Resistors in Parallel Calculator
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Resistors in Parallel Calculator
Total Equivalent Resistance (R_eq)
— Ω
Understanding Resistors in Parallel
When electronic components are connected in parallel, they are wired across each other, meaning they share the same two connection points. This is a fundamental configuration in circuit design. For resistors, connecting them in parallel offers a way to decrease the overall resistance of a section of a circuit. The current from the source splits, with each parallel path receiving a portion of the total current.
The Formula for Resistors in Parallel
The total equivalent resistance (Req) of resistors connected in parallel is calculated using the reciprocal of the sum of the reciprocals of each individual resistance. The formula is as follows:
$$ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + … + \frac{1}{R_n} $$
Where:
- Req is the total equivalent resistance in Ohms (Ω).
- R1, R2, R3, …, Rn are the resistances of each individual resistor in Ohms (Ω).
For the special case of only two resistors in parallel, a simplified formula can be derived:
$$ R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2} $$
This calculator implements the general formula, allowing for any number of resistors to be added.
Key Properties of Parallel Resistors:
- Voltage is the same across all parallel components.
- Current divides among the parallel paths. The path with lower resistance will draw more current.
- The total equivalent resistance is always less than the smallest individual resistance in the parallel combination.
When to Use This Calculator:
- Circuit Design: To determine the overall resistance needed for a specific part of a circuit, or to achieve a desired current division.
- Troubleshooting: To calculate the expected resistance of a parallel section in a circuit.
- Educational Purposes: To quickly verify calculations related to Ohm's Law and parallel circuits.
Example Calculation:
Let's say you have three resistors with the following values:
- R₁ = 100 Ω
- R₂ = 220 Ω
- R₃ = 470 Ω
Using the formula:
$$ \frac{1}{R_{eq}} = \frac{1}{100} + \frac{1}{220} + \frac{1}{470} $$
$$ \frac{1}{R_{eq}} \approx 0.01 + 0.004545 + 0.002128 $$
$$ \frac{1}{R_{eq}} \approx 0.016673 $$
$$ R_{eq} = \frac{1}{0.016673} \approx 59.98 \text{ Ω} $$
The total equivalent resistance is approximately 59.98 Ohms. Notice how this is less than the smallest individual resistor (100 Ω).
var resistorCount = 2; // Start with two resistors
function addResistorInput() {
resistorCount++;
var resistorInputsDiv = document.getElementById('resistorInputs');
var newDiv = document.createElement('div');
newDiv.className = 'input-group';
var newLabel = document.createElement('label');
newLabel.setAttribute('for', 'r' + resistorCount);
newLabel.textContent = 'Resistor ' + resistorCount + ' (R' + resistorCount + '):';
var newInput = document.createElement('input');
newInput.setAttribute('type', 'number');
newInput.setAttribute('id', 'r' + resistorCount);
newInput.setAttribute('placeholder', 'e.g., 100');
newInput.setAttribute('step', 'any');
newInput.setAttribute('min', '0');
newDiv.appendChild(newLabel);
newDiv.appendChild(newInput);
resistorInputsDiv.appendChild(newDiv);
}
function calculateParallelResistance() {
var totalReciprocal = 0;
var inputsAreValid = true;
var errorDiv = document.getElementById('errorMessage');
errorDiv.textContent = "; // Clear previous error messages
for (var i = 1; i <= resistorCount; i++) {
var resistorInput = document.getElementById('r' + i);
var resistanceValue = parseFloat(resistorInput.value);
if (isNaN(resistanceValue) || resistanceValue < 0) {
errorDiv.textContent = "Error: Please enter valid positive numbers for all resistor values.";
inputsAreValid = false;
break;
}
if (resistanceValue === 0) {
// If any resistor is 0 Ohms, the total resistance is effectively 0 Ohms.
// This is because a short circuit (0 Ohms) in parallel with anything else
// will draw all the current, resulting in zero voltage drop across that branch,
// and thus the equivalent resistance seen by the source is 0.
document.getElementById('result').textContent = "0 Ω";
return;
}
totalReciprocal += (1 / resistanceValue);
}
if (inputsAreValid) {
if (totalReciprocal === 0) {
errorDiv.textContent = "Error: Cannot calculate resistance when all values are zero or invalid.";
document.getElementById('result').textContent = "– Ω";
return;
}
var equivalentResistance = 1 / totalReciprocal;
document.getElementById('result').textContent = equivalentResistance.toFixed(2) + " Ω";
} else {
document.getElementById('result').textContent = "– Ω";
}
}