In this article, I will be explaining to you the basic use of capacitors to understand their capacitance. We will be using the RC time constant and coupling circuits for an explanation.

This article is the continuation of the Capacitor Principle working article given before. I’m sure that you have already understood it.

A capacitor is a small device but has great importance in many electronic circuits. They have some principles that are very important and must not be overlooked.

Uses of capacitors _ Capacitance _ RC circuit time constant and Coupling

Connection of series and parallel capacitors

Sometimes we need to use capacitors which have different capacitance from standard values. The adjustable capacitors are not usable for this purpose because of their small size.

This problem can be solved by connecting it in parallel or in series until you get your required capacity.

Parallel Circuit:

We often connect capacitors in parallel as shown in the diagram. For example, in power supplies, filter circuits, etc.

The total capacitance is calculated by the sum of all capacitances.

Parallel Capacitor Circuit

We should not use a lower voltage than our requirement. Otherwise, it will damage the circuit. This capacitor gives the total capacitance of 2000uF to 25V. It is able to withstand high voltage levels. The lowest level that it is able to withstand is 25V.

Take a look at an example. You have to build a DC power supply circuit but it is giving a high ripple because it has a low capacitance filter. Here we need to add more capacitance. Previously, I only had 1000uF 25V and 1,000uF 35V electrolytic capacitor.

Caution: You must not attach the wrong polarity as it will damage the electrolytic capacitor. The wrong electrical connection is created that way.

Series Circuit:

Sometimes we need to connect a capacitor in a series circuit. The total capacitance is calculated in 3 cases as follows;

Two Capacitors
The total capacitance produced by the capacitors is divided by their sum. See the formula below.

Parallel Capacitor Circuit

Three or more capacitors
In the series circuit, the CT is found using this formula. Look below:

More than 3 capacitor series and calculation formula

 

If each capacitor has the same value, the total capacitance is calculated by the value of capacitance divided by N. The N is the number of capacitors that are connected in series.

Each capacitor in the circuit is equal

For example 3 capacitors, 0.1 μF 100V.
CT = 0.1 μF ÷ 3 = 0.33 μF 300V.
Notice We can see that the rate of the voltage of total capacitance increases according to the capacitors. For example, 300V capacitors is gained from 3x100V.

Charge and energy stored

I, unfortunately, don’t like math because the calculations are very confusing at times. The electronics we love is but a big part of science in physics. This type of physics uses a lot of mathematical principles. I believe that difficult things are made up of simple things put together. So we will gradually learn together and improve our concepts.

Total charge (symbol Q) stored on capacitors can be found using the following formula:

Charge Q = C × V

Since
Q = charge in coulomb (C)
C = capacitance in farads (F)
V = Voltage in volts (V)

When they charge, capacitors store energy by:

Energy E = ½QV = ½CV² where E = energy in Joules (J)

Please note that Energy in the capacitor is always returned to the circuit.

It does not convert electrical energy into heat like it does in a resistor. The energy stored by the capacitor is much less than the energy stored in the batteries. Therefore, a capacitor cannot be used as an energy source.

Understand capacitor reactance Xc:

The capacitor reactance (symbol Xc) is the resistance value of the capacitor via AC (Alternating Current). It is measured in ohm.

Reactance is much more complicated than resistance. Its value depends on the frequency (f) of electrical signals passing through the capacitor (C)

Capacitive Reactance Xc = 1 / 2πfC

Since
Xc = reactance in ohms
f = frequency in hertz (Hz)
C = capacitance in Farads (F)

Xc reactance is high when the frequency is low and is low when the frequency is high. The constant DC current has zero frequency so its Xc reactance value is infinite (maximum resistance).

Therefore, because of these reasons capacitors allow AC to pass, but they block DC.

For example
A capacitor of 1µF has a reactance of 3.2kΩ at a frequency of 50Hz but at higher frequencies of almost about 10kHz, there is a reactance of only 16Ω.

Note: The Xc symbol is used to represent the reactance of a capacitor. The XL represents the reactance of the inductor.

The most important difference is that XL increases with frequency. (In contrast to Xc). The sum of reactance (X) is the difference between the pair if both XL and Xc are connected in a circuit.

Learning RC time constant

Charging of a capacitor

The capacitor (C) in the circuit diagram shown below is charged from a voltage source (Vs), and the current is flowing through the resistor (R).

The voltage across the capacitor (Vc) at the beginning is zero. As the capacitor starts to charge, its value will also begin to increase.

The charge will be full when Vc = Vs. The charged current (I) is determined by the voltage across the resistor (Vs – Vc):

  • Charged current I = (Vs – Vc) / R (if Vc voltage increases)
  • At first Vc = 0V. So, the beginning current Io = Vs / R
  • Vc increases instantly when the charge (Q) begins to start (Vc = Q / C). It causes the voltage drop across the resistor to decrease. The charged current will also decrease.
  • This means that the charge rate will continually decrease.

Meet the time constant

What is the time constant for an RC circuit? It is the measurement of time that the capacitor uses to charge the current through the resistor. It needs to work with both capacitor and resistor or RC network.

We can easily calculate the time constant with the following formula:

Time constant = R x C

Note:

  • Time constant has unit of second (s)
  • R is the resistance, has unit of ohm (Ω)
  • C is the capacitance, has a unit of Farad (F)

Time constant experiment

Let’s look at an example of a circuit.

When we press S1 the current will start to flow to C1 through R1 slowly. Here we will use the voltmeter to measure the VC. It will be VS or about 9V when time is constant.

Or we use will have to use a formula to find the time.

We will find the time constant from R1 x C1.
= 47K x 22 μF
= 1,034mS = 1.034S

Learn Charging of capacitors

The high time constant means the capacitor will slowly charge. In this situation we will calculate the time constant from the properties of capacitance and resistance in the circuit. It is not calculated by just using the properties of capacitors.

charging current

The time constant (RC) is the time taken for the charging (or discharging) current (I) to fall to 1/e of its initial value (Io). ‘e’ is an important value in mathematics (such as pi). We roughly say that the time constant is the time taken for the current to fall to 1/3 of its initial value.

After each time constant passes the current will drop by 1 / e (about 1/3)

Do you understand? I will explain to you more illustration. Look:

After 5RC, the current falls to less than 1% of the initial value. Now we can say that the current is fully charged. But in reality, the capacitor is actually fully charged forever.

Look at VC voltage

We have to try to observe the voltage in the capacitor given in the following table.

First, we have to observe the voltage in the capacitor. It will show that in the beginning there is an increase in voltage (V) when charging occurs. The voltage will increase quickly as the current has a high charge. But when the current starts to decrease the charge will also start to decrease and the increase in voltage also becomes slow.

Time Voltage Charge
0RC 0.0V 0%
1RC 5.7V 63%
2RC 7.8V 86%
3RC 8.6V 95%
4RC 8.8V 98%
5RC 8.9V 99%

The graph below shows the voltage that is charged in a capacitor during a time constant.

Discharging of capacitors

When a capacitor is discharged the Initial current (Io) is determined by the initial voltage across the capacitor (Vo) and resistor (R) as follows:

Initial Current Io = Vo/R

discharge RC time constant circuit

Observe the current

We notice that the charging and discharging current of the capacitor graph is the same. This graph is an example of exponential decay.

Discharge current graph for time constant

See the voltage
When we measure the voltage it will keep on decreasing at a time constant rate. See in the following table.

Looking at the graph makes things easier to understand.

Initially, the current will be very high because the voltage is high. So, the charge will run out quickly and the voltage will also decrease rapidly too.

Time Voltage Charge
0RC 9.0V 100%
1RC 3.3V 37%
2RC 1.2V 14%
3RC 0.4V 5%
4RC 0.2V 2%
5RC 0.1V 1%

When the charge is depleted, the voltage will reduce. It causes the current to become low. So, the rate of discharging becomes slower and longer.

After the 5 time constant (5RC), the voltage across the capacitor is zero and we can say that the capacitor is discharged completely. Even if it is not discharged, it will keep on releasing forever (Or until the circuit changes).

graph discharge voltage in time constant

Uses of capacitors

Capacitors are used for many purposes:

  • Control timing —used with IC timer 555 to control charging and discharging
  • Smoothing —in the power supply
  • Coupling —-connecting the audio system and speakers
  • Filtering — in the bass-treble tuning circuit of the audio system
  • Tuning — in a radio system
  • Store energy —in circuits, flashes, cameras

Read other uses: I have learned uses of capacitors from Capacitance @ https://electronicsclub.info/ This website is a good teacher for me and can be great for you too.

Capacitor coupling (CR-coupling)

In general, large electronic circuits usually consist of many sections together. Each section is connected by the capacitor.

The capacitor allows an AC signal (change) to pass but it blocks the DC signal (stable). This connection is called a coupling capacitor or CR-coupling.

We often use them to make a connection between sectors of the audio system. They let the audio signal (AC) to pass through and stops the voltage (DC). For example, connecting speakers in an OTL amplifier or Preamplifier circuits and more uses.

The precise characteristics of the coupling capacitors are determined by the time constant (RC).

Note: The resistance (R) may be within the part of the next circuit(the output) instead of the resistor.

Using coupling capacitors in audio systems is a great success. This means that the signal is not distorted and is clear.

signal of successful capacitor coupling

The time constant (RC) is greater than the time period (T) of the minimum frequency of the sound signal than required (usually 20Hz, T = 50ms).

Output in 3 cases of the time constant is shown below.

RC > T
When the time constant is much higher than the time period of the input signal, the capacitor doesn’t have enough time or is unable to charge and discharge. In this situation, the signal passes without any distortion.

RC time constant more than T

RC = T
When the time constant is equal to the time period of the input signal, the capacitor will have enough time to charge and discharge before the signal changes. This will make the signal passing through the CR-coupling become distorted.

RC time constant = T

Please notice that changing the input signal is quite sudden as it passes through the capacitor to the output.

RC < T
When the time constant is much smaller than the time period of signal input, the capacitor has full time to charge and discharge after each sudden change of the input signal.

The only effect of this sudden change is on the output and will appear as spikes alternately with positive and negative.

RC time constant = t2

This can be a useful application in systems that need to detect sudden changes in signals.

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