Basic Electronics On The Go -Capacitors in Series and Parallel

From http://www.electronicshub.org/capacitors-in-series-and-parallel/

Capacitors in series

Capacitors in series meanstwo or more capacitors are connected in a single line i.e positive plate of the one capacitor is connected to the negative plate of the next capacitor. All the capacitors in series have equal charge (Q) and equal charging current (iC).

Consider N- numbers of capacitors are connected in series, then

QT =Q1 = Q2 = Q3 = ———- = QN

IC = I1 = I2 = I3 = ——— = IN

Capacitors in a Series Connection

The following circuits show the series connection of group of capacitors.

series connection of N-number of capacitors.

series connection of two capacitors.

In this circuit the charge (Q) stored in all capacitors is same because every capacitor has the charge which is flowing from the adjacent capacitor. The voltage drop in all capacitors is different from each other. But the total voltage drop applied between input and output lines of the circuit is equal to the sum of all the individual voltage drops of each capacitor. The equivalent capacitance of the circuit is Ceq = Q/V.

Thus,

VT = V1 + V2

Ceq = Q/V1 + Q/V2

1/Ceq = (V1+ V2)/Q

VT = Q/Ceq = Q/C1 + Q/C2

Series Capacitors Equation

1/Ceq = 1/C1 + 1/C2 +……… + 1/CN

When the capacitors are in series connection the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances of the capacitors in the circuit.

From the figure 2, the reciprocal of equivalent capacitance value of the circuit is equal to the sum of reciprocal capacitances values of two capacitors C1 and C2, the expression is given below.

1/Ceq = 1/C1 + 1/C2

Capacitors in Parallel Circuits

Capacitors in parallel means two or more capacitors are connected in parallel way, i.e. both of their terminals are connected to each terminal of the other capacitor or capacitors respectively. All the capacitors which are connected in parallel have the same voltage and is equal to the VT applied between the input and output terminals of the circuit. Then, parallel capacitors have a ‘common voltage’ supply across them .i.e. VT = V1 = V2 etc.

Parallel connection of two capacitors

In  above figure  the total charge (Q) across the circuit is divided between the two capacitors, means the charge Q distributes itself between the capacitors connected in parallel. Because the voltage drop across individual capacitors is equal and also it is equal to the total voltage applied to the circuit. But the total charge Q is equal to the sum of all the individual capacitor charges connected in parallel. i.e. From the above figure the two different capacitors C1 and C2 have two different charges Q1 and Q2 respectively. Here Q=Q1+Q2

Now we see the equivalent capacitance of the capacitors C1 and C2 connected in parallel which shown in  the above figure.

We know the formula,

Q=Ceq VT

Here, Q = Q1+Q2

And VT = V1 = V2

Ceq=Q/VT = (Q1+Q2)/VT = (Q1/VT) + (Q2/VT)

Parallel Capacitors Equation

Ceq = C1+C2+C3+ ———— +CN

The equivalent capacitance of the capacitors which are connected in parallel is equal to the sum of the individual capacitances of the capacitors in the circuit.

From the figure 4, the equivalent capacitance (Ceq) value is equal to the sum of both the capacitance values of C1 and C2, the expression is shown below.

Ceq = C1+C2