Devices called capacitors are used to store electrical energy as an electric field. We frequently utilise several capacitors in many circuits. Depending on the needs, there are several ways to connect these capacitors. Capacitors are most frequently combined in two ways.
Series Combination
Parallel Combination
Capacitors in Series
A series combination is created when capacitors are connected one after the other so that the same charge passes through each one.
Combination of Capacitors
Key Points:
Each capacitor receives the same charge (Q), and the capacitors split the potential difference (V).
• The combination’s equivalent capacitance is lower than the series’ smallest capacitor.
Formula:
For capacitors C1,C2,C3 in series:
1Ceq = 1 / C1 + 1 / C2 + 1 / C3 +…
Example:
If C1 = 4 μF, C2 = 6 μF
1Ceq = 1 / 4 + 1 / 6 = 5 / 12 ⇒ Ceq =12 / 5 =2.4 μF
Capacitors in Parallel
Capacitors are called in a parallel combination when they are placed next to each other and have the same two points connected to their terminals.
Key Points:
The potential difference (V) across each capacitor is the same.
The charge (Q) gets divided among the capacitors.
The equivalent capacitance is the sum of the individual capacitances.
Formula:
For capacitors C1, C2, C3 in parallel:
Ceq = C1 + C2 + C3 +…
Example:
If C1 = 2 μF, C2 = 3 μF, then:
Ceq = 2 + 3 = 5 μF
Energy Stored in a Capacitor
The energy (U) stored in a capacitor is given by:
U = 1 / 2CV2
This energy depends on both the capacitance and the voltage applied.
Why Combine Capacitors?
There are several reasons why capacitors are combined:
To obtain a required value of capacitance.
To control the voltage distribution.
To share the load in a circuit.
To improve the performance or reliability of electronic devices.
Tips to Remember:
Combination Type | Charge (Q) | Voltage (V) | Capacitance (Cₑq) |
Series | Same for all | Divided | 1 / Ceq = 1 / Ci |
Parallel | Divided | Same for all | Ceq = Ci |
Mixed (Series + Parallel) Combinations
Capacitors can be connected in parallel or series in actual circuits. To address these issues:
1. Determine parallel groupings or simple series.
Determine their capacitance equivalent.
3. Use a single capacitor in their stead.
4. Continue until we obtain one last capacitance that is comparable.
Example Problem:
Q: Find the equivalent capacitance of the following combination:
C1 = 2 μF, C2 = 2 μF in series.
Their combination is in parallel with C3 = 3 μF.
Solution:
First, find the series combination:
1 / Cseries = 1 / 2 + 1 / 2 = 2 / 2 ⇒ Cseries = 1 μF
Now, add this to the parallel capacitor:
Ceq = Cseries + C3 = 1 + 3 = 4 μF
Summary
Designing and analysing circuits is much easier when one understands how capacitors work together. In parallel, the voltage stays constant while the charge divides, while in series, the charge stays constant while the voltage divides.
In a series combination, capacitors are connected end-to-end, and the same charge flows through each capacitor while voltage divides. In a parallel combination, capacitors are connected across the same two points, so the voltage remains the same across all, but the charge gets divided among them.
The formula for capacitors in series is:
1 / Ceq = 1 / C1 + 1 / C2 + 1 / C3+…
The equivalent capacitance is always less than the smallest individual capacitor in the series.
The formula for capacitors in parallel is:
Ceq = C1 + C2 + C3+…
The equivalent capacitance is always greater than the largest individual capacitor in the parallel group.
The total energy stored depends on the equivalent capacitance and the voltage across it. It is given by:
U = 1 / 2 CeqV2
Energy is redistributed based on the combination and voltage applied.
Capacitor combinations allow us to:
Achieve desired capacitance values not available as single capacitors,
Control voltage distribution,
Improve performance,
Share load or reduce the stress on individual capacitors.
Yes, in most practical circuits, mixed combinations (a combination of series and parallel) are common. To solve such problems, simplify the circuit step-by-step, combining series and parallel groups successively.
In a series combination, all capacitors carry the same charge.
In a parallel combination, the total charge divides among capacitors based on their capacitance values: