Capacitors in Series Calculator
Calculate equivalent capacitance, charge, voltage distribution, and energy stored for up to four capacitors connected in series.
Enter capacitance values for two to four capacitors and the total applied voltage to compute equivalent capacitance, charge, voltage across each capacitor, and total energy.
Capacitors in Series Calculator
Calculate equivalent capacitance, charge, voltage distribution, and energy stored for up to four capacitors connected in series.
Worked Examples
Click an example to load it into the calculator.
| Capacitor Configuration | Calculated Results | Application |
|---|---|---|
| C₁ = C₂ = 1 μF, V = 10 V | Ceq = 0.5 μF, V₁ = V₂ = 5 V, Q = 5 μC, E = 25 μJ | Two equal capacitors halve the capacitance and share voltage equally — classic for voltage-doubling circuits. |
| C₁ = 1 μF, C₂ = 2 μF, C₃ = 3 μF, V = 15 V | Ceq ≈ 0.545 μF, V₁ ≈ 8.18 V, V₂ ≈ 4.09 V, V₃ ≈ 2.73 V | Voltage divider: smaller capacitor receives higher voltage, confirming V ∝ 1/C. |
| C₁ = C₂ = C₃ = C₄ = 1 μF, V = 100 V | Ceq = 0.25 μF, each capacitor sees 25 V, E = 1.25 mJ | Four series capacitors distribute 100 V across four 25 V-rated components — a standard high-voltage technique. |
| C₁ = 1 μF, C₂ = 5 μF, V = 24 V | Ceq ≈ 0.833 μF, V₁ = 20 V, V₂ = 4 V, Q = 20 μC | Unequal capacitors: the 1 μF capacitor dominates, taking 83 % of the applied voltage. |
About the Capacitors in Series Calculator
When capacitors are connected in series — end-to-end in a single current path — they behave very differently from parallel connections. Understanding series capacitor behaviour is essential for voltage divider design, high-voltage applications, and AC coupling circuits.
The fundamental property of series-connected capacitors is that they all carry the same charge Q. When the circuit is energised, charge accumulates on the first capacitor's plate, inducing an equal and opposite charge on its second plate, which in turn induces charge on the adjacent capacitor, and so on. Since the same charge Q appears on every capacitor, the voltage across each is V_i = Q / C_i. Capacitors with smaller capacitance therefore develop higher voltage, which is the key insight for voltage divider design.
The equivalent (total) capacitance of n series capacitors is given by the reciprocal sum: 1/Ceq = 1/C₁ + 1/C₂ + ... + 1/Cₙ. Equivalently, Ceq is always less than the smallest individual capacitor. This can be understood physically: in series, the effective plate separation increases (the sum of all individual separations), while the plate area stays the same, reducing capacitance. For two capacitors the formula simplifies to Ceq = C₁C₂/(C₁+C₂), sometimes called the product-over-sum rule.
The total charge stored is Q = Ceq × V_total. Once Q is known, the voltage across each capacitor is V_i = Q / C_i, and the sum V₁ + V₂ + ... must equal V_total — a useful check. The total energy stored is E = ½ × Ceq × V_total², which is the same as the sum of individual energies ½ × C_i × V_i² since all charges are equal.
Practical applications include: (1) Voltage dividers for precision measurement circuits and signal conditioning, where the capacitor ratio sets the output voltage fraction. (2) High-voltage applications where a single capacitor's voltage rating is insufficient — series stacking distributes the voltage. (3) AC coupling (blocking capacitors) in audio and communication circuits, where the series combination creates a high-pass response. (4) Switched-capacitor circuits in power electronics, where series and parallel configurations are dynamically switched to achieve voltage conversion.
A critical practical consideration is voltage balancing. In a real circuit, component tolerances, leakage currents, and parasitic effects can cause the voltage to distribute unevenly — potentially exceeding the rated voltage of one capacitor. For high-voltage series stacks, equalising resistors (typically 1 MΩ to 10 MΩ) are placed in parallel with each capacitor to ensure long-term DC voltage balance.
How to Use the Capacitors in Series Calculator
- Enter the capacitance of the first capacitor (C₁) in farads. For microfarad values use 0.000001 (or 1e-6), for nanofarads use 0.000000001 (or 1e-9).
- Enter the capacitance of the second capacitor (C₂). At least C₁ and C₂ are required; C₃ and C₄ are optional — leave them blank to use a two- or three-capacitor series.
- Enter the total voltage applied across the entire series combination. This is the supply voltage the circuit will see.
- Click Calculate. The results show the equivalent capacitance, the shared charge, the energy stored, and the voltage distribution across each individual capacitor.
- Verify that the voltage across each capacitor does not exceed its rated voltage. If any capacitor receives more voltage than it can handle, increase its capacitance, use a higher-rated part, or add equalising resistors for DC balance.
Frequently Asked Questions
Why is the equivalent capacitance less than the smallest capacitor?
In a series connection, the physical effect is equivalent to increasing the total plate separation while keeping the plate area constant. Since capacitance C = ε₀εᵣA/d decreases with distance d, a larger total separation means smaller total capacitance. Mathematically, the reciprocal sum 1/Ceq = 1/C₁ + 1/C₂ + ... always produces a Ceq smaller than any individual term.
How is voltage distributed across capacitors in series?
Voltage distributes inversely proportional to capacitance: V_i = Q / C_i, where Q is the common charge. A capacitor with half the capacitance receives twice the voltage. For equal capacitors, voltage is shared equally. For unequal capacitors, the smallest capacitor dominates — it limits the total capacitance and takes the largest share of voltage. Always check that the calculated voltage on each capacitor is below its individual voltage rating.
What is the charge Q and why is it the same for all capacitors?
In series, the capacitors form a single loop without any branching paths for charge. Charge builds up on the outer plates of the series combination, and the electrostatic induction forces equal and opposite charges on all inner plates. As a result, each capacitor stores exactly the same charge Q = Ceq × V_total. This shared-charge property is the defining characteristic of series connections, in contrast to parallel connections where voltage is shared but charge adds.
What is the difference between series and parallel capacitor connections?
In series, capacitance decreases (Ceq < smallest C), charge is shared, voltage adds up. In parallel, capacitance adds up (Ceq = C₁ + C₂ + ...), voltage is shared equally, charges add. Series connections are used when you need to handle higher voltages or build a voltage divider. Parallel connections are used when you need more total capacitance or lower equivalent series resistance.
Do capacitors in series add energy storage?
No — series capacitors reduce the total capacitance, which reduces energy storage at the same voltage (E = ½CV²). If you need more energy storage, parallel connection is the right approach. Series connection sacrifices energy density in exchange for higher voltage handling and voltage-divider functionality.
Why do high-voltage circuits use capacitors in series?
If a required voltage exceeds the rating of available capacitors, connecting them in series distributes the voltage so no single capacitor exceeds its limit. For example, four 25 V-rated capacitors in series can handle 100 V total. In practice, balance resistors are added in parallel to ensure DC voltage is shared equally despite component tolerances and leakage differences.
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