Calculate the total resistance of resistors connected in parallel.
<!– Example:
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Total Resistance in Parallel:
— Ω
Understanding Parallel Resistor Calculations
In electrical circuits, components can be connected in series or in parallel.
When resistors are connected in parallel, the voltage across each resistor is the same,
but the current splits among them. This configuration results in a total resistance
that is always less than the smallest individual resistance in the circuit.
The Formula for Parallel Resistors
The total resistance (Rtotal) of resistors connected in parallel is calculated
using the reciprocal of the sum of the reciprocals of each individual resistance (R1, R2, R3, …).
For two resistors in parallel, the formula simplifies to:
Rtotal = (R1 * R2) / (R1 + R2)
For three or more resistors, the general formula is used:
To find Rtotal, you calculate the sum of the reciprocals and then take the reciprocal of that sum.
How the Calculator Works
This calculator takes the values of two resistors (in Ohms, Ω) connected in parallel and applies the simplified formula
Rtotal = (R1 * R2) / (R1 + R2)
to determine the equivalent total resistance.
If you need to calculate for more than two resistors, you can apply the formula iteratively. For example, to find the total resistance of R1, R2, and R3:
Calculate R1&2 = (R1 * R2) / (R1 + R2)
Then calculate Rtotal = (R1&2 * R3) / (R1&2 + R3)
Alternatively, you can use the general formula:
1 / Rtotal = 1 / R1 + 1 / R2 + 1 / R3
Use Cases
Circuit Design: Engineers use this to determine the overall resistance of a section of a circuit, which impacts current flow and voltage distribution.
Troubleshooting: Identifying potential issues in electronic devices by comparing expected resistance values with measured ones.
Component Selection: Choosing appropriate resistors to achieve a desired total resistance for a specific application.
Educational Purposes: Helping students understand the principles of parallel circuits in physics and electronics.
Example Calculation
Let's calculate the total resistance for two resistors connected in parallel:
As expected, the total resistance (68.75 Ω) is less than the smallest individual resistance (100 Ω).
function calculateParallelResistance() {
var r1 = parseFloat(document.getElementById("resistance1").value);
var r2 = parseFloat(document.getElementById("resistance2").value);
var errorMessageElement = document.getElementById("errorMessage");
var totalResistanceElement = document.getElementById("totalResistance");
// Clear previous error messages
errorMessageElement.textContent = "";
totalResistanceElement.textContent = "– Ω"; // Reset to default
// Input validation
if (isNaN(r1) || isNaN(r2)) {
errorMessageElement.textContent = "Please enter valid numbers for both resistances.";
return;
}
if (r1 <= 0 || r2 <= 0) {
errorMessageElement.textContent = "Resistances must be positive values.";
return;
}
var totalResistance;
// Use the simplified formula for two resistors
totalResistance = (r1 * r2) / (r1 + r2);
// Display the result
if (!isNaN(totalResistance)) {
totalResistanceElement.textContent = totalResistance.toFixed(2) + " Ω"; // Display with 2 decimal places
} else {
errorMessageElement.textContent = "Calculation resulted in an invalid value.";
}
}