equivalent resistance less in parallel circuits?
- In parallel circuits, current has multiple paths to flow, effectively increasing the total current for a given voltage. Since resistance is voltage divided by current, more current means less resistance.
- What happens if I add more resistors in parallel?
- Adding more resistors in parallel decreases the equivalent resistance. Each additional resistor provides another path for current, reducing the overall resistance.
- How do I calculate parallel resistance for two resistors?
- For two resistors R1 and R2 in parallel: R_eq = (R1 × R2) / (R1 + R2). This is simpler than using the reciprocal formula.
- Can I use this calculator for capacitors in parallel?
- This calculator is for resistors. For capacitors in parallel, the calculation is different: C_eq = C1 + C2 + C3 + ... (capacitances add directly in parallel).