Calculate total resistance for resistors in series or parallel circuits.
Total Resistance:
—Ω
Understanding Series and Parallel Resistance
Electrical circuits are fundamental to how we use electricity. Resistors are components that impede the flow of electric current. The way resistors are connected in a circuit significantly impacts the overall resistance and thus the current and voltage distribution. This calculator helps you determine the equivalent resistance for resistors connected in either a series or a parallel configuration.
Resistors in Series
When resistors are connected in series, they are arranged end-to-end, forming a single path for the current to flow. The current must pass through each resistor sequentially. To find the total equivalent resistance (Rtotal) of resistors in series, you simply add up the individual resistances:
Rtotal = R1 + R2 + R3 + ... + Rn
In a series circuit:
The total resistance is always greater than the largest individual resistance.
The current is the same through each resistor.
The voltage drops across each resistor add up to the total voltage.
Example: If you have three resistors in series with values of 100 Ω, 220 Ω, and 330 Ω, the total resistance would be:
Rtotal = 100 Ω + 220 Ω + 330 Ω = 650 Ω
Resistors in Parallel
When resistors are connected in parallel, they are connected across the same two points, providing multiple paths for the current to flow. The total current from the source splits and flows through each parallel branch. To find the total equivalent resistance (Rtotal) of resistors in parallel, you use the reciprocal of the sum of the reciprocals of the individual resistances:
For a circuit with only two resistors in parallel, a simplified formula can be used: Rtotal = (R1 * R2) / (R1 + R2
In a parallel circuit:
The total resistance is always less than the smallest individual resistance.
The voltage is the same across each parallel branch.
The total current is the sum of the currents through each branch.
Example: If you have three resistors in parallel with values of 100 Ω, 220 Ω, and 330 Ω, the calculation is:
1 / Rtotal = 1 / 100 Ω + 1 / 220 Ω + 1 / 330 Ω
1 / Rtotal = 0.01 + 0.004545... + 0.003030...
1 / Rtotal = 0.017575...
Rtotal = 1 / 0.017575... ≈ 56.89 Ω
Use Cases
Understanding and calculating equivalent resistance is crucial for:
Circuit Design: Engineers use these calculations to design circuits that meet specific current and voltage requirements.
Troubleshooting: Identifying faults in circuits often involves measuring or calculating expected resistance values.
Component Selection: Choosing the right resistors for a particular application depends on the desired overall resistance.
Power Distribution: Analyzing how power is distributed in a network of resistors.
This calculator simplifies these calculations, making them accessible for students, hobbyists, and professionals alike.
function toggleInputFields() {
var circuitType = document.querySelector('input[name="circuitType"]:checked').value;
var seriesInputs = document.getElementById('seriesInputs');
var parallelInputs = document.getElementById('parallelInputs');
if (circuitType === 'series') {
seriesInputs.style.display = 'block';
parallelInputs.style.display = 'none';
} else {
seriesInputs.style.display = 'none';
parallelInputs.style.display = 'block';
}
}
function calculateResistance() {
var circuitType = document.querySelector('input[name="circuitType"]:checked').value;
var totalResistanceValue = 0;
var isValid = true;
if (circuitType === 'series') {
var r1 = parseFloat(document.getElementById('r1').value);
var r2 = parseFloat(document.getElementById('r2').value);
var r3 = parseFloat(document.getElementById('r3').value);
if (isNaN(r1) || r1 < 0) { isValid = false; alert("Please enter a valid positive resistance for Resistor 1 (Series)."); }
if (isNaN(r2) || r2 = 0) {
totalResistanceValue += r3;
} else if (document.getElementById('r3').value !== "") {
// User entered something, but it's invalid, and not empty
isValid = false;
alert("Please enter a valid positive resistance for Resistor 3 (Series) or leave it blank.");
}
}
} else { // Parallel
var p1 = parseFloat(document.getElementById('p1').value);
var p2 = parseFloat(document.getElementById('p2').value);
var p3 = parseFloat(document.getElementById('p3').value);
if (isNaN(p1) || p1 <= 0) { isValid = false; alert("Please enter a valid positive resistance for Resistor 1 (Parallel)."); }
if (isNaN(p2) || p2 0) {
reciprocalSum += (1 / p3);
} else if (document.getElementById('p3').value !== "") {
// User entered something, but it's invalid, and not empty
isValid = false;
alert("Please enter a valid positive resistance for Resistor 3 (Parallel) or leave it blank.");
}
if (reciprocalSum === 0) { // Avoid division by zero if all inputs were somehow 0 (though checked above)
isValid = false;
alert("Sum of reciprocals cannot be zero.");
} else {
totalResistanceValue = 1 / reciprocalSum;
}
}
}
if (isValid) {
document.getElementById('totalResistance').textContent = totalResistanceValue.toFixed(2); // Display with 2 decimal places
} else {
document.getElementById('totalResistance').textContent = '–'; // Reset if invalid input
}
}
// Initialize the display based on the default checked radio button
document.addEventListener('DOMContentLoaded', toggleInputFields);