Resistance Calculator

Resistance Formulas:

\[ R_{total} = R_1 + R_2 + \dots + R_n \quad \text{(Series)} \] \[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n} \quad \text{(Parallel)} \]

Total Resistance:

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1. What is Total Resistance?

Total resistance (R_total) is the equivalent resistance of a network of resistors. It represents the single resistance value that could replace the entire network without changing the current or voltage in the circuit.

2. Series vs Parallel Circuits

The way resistors are connected affects the total resistance:

\[ \text{Series: } R_{total} = R_1 + R_2 + \dots + R_n \] \[ \text{Parallel: } \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n} \]

Key Differences:

Series: Current same through all resistors, voltages add up
Parallel: Voltage same across all resistors, currents add up
Series increases total resistance
Parallel decreases total resistance

3. How the Calculator Works

The calculator:

Takes input values (comma-separated resistances)
Determines connection type (series or parallel)
Applies the appropriate formula
Returns the calculated total resistance

4. Using the Calculator

Instructions:

Select connection type (series or parallel)
Enter resistor values separated by commas (e.g., "10, 20, 30")
Click Calculate to get the total resistance

5. Frequently Asked Questions (FAQ)

Q1: What happens if I enter 0 ohm in parallel?
A: A 0 ohm resistor in parallel creates a short circuit, making total resistance 0.

Q2: How do I calculate for mixed series-parallel circuits?
A: Break the circuit into series and parallel sections, calculate each separately, then combine.

Q3: Why does parallel resistance decrease?
A: More parallel paths means more ways for current to flow, effectively reducing resistance.

Q4: What's the minimum number of resistors needed?
A: The calculator works with any number ≥1, but parallel needs ≥2 for meaningful calculation.

Q5: How precise are the results?
A: Results are rounded to 2 decimal places. For exact fractions, use manual calculation.