Calculate the total capacitance of capacitors connected in series.
Total Capacitance (Ctotal)
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Understanding Series Capacitors and the Calculation
Capacitors are fundamental electronic components used to store electrical energy in an electric field. They are typically measured in Farads (F). When multiple capacitors are connected in series, their combined capacitance is less than the capacitance of any individual capacitor. This calculator helps you determine the total equivalent capacitance for capacitors wired in series.
The Physics of Series Capacitors
When capacitors are connected in series, they are placed end-to-end, forming a single path for charge to flow. The key principle here is that the same amount of charge (Q) accumulates on each capacitor plate. However, because they share the same charge but are separated, the voltage across each capacitor is different, and their sum equals the total applied voltage (Vtotal = V1 + V2 + … + Vn).
Recall the relationship between capacitance (C), charge (Q), and voltage (V): C = Q / V. Rearranging this, we get V = Q / C.
For capacitors in series:
Vtotal = V1 + V2 + ... + Vn
Substituting V = Q / C for each capacitor:
Q / Ctotal = Q / C1 + Q / C2 + ... + Q / Cn
Since the charge (Q) is the same for all capacitors in series, we can divide both sides by Q:
1 / Ctotal = 1 / C1 + 1 / C2 + ... + 1 / Cn
This is the fundamental formula for calculating the total capacitance of capacitors connected in series. The reciprocal of the total capacitance is equal to the sum of the reciprocals of the individual capacitances.
How This Calculator Works
This calculator implements the formula above. You can enter the capacitance values for up to four capacitors. If you have fewer than four, you can leave the optional fields blank. The calculator will sum the reciprocals of the entered capacitance values, and then take the reciprocal of that sum to provide the total equivalent capacitance in Farads.
For example, if you have two capacitors, C1 = 10µF (10 x 10-6 F) and C2 = 22µF (22 x 10-6 F):
The reciprocals are: 1 / (10 x 10-6 F) = 100,000 F-1 and 1 / (22 x 10-6 F) = 45,454.55 F-1.
Sum of reciprocals: 100,000 + 45,454.55 = 145,454.55 F-1.
Total Capacitance (Ctotal): 1 / 145,454.55 F-1 ≈ 6.87 x 10-6 F, or 6.87µF.
Notice that the resulting capacitance (6.87µF) is smaller than either of the individual capacitances (10µF and 22µF), as expected for series connections.
Use Cases for Series Capacitors
Voltage Multipliers: Specific voltage multiplier circuits (like Cockcroft-Walton generators) use capacitors in series to achieve higher DC voltages.
Filtering and Smoothing: In power supply circuits, series capacitors can be part of filtering networks, though parallel configurations are more common for increasing capacitance.
Frequency Response Shaping: In audio circuits and signal processing, series capacitors can block DC current while allowing AC signals to pass, influencing the circuit's frequency response.
Improving Voltage Rating: By connecting capacitors in series, the total voltage rating of the combination increases, allowing the circuit to handle higher voltages than a single capacitor could.
function calculateSeriesCapacitance() {
var c1 = parseFloat(document.getElementById("capacitor1").value);
var c2 = parseFloat(document.getElementById("capacitor2").value);
var c3 = parseFloat(document.getElementById("capacitor3").value);
var c4 = parseFloat(document.getElementById("capacitor4").value);
var validInputs = [];
if (!isNaN(c1) && c1 > 0) validInputs.push(c1);
if (!isNaN(c2) && c2 > 0) validInputs.push(c2);
if (!isNaN(c3) && c3 > 0) validInputs.push(c3);
if (!isNaN(c4) && c4 > 0) validInputs.push(c4);
if (validInputs.length === 0) {
document.getElementById("result").innerText = "Please enter at least one valid capacitance value.";
return;
}
var reciprocalSum = 0;
for (var i = 0; i < validInputs.length; i++) {
reciprocalSum += (1 / validInputs[i]);
}
if (reciprocalSum === 0) {
document.getElementById("result").innerText = "Calculation Error: Sum of reciprocals is zero.";
return;
}
var totalCapacitance = 1 / reciprocalSum;
// Format the output for better readability, especially for very small or large numbers
var formattedCapacitance;
if (totalCapacitance < 1e-9) { // Less than 1 nanoFarad
formattedCapacitance = totalCapacitance.toExponential(3) + " F";
} else if (totalCapacitance < 1e-6) { // Less than 1 microFarad
formattedCapacitance = (totalCapacitance * 1e9).toFixed(3) + " nF";
} else if (totalCapacitance < 1e-3) { // Less than 1 milliFarad
formattedCapacitance = (totalCapacitance * 1e6).toFixed(3) + " µF";
} else {
formattedCapacitance = totalCapacitance.toFixed(3) + " mF";
}
document.getElementById("result").innerText = formattedCapacitance;
}