Resistance Calculator Parallel

Parallel Resistance Equation:

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

Equivalent Resistance (R_eq):

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1. What is Parallel Resistance?

Parallel resistance occurs when multiple resistors are connected across the same two points in a circuit, providing multiple paths for current flow. The equivalent resistance is always less than the smallest individual resistor in the parallel combination.

2. How Does the Calculator Work?

The calculator uses the parallel resistance formula:

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

Where:

\( R_{eq} \) — Equivalent parallel resistance (ohms)
\( R_i \) — Individual resistor values (ohms)
\( \sum \) — Summation of all reciprocal values

Explanation: For two resistors in parallel, the formula simplifies to: \( R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2} \)

3. Importance of Parallel Resistance Calculation

Details: Calculating parallel resistance is essential for circuit design, analyzing current distribution, determining total circuit resistance, and ensuring proper component selection 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 representing resistance in ohms. The calculator will ignore any invalid entries.

5. Frequently Asked Questions (FAQ)

Q1: Why is parallel resistance always less than the smallest resistor?
A: Adding more parallel paths decreases total resistance because current has multiple routes to flow, effectively increasing the total cross-sectional area for current.

Q2: What happens if one resistor in parallel fails open?
A: If one resistor fails open, the total resistance increases, but the circuit may still function through the remaining parallel paths.

Q3: Can I mix different resistor values in parallel?
A: Yes, resistors of different values can be connected in parallel. The equivalent resistance will be dominated by the smallest resistor value.

Q4: How does parallel resistance affect current?
A: In parallel circuits, current divides among the branches inversely proportional to their resistance values (higher current through lower resistance paths).

Q5: What are common applications of parallel resistors?
A: Current dividing circuits, load sharing in power supplies, creating specific resistance values not available as standard components, and circuit protection.