Series Capacitor Voltage Calculator and Formula

A series capacitor voltage calculator estimates the voltage across each capacitor when capacitors are connected in series and the total applied voltage is known. Enter the total voltage and each capacitance; the calculator returns each capacitor’s voltage, along with the equivalent capacitance and stored charge for an ideal series string.

Formula

For two ideal capacitors in series, both capacitors carry the same charge. Since a capacitor’s voltage is charge divided by capacitance, the smaller capacitance receives the larger share of the total voltage.

• Capacitor 1 voltage: V₁ = V × C₂ / (C₁ + C₂)
• Capacitor 2 voltage: V₂ = V × C₁ / (C₁ + C₂)
• Equivalent capacitance: Cₑq = C₁C₂ / (C₁ + C₂)
• Charge: Q = Cₑq × V

Here, V is the total applied voltage in volts (V), C₁ and C₂ are capacitances in microfarads (uF), V₁ and V₂ are the individual voltages in volts, Cₑq is equivalent capacitance in uF, and Q is charge in microcoulombs (uC). The input capacitance units can be any common unit as long as both values use the same unit; the displayed charge unit corresponds to the calculator’s uF inputs because 1 uF × 1 V = 1 uC. The formula assumes the entire specified voltage is across the capacitor string.

Worked Example

Use the defaults: total voltage V = 12 V, C₁ = 10 uF, and C₂ = 20 uF.

1. Find the total capacitance denominator: C₁ + C₂ = 10 + 20 = 30 uF.
2. Calculate capacitor 1 voltage: V₁ = 12 × 20 / 30 = 8.00 V.
3. Calculate capacitor 2 voltage: V₂ = 12 × 10 / 30 = 4.00 V.
4. Calculate equivalent capacitance: Cₑq = 10 × 20 / 30 = 6.667 uF.
5. Calculate charge: Q = 6.667 × 12 = 80.000 uC.

The voltage checks: 8.00 V + 4.00 V = 12.00 V. The results are rounded to the precision specified in the calculator.

How Series Voltage Division Works

In a series connection, the same charge passes onto each capacitor plate pair. The voltage across each one is Q/C, so equal charge does not mean equal voltage unless the capacitances are equal. A 10 uF capacitor therefore has twice the voltage of a 20 uF capacitor in the example.

For n capacitors, the general relationship is 1/Cₑq = 1/C₁ + 1/C₂ + … + 1/Cₙ. The voltage on capacitor i can be found from Vᵢ = V × Cₑq/Cᵢ. This calculator accepts two capacitors to keep its inputs straightforward; for a longer string, calculate the equivalent capacitance and apply the same charge-based relationship, or calculate each voltage from the reciprocal-capacitance sum. The individual voltage drops should add to the total.

When to Use the Calculator

Use it for an idealized DC series string when you know the total voltage and the capacitance values. It is useful for checking a textbook problem, understanding how capacitance affects voltage division, or estimating the steady-state division in a simple circuit. Enter capacitances using the same unit, such as uF for both; do not enter one value in uF and the other in nF without converting.

For example, 0.01 uF equals 10 nF. If the two capacitances are equal, each ideally receives half the total voltage. If they differ, the lower value receives a larger share. The equivalent capacitance of series components is always less than the smallest individual capacitance.

Important Limits and Real-World Effects

The calculation is an ideal steady-state result, not a complete prediction of a circuit. Component tolerance means the actual capacitance can differ from its marked value, changing the voltage division. Leakage current, dielectric behavior, temperature, frequency, and circuit connections can also affect real measurements. In particular, the two-capacitor formula does not model transient switching or AC impedance in a complete circuit.

Do not assume that a capacitor’s voltage rating can be selected by dividing the total voltage evenly. Unequal capacitors may receive unequal voltages, and real components can share voltage differently from the ideal calculation. Capacitor selection, balancing components, discharge practices, and voltage ratings are design and safety matters; consult the component documentation and a qualified electronics professional for an actual circuit. Stored charge can remain after power is removed.

Common Mistakes

• Assuming equal voltage: Equal sharing applies only to equal capacitances under the ideal model.
• Mixing units: Convert nF, uF, and F to a common unit before comparing values or calculating.
• Using a parallel formula: In series, reciprocals add; in parallel, capacitances add directly.
• Ignoring the total: The individual voltage results should add to the voltage actually across the string, not necessarily the supply voltage if other circuit elements are in series.
• Reading extra decimals as certainty: Calculator precision does not remove component tolerance or measurement uncertainty.

Frequently Asked Questions

How do you calculate voltage across capacitors in series?
For two ideal capacitors, multiply the total voltage by the other capacitor’s capacitance and divide by the sum of both capacitances. The smaller capacitor gets the larger voltage share.

Do capacitors in series have the same voltage?
No. They carry the same charge in the ideal series model, but their voltages depend on capacitance. Equal capacitances produce equal voltage drops; unequal values do not.

What happens if the capacitors have different capacitances?
The lower-capacitance capacitor has the higher voltage. The voltage ratio is inverse to the capacitance ratio: V₁/V₂ = C₂/C₁.

How do I find the equivalent capacitance in series?
For two capacitors, use Cₑq = C₁C₂/(C₁ + C₂). For multiple capacitors, add their reciprocals and take the reciprocal of that sum.

Can I use this for AC circuits?
The equations describe ideal capacitors under a steady applied voltage and do not by themselves analyze a full AC circuit. AC behavior depends on frequency, component characteristics, and the rest of the circuit.

Related

• Muscle Legends Events Schedule & Times
• OnePlus Pixel Mysterious Device on Benchmark Site?
• Convert FAT to NTFS: Guide & Steps

in v | Total voltage | V | 12 | 0
in c1 | Capacitor 1 capacitance | uF | 10 | 0.000001
in c2 | Capacitor 2 capacitance | uF | 20 | 0.000001
out v1 | Capacitor 1 voltage | V | v * c2 / (c1 + c2) | 2
out v2 | Capacitor 2 voltage | V | v * c1 / (c1 + c2) | 2
out ceq | Equivalent capacitance | uF | c1 * c2 / (c1 + c2) | 3
out q | Series charge | uC | ceq * v | 3