Calculate Resistance in Parallel

Parallel Resistance Formula:

\[ \frac{1}{R_{eq}} = \sum \frac{1}{R_i} \]

Equivalent Resistance (R_eq):

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1. What is Parallel Resistance?

Parallel resistance refers to the equivalent resistance of multiple resistors connected in parallel in an electrical circuit. The combined resistance is always less than the smallest individual resistor in the parallel network.

2. How Does the Calculator Work?

The calculator uses the parallel resistance formula:

\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n} \]

Where:

\( R_{eq} \) — Equivalent parallel resistance (Ω)
\( R_1, R_2, \ldots, R_n \) — Individual resistor values (Ω)

Explanation: The reciprocal of the equivalent resistance equals the sum of the reciprocals of each individual resistance.

3. Importance of Parallel Resistance Calculation

Details: Calculating parallel resistance is essential for designing circuits, determining current flow, and ensuring proper voltage distribution in electronic systems.

4. Using the Calculator

Tips: Enter resistor values separated by commas (e.g., "100, 200, 300"). All values must be positive numbers. The calculator will ignore any non-numeric values.

5. Frequently Asked Questions (FAQ)

Q1: What happens if I enter a zero or negative resistance?
A: The calculator will ignore any zero or negative values as they are not physically meaningful for resistors.

Q2: What's the difference between series and parallel resistance?
A: In series, resistances add directly (R_total = R₁ + R₂ + ...). In parallel, reciprocals add (1/R_total = 1/R₁ + 1/R₂ + ...).

Q3: Why is parallel resistance always less than the smallest resistor?
A: Because current has multiple paths to flow through, effectively reducing the overall resistance.

Q4: How do I calculate parallel resistance for two resistors?
A: You can use the simplified formula: R_eq = (R₁ × R₂)/(R₁ + R₂).

Q5: What units should I use?
A: The calculator uses ohms (Ω), but any consistent unit will work (kΩ, MΩ, etc.) as long as all resistors use the same unit.