1. What is Equivalent Resistance?

Equivalent resistance (R_eq) is the single resistance that can replace a combination of resistors in a circuit without changing the current-voltage characteristics. It simplifies complex circuits for analysis.

2. Series vs Parallel Connections

Series Connection: Resistors are connected end-to-end. Current through each resistor is the same, while voltage divides.

Parallel Connection: Resistors are connected across the same two points. Voltage across each resistor is the same, while current divides.

3. Calculation Methods

The calculator uses these fundamental formulas:

Special Cases:

• Two parallel resistors: \( R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2} \)
• N identical parallel resistors: \( R_{eq} = \frac{R}{N} \)

4. Using the Calculator

Instructions:

1. Select connection type (series or parallel)
2. Enter resistor values separated by commas (e.g., 100, 200, 300)
3. All values must be positive numbers
4. Click Calculate to get the equivalent resistance

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between series and parallel resistance?
A: Series increases total resistance, parallel decreases it. In series, R_eq > any individual R. In parallel, R_eq < any individual R.

Q2: How do I calculate for mixed series-parallel circuits?
A: Break the circuit into series and parallel sections, calculate each section's R_eq, then combine step by step.

Q3: What happens if I connect resistors of different values in parallel?
A: The equivalent resistance will be less than the smallest resistor in the group.

Q4: Why does parallel resistance decrease?
A: More parallel paths create more ways for current to flow, effectively reducing overall resistance.

Q5: Can I use this for AC circuits?
A: For purely resistive AC circuits, yes. For circuits with capacitors/inductors, you need impedance calculations.