How Capacitors are Connected

A capacitor is a component that, like a small rechargeable battery, can retain energy in the shape of an electrical charge that produces a potential difference across its plates. Capacitors come in various sizes and shapes, varying from tiny capacitor beads used in resonance circuits to enormous power converter capacitors. However, they all have a similar goal, to retain energy. Capacitor combinations can be made in many ways. A capacitor can be linked in parallel or series in a circuit. The type of capacitor connection affects the currents and voltages if a set of capacitors is linked in a circuit. Capacitor combinations can be made in many ways, and other more complicated combinations also exist.

When capacitors connect one after the other in a single line, they are connected in a series. It is like a daisy chain of capacitors. Since the charging current follows only one path in such a connection, it is the same across all the capacitors.

Therefore, because the charging current is the same across all the capacitors, the individual capacitors will all be storing an equal amount of charge on their plates irrespective of their capacitance. This is because the charge on one plate of a capacitor comes from the adjacent capacitor’s plate. So, the capacitors connected in a series all carry a similar charge.

 So Q_T = Q₁ = Q₂ = Q₃ ….etc

Capacitors in Series

Consider the combination where the capacitors C₁, C₂ & C₃ connect in series. The 1st capacitor connects to the left plate of the 2nd capacitor. And the right plate of the second plate connects to the left plate of the 3rd capacitor. 

If it is a DC-connected circuit, then it means that the second circuit is isolated. This results in the plate area connecting to the minimum individual capacitance possible in the setup. So, subject to the individual values of the capacitances, every capacitor’s voltage drop will vary. Consequently, if Kirchhoff’s Voltage Law is applied across this circuit, we will obtain

V_total = V_C1 + V_C2 + V_C3 

V_C1 = Q_T/C₁, V_C2 = Q_T/C₂, V_C3 = Q_T/C₃

We know that Q = CxV. So from this, we get that V = Q/C. If V is substituted by it in the above equation, the resulting equation is

V_total = Q_T/C_T = Q_T/C₁ + Q_T/C₂ + Q_T/C₃

The series capacitance equation can be obtained by dividing each term by Q., So the equation is

1/C_T = 1/C₁ + 1/C₂ + 1/C₃ +…etc

From this, we can infer that when capacitors in a series are added together, they are added in reciprocals, so the total value of the capacitance in the series is the sum of the reciprocals of all the capacitors.

Capacitors in Parallel

When both the terminals of a circuit are connected to each terminal of the capacitors, then the capacitors are said to be in parallel. When capacitors are connected in parallel, the voltage across all the capacitors is the same. The capacitors have a standard voltage supply which gives the following equation

V_C1 = V_C2 = V_C3 = V_total 

Let us take an example where C₁, C₂, and C₃ capacitors remain parallel. And the terminals of the circuit are A & B.

In a circuit where capacitors are connected in parallel, the equivalent capacitance of the combination is calculated simply by obtaining the sum of every individual capacitance of the capacitors. The first capacitor’s top plate connects to the second capacitor’s top plate, and this same plate connects to the third capacitor’s top plate. The same holds for the bottom plates as well. This combination results in the plates functioning like one single plate, thus increasing the overall area of the plates.

Thus, we can calculate the whole capacitance of capacitors in parallel, in the same manner, we calculate the total resistance of resistors in parallel. The current in each capacitor in a parallel arrangement is related to the voltage. So, if Kirchhoff’s law is applied to a combination of capacitors arranged parallelly we get full voltage

i₁ = C₁ dv/dt, i₂= C₂ dv/dt, i₃ = C₃ dv/dt, 

i_T = i₁ + i₂ + i₃

Therefore, i_T = C₁ dv/dt + C₂ dv/dt+ C₃ dv/dt, 

It can also be written as the following

i_T = (C₁ + C₂ + C₃) dv/dt,

Or i_T = C_T dv/dt

So, the parallel equation comes to be

C_T = C₁ + C₂ + C₃ +…. etc

Conclusion

A capacitor is a device that is a passive component in an electrical field and is used for storing electrical energy. They are combined to make circuits required for different kinds of voltage outputs. Capacitor combinations can be made in many ways. Two frequently used methods of combination are capacitors combined in a series and capacitors arranged in parallel; for capacitors combined in a series, the equivalent capacitance of the combination decreases, and for capacitors combined in parallel, the capacitance increases.