Parallel Resistance Calculator

How to Calculate Parallel Resistance

When resistors are connected in parallel, the total equivalent resistance is always less than the smallest individual resistance. This calculator helps you determine the total resistance based on the values of the parallel resistors.

Parallel Resistance Formula

The formula for calculating the total resistance of parallel resistors is:

\[\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots + \frac{1}{R_n}\]

Where:

• R_T is the total equivalent resistance in ohms (Ω)
• R₁, R₂, R₃, ..., R_n are the individual resistances connected in parallel, also in ohms (Ω)

Calculation Steps

1. Identify the values of the individual resistances (R₁, R₂, R₃, ..., R_n) in ohms
2. Calculate the reciprocal (1/R) of each individual resistance
3. Add the reciprocals together to find the sum of the reciprocals
4. Take the reciprocal of the sum to obtain the total equivalent resistance (R_T)

Example Calculation

Let's walk through an example calculation using our parallel resistance calculator:

Given:

• R₁ = 10 Ω
• R₂ = 20 Ω
• R₃ = 30 Ω

Step 1: Calculate the reciprocals of the individual resistances:

\[\frac{1}{R_1} = \frac{1}{10} = 0.1\] \[\frac{1}{R_2} = \frac{1}{20} = 0.05\] \[\frac{1}{R_3} = \frac{1}{30} = 0.0333\]

Step 2: Add the reciprocals together:

\[\frac{1}{R_T} = 0.1 + 0.05 + 0.0333 = 0.1833\]

Step 3: Take the reciprocal of the sum to find the total equivalent resistance:

\[R_T = \frac{1}{0.1833} = 5.45 \text{ Ω}\]

Therefore, the total equivalent resistance of the three parallel resistors in this example is approximately 5.45 ohms.

Parallel Resistors Diagram

This diagram illustrates resistors connected in parallel. The total equivalent resistance is always less than the smallest individual resistance in the parallel network.