How do you calculate total resistance in parallel?

In a parallel circuit, total resistance is calculated using the formula: 1/Rt = 1/R1 + 1/R2 + ... + 1/Rn. The total resistance is always less than the smallest individual resistor. For two resistors, use: Rt = (R1 × R2) / (R1 + R2).

What is the difference between series and parallel resistance?

In series, resistors are connected end-to-end and total resistance equals the sum of all resistors (Rt = R1 + R2 + ... + Rn). In parallel, resistors are connected across the same two points and total resistance is the reciprocal of the sum of reciprocals. Series increases resistance; parallel decreases it.

Why is parallel resistance less than the smallest resistor?

Each additional resistor in parallel creates a new path for electric current to flow. More paths mean less overall opposition to current, just like adding more lanes to a highway reduces traffic congestion. The total conductance (1/R) adds up, making total resistance decrease.

🔬 Parallel & Series Resistance Calculator

Calculate total resistance for any number of resistors in parallel or series. Add or remove resistors dynamically, compare results side by side.

Calculator

Source Voltage (V): Volts

Results

Parallel Resistance

— Ω

Series Resistance

— Ω

Per-Resistor Details

Resistor	Value	Current	Power

Formula Reference

Series: R_total = R₁ + R₂ + R₃ + …
Parallel: 1 / R_total = 1 / R₁ + 1 / R₂ + 1 / R₃ + …
2 Resistors Parallel: R_total = (R₁ × R₂) / (R₁ + R₂)

Frequently Asked Questions

Parallel resistance is calculated using the reciprocal formula: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + … + 1/R_n. For two resistors, you can use the simplified formula: R_total = (R₁ × R₂) / (R₁ + R₂). The total parallel resistance is always less than the smallest resistor value.

In a series circuit, resistors are connected end-to-end, and the total resistance is simply the sum of all individual resistances: R_total = R₁ + R₂ + R₃ + … + R_n. Unlike parallel resistance, series resistance is always greater than the largest individual resistor value.

The reciprocal formula for parallel resistance states that the reciprocal of the total resistance equals the sum of the reciprocals of each individual resistance: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + … + 1/R_n. After summing the reciprocals, take the reciprocal of the result to find R_total.

🔬 Parallel & Series Resistance Calculator

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