Friday, January 20, 2017

Basic Electronics On The Go - Capacitor Characteristics

From www.electronicshub.org/capacitor-characteristics/


Introduction

A capacitor has large number of specifications and characteristics. By observing the information printed on the body of a capacitor, we can understand very well about the characteristics of a capacitor. But some capacitors have colors or numeric codes on their body, due to this it is difficult to understand about characteristics. Each type or family of capacitor has its own set of characteristics and identification system. Some capacitors identification systems are easy to understand their characteristics and others use misleading symbols, letters and colors.
To understand the characteristics of a particular capacitor easily, first find out the capacitor family whether it is ceramic, plastic, film or electrolytic and from that it is easy to identify the characteristics.Even though capacitors have same capacitance value they may have different working voltages. If you use a capacitor which has low working voltage in place of a capacitor which has high working voltage then the increased voltage may damage the low voltage capacitor even though both capacitors have same capacitance.

Already we know that electrolytic capacitor has polarities, so while connecting the electrolytic capacitor in the circuit, positive terminal must connect to the positive connection and negative terminal of capacitor to negative connection otherwise the capacitor may damage. So it is always better to replace the damaged or old capacitor in the circuit with the new one which has same characteristics.The figure below figure shows the characteristics of a capacitor.



A capacitor comes with a set of characteristics. All these characteristics can be found in datasheets that are provided by capacitor manufacturers. Now let us discuss some of them.

Nominal Capacitance (C)


One of the most important one among all capacitor characteristics is the nominal capacitance (C) of a capacitor.This nominal capacitance value is generally measured in pico-farads (pF), nano-farads (nF) or micro-farads (uF), and this value is indicated with colors, numbers or letters on the body of a capacitor. This nominal capacitance value, which is printed on the side of a capacitor body, is not necessary to equal to its actual value.
The nominal capacitance value may change with working temperatures and with the circuit frequency. These nominal values are as low as one pico-farad (1pF) for smaller ceramic capacitors and as high as one farad (1F) for electrolytic capacitors. All capacitors have a tolerance rating that ranges from -20% to +80%.



Working Voltage (WV)


The working voltage is one more important characteristic of all capacitor characteristics. The maximum amount of voltage which is applied to a capacitor without failure during its working life is called as working voltage (WV). This working voltage is expressed in terms of DC and also it is printed on the body of a capacitor.

Generally working voltage which is printed on the body of a capacitor , refers  its DC voltage but not its AC voltage , because the AC voltage is in its rms value.So capacitor working voltage must be greater than the 1.414 (Vm = Vrms x√2) times of its actual AC value to apply AC voltage to the capacitor. This specified DC working voltage of a capacitor(WV-DC) is valid only within in a certain temperature range, such as -300C to +700C. If you apply a DC or AC voltage which is greater than the working voltage of a capacitor then the capacitor may damage.
The working voltages which are commonly printed on the body of a capacitor are 10V, 16V,25V, 35V, 50V, 63V, 100V, 160V, 250V, 400V and also 1000V. All the capacitors will have a longer working life if they operated within their rated voltage values and in a cool environment.



Tolerance (±%)


Tolerance is the permissible relative deviation of the capacitance from the rated value, which is expressed in per cent. Like resistors, the tolerance value for capacitor also exists in either plus or minus values. This tolerance value is generally measured in either pico-farads (+/-pF) for low value capacitors which are less than 100pF or in percentages (+/-%) for higher value capacitors, which are greater than 100pF.
The tolerance value of a capacitor is measured at a temperature of +20°C and it is valid only at the time of its delivery. If a capacitor may be used after a longer period of storage then the tolerance value will increase, but according to the standard specifications, this value will not exceed twice the value which is measured at the time of its delivery. The delivery tolerances usually for wound capacitors are +/-(1%,2.5%,5%,10%,20%). The very general tolerance values variation for capacitors is 5% or 10%, and this is rated as low as +/-1% for plastic capacitors.


Leakage Current (LC)


All dielectric materials which are used in the capacitors to separate the metal plates of capacitors are not perfect insulators. They allow the small amount of current, such as leakage current to flows through it. This effect is because of the high powerful electric field which is formed by the charge particles on the plates of a capacitor when supply voltage (V) is applied to it.

The leakage current of a capacitor is a small amount of DC current which is in nano-amps (nA). This is because of the flowing of electrons through the dielectric material or around its edges and also by discharging it overtime when the power supply is removed.

Leakage current is defined as transferring of unwanted energy from one circuit to another circuit. One more definition is the leakage current is a current when ideal current of the circuit is zero. Capacitors leakage current is a considerable factor in amplifier coupling circuits and in power supply circuits.
The leakage current is very low in film or foil type capacitors and it is very high (5-20 uA per uF) in electrolytic (tantalum and aluminium) type capacitors, where their capacitance values are also high.

Working Temperature

The capacitance value of a capacitor varies with the changes in temperature. The changes in temperature changes the properties of the dielectric. Working Temperature is the temperature of a capacitor which operates with nominal voltage ratings. The general working temperatures range for most capacitors is -30°C to +125°C. In plastic type capacitors this temperature value is not more than +700C.
The capacitance value of a capacitor may change, if air or the surrounding temperature of a capacitor is too cool or too hot. These changes in temperature will cause to affect the actual circuit operation and also damage the other components in that circuit.I think it is not a simple thing to keep the temperatures stable to avoid capacitors from frying.

The liquids within the dielectric can be lost to evaporation especially in electrolytic capacitors (aluminum electrolytic capacitors) when they will operate at high temperatures (over +850C)and also the body of the capacitor would become damaged due to the leakage current and internal pressure. And also the electrolytic capacitors cannot be used at low temperatures, such as below -100C.


Temperature Coefficient


The temperature coefficient (TC) of a capacitor describes the maximum change in the capacitance value with a specified temperature range. Generally the capacitance value which is printed on the body of a capacitor is measured with the reference of temperature 250C and also the TC of a capacitor which is mentioned in the datasheet must be considered for the applications which are operated below or above this temperature.Generally the temperature coefficient is expressed in the units of parts per million per degree centigrade (PPM/0C) or as a percent change with a particular range of temperatures.

Some capacitors are linear (class 1 capacitors), these are highly stable with temperatures; such capacitors have a zero temperature coefficient. Generally Mica or Polyester capacitors are examples for the Class 1 capacitors. TC specification for class 1 capacitors will always specifies the capacitance change in parts per million (PPM) per degrees centigrade.

Some capacitors are non linear (class 2 capacitors), these capacitors temperatures are not stable like class1 capacitors, and their capacitance values will increase by increasing the temperature values, Hence these capacitors give a positive temperature coefficient. The main advantage of the class 2 capacitors is their volumetric efficiency. These capacitors are mainly used in the applications where high capacitance values are required, while stability and quality factor with temperatures are not main factors to consider. The Temperature Coefficient (TC) of class 2 capacitors is expressed directly in percentage. One of the useful applications of temperature coefficient of capacitors is to use them to cancel out the effect of temperature on other components within a circuit such as resistors or inductors etc.

(to be updated)


Wednesday, January 18, 2017

Basic Electronics On The Go - Capacitance and Charge

From http://www.electronicshub.org/capacitance-and-charge/

Capacitance

Capacitance of a capacitor is defined as the ability of a capacitor to store the maximum electrical charge (Q) in its body. Here the charge is stored in the form of electrostatic energy. The capacitance is measured in the basicSI units i.e. Farads. These units may be in micro-farads, nano-farads, pico-farads or in farads. The expression for the capacitance is given by,
C = Q/V = εA/d = ε0 εr A/d

In the above equation
C is the capacitance,
Q is the charge,
V is the potential difference between the plates,
A is the area between the plates,
d is the distance between the plates.
ε permittivity of dielectric
ε0 permittivity free space
εr relative permittivity 

Self-capacitance

Self-capacitance property is related to the capacitors especially to the isolated conductors. As the name indicates the self capacitance is  the amount of electric charge that must be added to an isolated conductor to raise its electric potential by one unit (i.e. one volt, in most measurement systems) .Generally normal conductors will have mutual capacitance. This is also measured in the S.I units i.e. Farads.
The self-capacitance of a conducting sphere which has the radius ‘R’ is given by,
                                                       C=4 πɛoR

Self-capacitance values of some standard devices are given below.
  •  For the top plate of a van de Graff generator which is having radius of 20 cm self capacitance is 22.24 pF.
  •  For the planet EARTH self capacitance is 710 uF.

Stray capacitance

Stray capacitance is the unwanted capacitance.The capacitors introduce some capacitance in circuits. But the components like resistors,inductors, even wire will have some capacitance. This is called stray capacitance. Generally at high frequencies this will introduce noise to the circuit. This undesired capacitance is small unless the conductors are close together for long distances or for a large area.


The stray capacitance cannot be eliminated completely but it can be reduced. Circuit designers should take care of stray capacitance while designing the circuit. The separation between the components and the lines should be maintained in order to reduce the unwanted capacitance.
It is also measured in S.I units  i.e. Farads.

Examples are capacitance between the turns of the coil, capacitance between two adjacent conductors.

Capacitance of simple systems

Calculation of the capacitance is nothing but solving the Laplace theorem ∇ 2φ = 0 with a constant potential on the surface of a capacitor. The capacitance values and equations for some simple systems are given below. (Click on table to see larger view)

Charge on a Capacitor

The ability of a capacitor to store maximum charge (Q) on its metal plates is called its capacitance value (C). The polarity of stored charge can be either negative or positive.Such as positive charge (+ve) on one plate and negative charge (-ve) on another plate of the capacitor. The expressions for charge, capacitance and voltage are given below.
C = Q/V, Q = CV, V = Q/C
Thus charge of a capacitor is directly proportional to its capacitance value and the potential difference between the plates of a capacitor.Charge is measured in coulombs.

One coulomb:
One coulomb of charge on a capacitor can be defined as one farad of capacitance between two conductors which operate with a voltage of one volt.


Charging & Discharging of a Capacitor

The below circuit is used to explain the charging and discharging characteristics of a capacitor. Let us assume that the capacitor, which is shown in the circuit, is fully discharged. In this circuit the capacitor value is 100uF and the supply voltage applied to this circuit is 12V.
Now the switch which is connected to the capacitor in the circuit is moved to the point A. Then the capacitor starts charging with the charging current (i) and also this capacitor will fully charge. The charging voltage across the capacitor is equal to the supply voltage when the capacitor is fully charged i.e. VS = VC = 12V. When the capacitor is fully charged means that the capacitor maintains the constant voltage charge even if the supply voltage is disconnected from the circuit.
In the case of ideal capacitors the charge remains constant on the capacitor but in the case of general capacitors the fully charged capacitor is slowly discharged because of its leakage current.
When the switch is moved to the position B, then the capacitor slowly discharges by switching on the lamp which is connected in the circuit. Finally it is fully discharged to zero. The lamp glows brightly initially when the capacitor is fully charged, but the brightness of the lamp decreases as the charge in the capacitor decreases.



Current through a Capacitor

The current (i) flowing through any electrical circuit is the rate of charge (Q) flowing through it with respect to time. But the charge of a capacitor is directly proportional to the voltage applied through it. The relation between the charge, current and voltage of a capacitor is given in the below equation.
I (t) = d Q(t)/dt = C dV(t)/dt
We know that
Q = CV
V = Q/C
V (t) = Q(t)/C
Q(t) =C V(t)
The current to voltage relation is given by, I (t) = C dV(t)/dt

From this relation we observed that the current flowing through the capacitor in the circuit is the product of the capacitance and the rate of change of voltage applied to the circuit. 



Unit of capacitance (Farad)

Josiah Latimer Clark in the year of 1861first used the termFarad. Farad is a standard unit of the capacitance. This is an extremely a large unit for the capacitance.
One farad of capacitance is defined as the capacitance with one coulomb of charge which operates at the voltage of one volt.
C = Q/V

1Farad = 1Colomb/1Volt


Now capacitors are available with large capacitance values of hundreds of farads. These capacitors with high capacitance values are called as “super capacitors”. These capacitors are utilizing large surface area to deliver high energy because these have high capacitance values.
At low voltage, super capacitors have the ability to store high energy with high capacitance values. These high energy super capacitors are used in hand held portable devices to replace large, heavy and expensive lithium type capacitors, because they store high energy, like batteries. These capacitors are also used in audio and video systems in vehicles by replacing the high batteries.

Energy in a Capacitor

Energy is the amount of some work against the electro-static field to charge the capacitor fully. In the capacitor at initial stage of charging, the charge Q is transferred between the plates from one plate to another plate. This charge either +Q or –Q is interchanged between two plates of a capacitor. After transformation of some charge, an electric field is formed between the plates, in that case we need some extra work to charge the capacitor fully. This extra work is called as the energy stored in a capacitor. The energy is measured in the units of Joules (J). Now we see the equations for this energy and work.
dW = V dQ
dW = (Q/C) dQ


After integration of the above equation is,
W = Q2/2C
W = (CV)2/2C
W= CV2/2 Joules
Finally we get the energy stored in a capacitor is
Energy (W) = CV2/2 Joules
Now we calculate the energy stored in a capacitor of capacitance 200 uF which operate with voltage of 12V.
W = CV2/2
W = (200×10-6×122)/2 = 14.4 m J

Tuesday, January 17, 2017

Basic Electronics On The Go - Capacitor Color Codes

Introduction

Capacitance of a capacitor is the ability of a capacitor to store maximum charge on its plates. The capacitance of a capacitor is measured in the units of Farads. Generally the capacitance values, working voltage and tolerance values are indicated on the body of a capacitor.
But sometimes it is difficult to identify these capacitance and voltage values on the capacitor body in the case of decimal values. It also causes misreading of the actual capacitance and voltage values. So , a technique was used to identify the capacitance values by using the letters like p (pico) and n (nano) instead of decimal values (such as 200 k=200*1000 pF=200 nF and 47 n=47 nF,  n47=0.47nF etc).

So to avoid these problems a color scheme was introduced for capacitors like resistors. This colour scheme for capacitors is usually called  capacitor color coding. In this scheme each color of a capacitor indicates a specific capacitance value. Using this color scheme we can easily identify the capacitance values, voltages and tolerance values of any capacitor. These color schemes, color coding and colors assigned for values are explained  below.





Table :Capacitor Voltage Color Code



Capacitor Voltage Reference

The capacitor has the capacitance value, voltage , tolerance and manufacturer numbers on the body of a capacitor. Some voltage values are used as references for working voltages of a capacitor. In this representation we see some letters or characters like J, K, N, M etc. Now let us the meaning of those letters which are used on the body of a capacitor.
J-Type => Dipped Tantalum type capacitors
K-Type => Mica type capacitors
L-Type +> Polyester (or) Polystyrene type capacitors
M-Type => Electrolytic 4 Band type capacitors
N-Type => Electrolytic 3 Band type capacitors


Metalized Polyester Capacitor




The capacitors which are shown in the above figure are metalized polyester capacitors with color codes. In this each color represents a specific parameter for capacitance values, tolerance and working voltages. All the above capacitors have different capacitance and tolerance values.These values can be understood by the color code table which is given at the side of capacitors in the above figure.



Disc & Ceramic Capacitor



The above figure shows the Disc and Ceramic capacitors with color codes. These colour codes are used for many years for non-polarized capacitors like disc and ceramic capacitors. But it is difficult to identify the values in the case of old capacitors. So these old capacitors are now replaced with new numbers.

In three digit number representation , the third number represents number of zeros, such as 471=470pF, 101=100pF. In the case of two digit number representation tolerance is also identified. In two number representation, disc or film capacitors have the capacitance value usually in pico-Farads, for example 47=47pF, 20=20pF. In the above figure we observe that  the capacitance values and tolerance for small disc or large disc capacitors can be calculated by using the color code which is shown at the side of capacitors.



Capacitor Tolerance Letter Codes Table


Capacitor has numbers and letters on its body to identify the capacitance values and tolerance values respectively.Letters for the specific tolerance value representation is shown in the below table. Now we will see one example to understand this concept below.




The capacitor which is shown in the above figure has 473 J code on its body. Here 4 is first digit, 7 is second digit and 3 is the number of zeros i.e. the capacitance value is 47*1000pF=47000pF=47nF=0.047uF. Here letter ‘J’ denotes the tolerance of a capacitor, referring to above table , tolerance of this capacitor is +/-5%. In this way by just using numbers and letters on the body of a capacitor, we can easily determine the capacitance values and tolerances of capacitors.

Table:Capacitor Letter Codes


The capacitance values of capacitor are  measured in pico-Farads, nano-Farads, or micro-Farads. The relation between these values for different letter codes is shown in the above table. From this table we clearly can understand about the units of capacitance. The basic relation between them is 1uF=1000nf=1000000pF




Monday, January 16, 2017

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


Sunday, January 15, 2017

Basic Electronics On The Go -Capacitive Voltage Divider

From http://www.electronicshub.org/capacitive-voltage-divider/

Introduction

In a voltage divider circuit,the supply voltage or circuit voltage is distributed among all the components in the circuit equally,depending on the capacity of those components.
The construction of capacitive voltage divider circuit is the  same as the resistive voltage divider circuit. But like resistors, the capacitive voltage divider circuit is not affected by the changes in the frequency even though it uses reactive elements.

The capacitor is a passive component which stores electrical energy in the metal plates. A capacitor has two plates and these two are separated by non-conducting or insulating material, such as called as “dielectric”.
Here the positive charge is stored on one plate and negative charge is stored on another plate.


When DC current is applied to the capacitor, it charges fully. The dielectric material between the plates acts as insulator and also it opposes the current flow through the capacitor.
This opposition to supply current through the capacitor is called reactance (XC) of a capacitor. The capacitor reactance is also measured in ohms.

A fully charged capacitor acts as an energy source, because a capacitor stores energy and discharges it to the circuit components.



Voltage Distribution in Series Capacitors

If the capacitors are connected in series , the voltage distribution between the capacitors is calculated. Because the capacitors have different voltage values depending on the capacitance values in series connection.

The reactance of a capacitor which opposes the flow of current , depends on the value of capacitance and frequency of the applied current.

So now let us see how the reactance affects the capacitors , by calculating the frequency and capacitance values. Below circuit shows the capacitive voltage divider circuit in which 2 capacitors are connected in series.


Capacitive Voltage Divider


The two capacitors which are connected in series have the capacitance values of 10uF and 22uF respectively. Here the circuit voltage is 10V,this voltage is distributed between both capacitors.
In the series connection all the capacitors have same charge (Q) on it but the supply voltage (VS) is not same for all capacitors.
The circuit voltage is shared by the capacitors depending on the capacitance values of the capacitors.i.e. in the ratio of V = Q/C.

From these values we have to calculate the reactance (XC) of each capacitor by using frequency and capacitance values of capacitors.


Capacitive Voltage Divider Example No1

Now we will calculate the voltage distribution to the capacitors 10uF and 22uF which are given in the above figure which have 10V supply voltage with 40HZ frequency.
Reactance of 10uF capacitor,
XC1 = 1/2πfC1 = 1/(2*3.142*40*10*10-6) = 400Ω
Reactance of 22uF capacitor,
XC\2 = 1/2πfC2 = 1/(2*3.142*40*22*10-6) = 180Ω
Total capacitive reactance of a circuit is,
XC= XC1+ XC2= 400Ω + 180Ω = 580Ω
CT= C1C2/(C1+C2) = (10*22*10-12)/(32*10-6) = 6.88uF
XCT = 1/2πfCT = 1/(2*3.142*40*6.88*10-6) = 580Ω
The current in the circuit is,
I = V/XC = 10V/580Ω = 17.2mA
Now, the voltage drop across each capacitor is,
VC1 = I*XC1 = 17.2mA*400Ω = 6.9V
VC2 = I*XC2 =17.2mA*180Ω = 3.1V


Summary

  • The opposition for the flow of current in the capacitor is known as reactance (XC) of a capacitor. This capacitive reactance is influenced by the parameters like capacitance value,frequency of supply voltage and also these values are inversely proportional to the reactance.
  • The AC voltage divider circuit will distribute the supply voltage to all the capacitors depending on their capacitance value.
  • These voltage drops for the capacitors are same for any frequency of supply voltage. i.e. the voltage drops across capacitors are independent on frequency.
  • But the current flowing is depending on frequency and also these two are directly proportional to each other.
  • But in DC voltage divider circuits, it is not an easy task to calculate the voltage drops across capacitors as it depends on reactance value, because the capacitors block DC current flow through it after fully charged.
  • The capacitive voltage divider circuits are used in large electronics applications.Mainly used in capacitive sensitive screens those change their output voltage when it is touched by a person's finger.
  • And also used in transformers to increase voltage drop where generally the mains transformer contains low voltage drop chips and components.
  • Finally one thing to say is in voltage divider circuit the voltage drops across capacitors are same for all frequency values.



Friday, January 13, 2017

Basic Electronics On The Go - Capacitance in AC Circuits

From http://www.electronicshub.org/capacitance-in-ac-circuits/

Introduction

When DC supply voltage is applied to the capacitor,the capacitor is charged slowly and finally it reaches to fully charged position. At this point the charging voltage of a capacitor is equal to the supply voltage. Here the capacitor acts as an energy source as long as voltage is applied. Capacitors don’t allow current (i) through them after they are fully charged.The current flowing through the circuit depends on the amount of charge in the plates of capacitors and also the current is directly proportional to the rate of change of voltage applied to the circuit. i.e. i = dQ/dt = C dV(t)/dt.

If AC supply voltage is applied to the capacitor circuit then the capacitor charges and discharges continuously depending on the rate of frequency of supply voltage.  In AC circuits the capacitors allow current when the supply voltage is continuously changing with respect to time.



AC Capacitor Circuit


In the above circuit we observed that a capacitor is directly connected to the AC supply voltage. Here the capacitor continuously charges and discharges depending on the changes in supply voltage, because the AC supply voltage value is constantly increasing and decreasing. We all know that the current flowing through the circuit is directly proportional to the rate of change of voltage applied.

Here the charging current has its high value, if the supply voltage crosses its value from positive half cycle to the negative half cycle and vice versa. i.e. at  00 and 1800 in sine wave signal. The current through the capacitor has its minimum value when the supply voltage in sine wave crosses over at its maximum or minimum peak value (Vm). Hence we can say that the charging current flowing through the circuit is maximum or minimum depending on the supply voltage levels in sine wave.


AC Capacitor Phasor Diagram

The phasor diagram of AC capacitor is shown in the above figure, here the voltage and currents are represented in sine wave forms. In the above figure we observed that at 0the charging current is at its maximum value because the voltage is increasing slowly in positive direction. At 900 there is no current flow through the capacitor because at this point the supply voltage is at its maximum peak value.
At 1800 point the voltage slowly decreases to zero and current is at maximum value in the negative direction. Again the charging reaches to its maximum value at 3600, because at this point the supply voltage is at minimum value.

From the waveforms in the above figure we can see that, the current is leading the voltage by 900. Hence we can say that in an ideal capacitor circuit the AC voltage lags the current by 900.



Capacitive Reactance


We know that the current flowing through the capacitor is directly proportional the rate of change of applied voltage but capacitors also offer some form of resistance against the current flow same as like resistors. This resistance of capacitors in AC circuits is called  capacitive reactance . Capacitive reactance is the property of a capacitor which opposes the flow of current in AC circuits. It is represented with symbol Xc and measured in Ohms same as like resistance.


We need some extra energy over capacitive reactance to charge up a capacitor in the circuit. This value is inversely proportional to the capacitance value and the frequency of supply voltage.
Xc∝ 1/c and Xc∝ 1/f.
The equation for capacitive reactance and parameters which influences them are discussed below.
Capacitive Reactance,
X_C = 1/2πfC = 1/ωC
Here,
X_C = Reactance of capacitor
f = frequency in HZ
C = Capacitance of a capacitor in Farads

ω (omega) = 2πf

From the above equation we understood that capacitive reactance is high where the frequency and capacitance values are at low and at this stage the capacitor acts as a perfect resistor. If the frequency of supply voltage is high then the reactance value of capacitor is low and also at this stage capacitor acts as a good conductor. From the above equation it is clear that the reactance is zero if the frequency is infinity and the reactance value is infinity where the frequency is at zero.



Capacitive Reactance against Frequency




The above figure shows the relation between the capacitive reactance, current and frequency of the supply voltage. Here we observed that if frequency is low then the reactance is high. The charging current increases with increase in frequency, because the rate of change of voltage increases with time.The reactance is at infinite value where the frequency is zero and vice versa.


AC Capacitance Example No1

Find the rms value of current flowing through the circuit having 3uF capacitor connected to 660V and 40Hz supply.
Capacitive Reactance,
XC = 1/2πfC
Here,
f = 40HZ
C = 3uF
Vrms = 660V
Now,
XC = 1/(2 × 3.14 × 40HZ  × 3 × 10-6) = 1326Ω
Irms = Vrms/XC = 660V/1326Ω = 497mA