Serial Connected Capacitors

Serial Connected Capacitors are serially connected when connected to each other on a single line. The charging current for serially connected capacitors (iC flowing from the capacitor) is the same in all of them.

All serially connected capacitors have the same current as iT = i1 = i2 = i3. Therefore, each capacitor will store the same amount of electric charge Q on its plates, regardless of its capacitance.This is because anythe load stored by the capacitor's platemust have come from the capacitor's license plate.Therefore, serially connectedcapacitors must have the same load.

Q T = Q 1 = Q 2 = Q 3 ….vb

Serial Connected Capacitors
Serial Connected Capacitors

In the previous parallel circuit, we found that the total capacitance of the circuit was equal to the sum of all individual capacitors added together with CT.However, in a series-dependent circuit, the total or equivalent capacitance cT is calculated differently.

As a result, the active plate area depends on the smallest individual capacitanceconnected to the serial chain.Therefore, the voltage drop on each capacitor will differ depending on the individual capacitance values.

We then apply Kirchhoff's Voltage Law (KVL) to the above circuit to obtain:

Serial Connected Capacitors

He continued:

Serial Connected Capacitors

After dividing each section by QT, we have such an equation:

Serial Connected Capacitors
Serial Connected Capacitors

When bringingcapacitors together in series, all individual capacitors (1/C) are collected (just like parallel resistors) instead of the capacitance itself.Then the total value of capacitors in the series is equal to the sum of the reciprocal of individual capacitances.

Serial Connected Capacitors Question Example 1

Taking the value of three capacitors from the example above, we can calculate the total capacitance, C T,for the three capacitors in the series as follows:

Serial Connected Capacitors

An important point to note is that in serial connected capacitor circuits, the total circuit capacitance will always be smaller than the value of the smallest capacitor. If we examine this topic from the example above, the calculated total capacitance = CT = 0.055μF, and the smallest capacitor value is 0.1μF.

This method of mutual calculation can be used to calculate any number of independent capacitors connected to each other in a single serial network.However, if there are only two capacitors in series, a much simpler and faster formula can be used and given as follows:

Serial Connected Capacitors

Two series-boundIf the capacitor is equal and of the same value, that is: C 1 = C 2 , we can further simplify the equation above to find the total capacitance of the series combination as follows.

Serial Connected Capacitors

Then we can see that if only two series of connected capacitors are the same and equal, then the total capacitance, CT, will be exactly half the value of capacitance, that is: C/2 .

With serially connected resistors, the sum of all voltage drops during the series circuit will be equal to the applied voltage VS(Kirchhoff's Voltage Law) and also applies to capacitors in this series.

Series connectedIn capacitors, capacitive reactance of the capacitor acts as an impedance due to the feeding frequency.This capacitive reassurancethe capacitor produces a voltage drop, so the seriescapacitors act as a capacitive voltage dividing network.

As a result, the voltage divider formula applied to the resistors isit can also be used to find separate voltages for the capacitor.

Serial Connected Capacitors

Where: CX is the capacitor, VS is the feed voltage along the serial chain, and VCX is the voltage drop along the target capacitor.

Serial Connected Capacitors Question Example 2

When connected to the 12V AC feed, find total capacitance and individual rms voltage drops in the following series connected two capacitor sets:

  • a) two capacitors, each with a capacitance of 47nF
  • b) 470nF capacitor rseri connected to 1μF capacitor

a) Total Self-Worth Capacity,

Serial Connected Capacitors

Voltage drop along two identical 47nF capacitors,

Serial Connected Capacitors

b) Total Non-Core Capacity,

Serial Connected Capacitors

Voltage drop between two non-identical capacitors: C 1 = 470nF and C 2 = 1μF .

Serial Connected Capacitors
Serial Connected Capacitors

Since Kirchhoff's voltage law applies to this and every circuit connected to the series, the sum of individual voltage drops will be equal in value to the feed voltage, VS = 8.16 + 3.84 = 12V .

Also, if the capacitor values are the same in our first example, 47nF , as the supply voltage is shown, eachwill be divided evenly into the capacitor.This is because everythe capacitor shares an equal and complete load amount ( Q = C x V = 0.564μC) and therefore half (or more than two) of the voltage appliedpercentage fraction for capacitor), VS.

However, the serieswhen capacitor values are different, the largerthe capacitor itself to a lower voltage, smaller valuethe capacitor will charge to a higher voltage, and in our second example above it is shown to be 3.84 and 8.16 volts, respectively.This difference in voltage,allows each capacitor to hold the same amount of Q load on its plates, as shown by the capacitors.

Serial Connected Capacitors

Two series-boundNote that the proportions of voltage drops between the capacitors will always remain the same regardless of the feeding frequency, regardless of their reassurance, XC will remain proportionally the same.

Then in our simple example, the two voltage drops of 8.16 volts and 3.84 volts above will remain the same even if the feed frequency is increased from 100Hz to 100kHz.

For different capacitance values, eachalthough the voltage drops on the capacitor are different, allSince capacitors are fed in the same number or quantity, the Coulomb load between the plates will be equal, since the same amount of current flow is present during a series of circuits.

In other words, because Q is fixed, eachif the load on the capacitor plate is the same, as the capacitance decreasesvoltage drop increases along the capacitor plates, since the load is larger than the capacitance.Similarly, a larger capacitance will cause a smaller voltage drop along the plates, since the load is small compared to capacitance.

Summarize

The total or equivalent capacitance of a circuit containing serially connected capacitors, CT, is the opposite of the sum of the reciprocal of all individual capacitances added together.

Since the load ( Q ) is equal and constant,the voltage drop on the capacitor is determined only by the value of the capacitor in V = Q ÷ C.A small capacitance value causes a larger voltage, while a large capacitance value causes a smaller voltage drop.

An important point to make is that in serial connected capacitor circuits, the total circuit capacitance will always be smaller than the value of the smallest capacitor.