Welcome to the Parallel Resistor Calculator. Quickly determine the total equivalent resistance ($R_{eq}$) of up to five resistors connected in a parallel circuit using the reciprocal formula.
Parallel Resistor Calculator
Calculation Steps
Parallel Resistor Calculator Formula
The total equivalent resistance ($R_{eq}$) for resistors connected in parallel is calculated using the reciprocal formula:
$$ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + … + \frac{1}{R_n} $$
Alternatively, the equivalent resistance is the reciprocal of the sum of the conductances:
$$ R_{eq} = \frac{1}{\sum_{i=1}^{n} \frac{1}{R_i}} $$
Formula Source: Wikipedia: Series and parallel circuits | All About Circuits: Parallel Circuits
Variables Used in the Calculator
- Resistor 1 to 5 ($R_n$): The resistance value of each individual resistor in Ohms ($\Omega$). Must be a positive value.
- Equivalent Resistance ($R_{eq}$): The single resistance value that could replace the entire parallel network, in Ohms ($\Omega$).
What is a Parallel Resistor Circuit?
A parallel circuit is characterized by having all components connected across the same two points, creating multiple paths for current to flow. In contrast to a series circuit, where resistance values are simply summed up, the addition of a new resistor in a parallel configuration always decreases the total equivalent resistance.
This decrease occurs because adding a parallel path increases the total conductance (the ability of the circuit to conduct electricity), thus lowering the overall resistance. The equivalent resistance of a parallel circuit will always be less than the smallest individual resistance value in the circuit. This calculator automates the reciprocal calculation required to find $R_{eq}$.
This type of configuration is widely used in household wiring, where all electrical devices are connected in parallel to ensure they all receive the full line voltage (e.g., 120V or 230V).
How to Calculate Equivalent Resistance (Example)
Let’s find the equivalent resistance ($R_{eq}$) for three resistors: $R_1 = 100 \Omega$, $R_2 = 50 \Omega$, and $R_3 = 200 \Omega$.
- Step 1: Find the reciprocal of each individual resistance (Conductance). $$ \frac{1}{R_1} = \frac{1}{100} = 0.01 $$ $$ \frac{1}{R_2} = \frac{1}{50} = 0.02 $$ $$ \frac{1}{R_3} = \frac{1}{200} = 0.005 $$
- Step 2: Sum the reciprocals. $$ \frac{1}{R_{eq}} = 0.01 + 0.02 + 0.005 = 0.035 $$
- Step 3: Take the reciprocal of the total sum to find the Equivalent Resistance ($R_{eq}$). $$ R_{eq} = \frac{1}{0.035} \approx 28.5714 \Omega $$
Frequently Asked Questions (FAQ)
Is there a simpler formula for only two parallel resistors?
Yes. For only two resistors ($R_1$ and $R_2$), you can use the product-over-sum rule: $$ R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2} $$
Why is the equivalent resistance always lower than the smallest resistor?
Adding a parallel path provides an alternative route for the current, effectively increasing the total cross-sectional area for electron flow. This increase in total conductivity inherently leads to a decrease in overall resistance.
What is the unit of measurement for resistance?
Resistance is measured in Ohms, symbolized by the Greek capital letter Omega ($\Omega$). It is named after the German physicist Georg Simon Ohm.
What is the opposite of resistance?
The opposite of resistance is conductance, which is the ease with which current flows through a material. Conductance is measured in Siemens (S), which is the reciprocal of the Ohm ($1/\Omega$).
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