In the previous tutorials, we discussed setting up an electronics lab and learned rudimentary know-how of resistors. Moving on with a discussion on passive components, let’s talk about the capacitor.

**Let us begin with a fictitious circuit
**Imagine a purely resistive circuit driven by an ideal voltage source or ideal current source. In such a fictitious ideal circuit, purely resistive components (of purely resistive load circuit) have fixed voltage drops across them in no time. Once the circuit is powered, the voltage drops across the components become constant and constant currents flow through them all the time.

**Let’s get back to reality
**Practically, no electronic or electrical circuit behaves like our fictitious circuit. There are no purely resistive components (even resistors show some reactance), no ideal voltage sources and no ideal current sources. Even if a resistive circuit is powered by a constant voltage source or constant current source, it passes through a transient state before reaching a fixed, stable state. So, all circuits and their components on the application of a voltage or current, experience change in voltage or current through them. A circuit may reach a stable state only after some time.

**DC circuits & DC signals
**Broadly, electrical signals can be classified as DC and AC signals. Any voltage or current source is a two-terminal device with the possibility of conducting current in two directions in any circuit. A DC circuit is a circuit in which current flows only in one direction from the voltage or current source driving it. So, DC signals can be defined as electrical signals which have a fixed polarity and in which voltage and current changes only in one direction. There is no reverse of polarity or change in the direction of current across the source driving the circuit.

Practically, DC is a generalized term. It may also refer to a DC component of an electrical signal or DC behavior of an electrical or electronic component. A DC signal may have voltage or current varying with time but never involves the reversal of voltage polarity or reversal of direction of the current.

**AC circuits & AC signals
**A voltage source that supplies voltage in which polarity keeps on reversing alternatively is called AC voltage source. Similarly, a current source that supplies current in which the direction keeps on alternating is called an AC source. A circuit powered by AC voltage source or an AC source has a reversal of voltage polarity and direction of current alternatively. Such circuits, in which voltage and current keeps on changing direction periodically are called AC circuits. An AC signal can be defined as an electrical signal, in which, voltage polarity and direction of current keeps on alternating periodically. The voltage and current rise to a peak value, drop to zero reversing direction, again rise to a peak value in the opposite direction, and then drop to zero, reversing direction. This continues until the signal remains live.

**Signals, DC circuits & AC circuits
**The changing magnitude (and direction) of voltage and current are all for the sake of good. If signals do not change with time, they are of no practical use. After all, electronics is all about processing electrical signals. DC circuits process electrical signals in which voltage and/or current changes only in one direction. AC circuits process electrical signals in which voltage and current not only change in magnitude but also keep on changing direction alternatively.

**More opposition to current****:** **capacitance & inductance
**Similar electronic materials and components show some natural opposition to the flow of current. This is defined by “resistance.” They also show opposition to any change in magnitude and direction of the current. This is defined as “inductance”. The inductance comes from opposing magnetic field induced in electronic materials and components in response to changing or alternating current.

Similarly, electronic materials and components show opposition to current due to opposing electrical field induced due to retaining or storing of charge carriers by them. This is defined as “capacitance.” The resistance remains present in DC as well as AC circuits and show similar signal behavior to DC and AC signals. The inductance and capacitance are shown by only AC circuits or DC circuits with pulsating DC signals. In DC circuits involving constant DC signals, inductance and capacitance are not much significant (and are also unwanted).

While resistance dissipates electrical energy in the form of heat, inductance and capacitance temporarily stores electrical energy in the form of magnetic and electrical fields respectively and give it back to the circuit again in the form of electrical energy. So, there is no loss of energy due to inductance or capacitance, unlike in case of resistance.

**Capacitance
**Capacitance is the property of an electronic material or component by which it can temporarily store electrical charge in it. Capacitance is defined as the amount of charge stored by an electronic entity per unit volt of applied potential difference.

C = Q/V

Where,

C = Capacitance (in Farad)

Q = Stored charge (in Coulombs)

V = Applied voltage (in Volts)

Obviously, a component having higher capacitance can store a greater amount of charge per unit applied voltage. Not all materials or components show the capability to store charge in response to an applied potential difference. Some special insulating materials that can polarize in response to applied potential difference show capacitance. Such electronic materials are called dielectric materials or simply dielectrics. Fortunately, even air or vacuum can serve as a dielectric medium as they allow the electric field to set up between two conductors in response to an applied voltage.

The devices that are designed to store charge in the form of an electrical field in response to the applied potential difference (voltage) are called capacitors. The simplest capacitor can be two metal plates (electrodes) separated by air or vacuum. If the two plates are shorted, they are nothing more than a connecting wire. The presence of air or vacuum, which is a dielectric medium, between the plates, make this whole setup capable of storing electric charge with an application of some potential difference (voltage).

So, any capacitor is basically a setup of two electrodes (conducting materials) separated by a dielectric medium. The unit of capacitance is Farad (Coulomb/Volt), in honor of Michael Faraday. The property of a dielectric medium determining charge stored per unit volume on the application of unit voltage is called its permittivity. The permittivity of free space or vacuum is a constant called absolute permittivity and is equal to 8.85×10^{-12} Farad/Metre. The permittivity of a dielectric medium relative to absolute permittivity is called its relative permittivity or dielectric constant. The capacitance of a capacitor depends upon the permittivity of the dielectric medium used in it, shape, size and construction of the capacitor.

**Unit of capacitance
**Farad is too large of a unit for expressing capacitance of standard capacitors. So, the capacitance of standard capacitors is expressed in sub-multiples of Farad like Microfarad (10

^{-6}F), Nanofarad (10

^{-9}F) and Picofarad (10

^{-12}F).

**Signal analysis of capacitors
**The capacitors are designed to store charge temporarily in a circuit. Let us first see the behavior of a capacitor in a DC circuit. The most simple DC circuit with a capacitor can be a capacitor connected with a voltage source via a switch. A resistor (remember bleeding resistors) can be connected in parallel to the capacitor via another switch for discharging the capacitor.

Initially, there is no potential difference across the capacitor and let us assume that no charge is initially stored in the capacitor. When the voltage source is connected to the capacitor, a potential difference of equal voltage is applied across the capacitor. In response to an applied voltage, the dielectric medium of the capacitor starts polarizing and begins storing charge in the form of an electric field. The following equation gives the charge that can be stored by the capacitor:

Q = CV

So, the current through the capacitor is given by the following equation:

i = dQ/dt

= d(CV)/dt

= C dV/dt

And, the voltage across the capacitor is given by the following equation:

dV = i/C . dt

So, ∫dV = 1/C * ∫i.dt

= 1/C * _{0}∫^{t} i.dt

**Charging of the capacitor**

Voltage across the capacitor is proportional to the charge stored by it and inversely proportional to the capacitance of the capacitor. The charge is not stored instantaneously within the capacitor in response to an applied voltage. When voltage is applied across the capacitor, it acts as a short circuit, and maximum current flows through the capacitor. The current through the capacitor decreases exponentially with charge stored by it and voltage across it increasing by the same rate. The current through the capacitor ceases when the voltage across the capacitor rises equal and opposite to the applied voltage. Now, the capacitor acts as an open circuit, and no current flows through it while an equal and opposite voltage has developed across it. So, current flows through the capacitor only till the voltage across it is changing. Once, the voltage across the capacitor becomes constant (equal and opposite to applied voltage), it has no current flowing through it. The voltage across the capacitor remains even when no current is flowing through it. As the rate of change of voltage across the capacitor is proportional to current and inversely proportional to capacitance, the greater is the capacitance of a capacitor, slower is the rate of change of voltage (rise of voltage) across it.

**Discharging of the capacitor**

Once the capacitor has equal and the opposite voltage across it, it is fully charged, retaining a charge equal to CV and no current flows through it. Now, there will be no change in current or voltage across the capacitor until the applied voltage is changed or varied. So, in a constant DC circuit, the capacitor will get fully charged (exponentially) and eventually become open circuit. Now, it needs to be discharged either by shorting its terminals or through a bleeding resistor. By either way, a discharging current flows through the capacitor in the opposite direction to that of the charging current. Like charging current, the discharging current is initially maximum and decreases exponentially. The voltage across the capacitor also decreases exponentially along with the discharging current. The discharging current ceases as the voltage across the capacitor reduces to zero.

**Capacitor in AC circuit
**Now, let us assume that the voltage source is AC. As a sinusoidal voltage source, the applied voltage will be given by the following equation:

V = V

_{m}sin(ωt)

Where,

V = Voltage of waveform at an instant

V

_{m}= Peak voltage of the waveform

ω = Frequency of the waveform

t = time instant

The following equation will give the current through the capacitor:

i = C dV/dt

= C d(V_{m} sin(ωt))/dt

= ω C V_{m} cos(ωt)

= I_{m} cos(ωt) where I_{m} = ω C V_{m
}= I_{m} sin(ωt + 90°)

The opposition to the current by the capacitor is called Capacitive Reactance. It is given by the following equation:

X_{c} = V/I

= V_{m}/I_{m} OR V_{rms}/I_{rms
}= 1/ωC

We can see, then, that current through a capacitor in an AC circuit leads voltage by 90° or 1/4 of the frequency. As the applied voltage rises to peak value, the capacitor charges and charging current decreases exponentially from the maximum value to zero, while the voltage across the capacitor rises exponentially, rising equal and opposite to the applied voltage. So, at 90° phase angle of the applied voltage signal (1/4 of the signal frequency), the charging current through the capacitor has reduced to zero (from maximum), and the voltage across the capacitor has raised from zero to peak voltage.

Now, as the applied voltage drops from peak value to zero, a current in reverse direction flows through the capacitor, which rises from zero to a maximum value. The voltage across the capacitor drops along with the applied voltage, reducing to zero and so discharging the capacitor. Therefore, at a 180° phase angle of the applied voltage signal (1/2 of the signal frequency), the discharging current (here, current in reverse direction due to decreasing applied voltage) flows in the opposite direction, rising from zero to maximum value and voltage across the capacitor drops from peak value to zero.

Now, the applied voltage signal reverses the polarity, and the applied voltage rises from zero to peak value in the opposite direction. This again starts charging the capacitor, increasing the voltage across the capacitor equal and opposite to peak voltage (in reverse direction) and reducing the current through the capacitor from peak value to zero. So, at a 270° phase angle of the applied voltage signal (3/4 of the signal frequency), the voltage across the capacitor has raised to a peak value with opposite polarity, and current through the capacitor flowing in the opposite direction drops to zero from peak value (in the reverse direction).

Now as the applied voltage drops from peak value to zero in reverse polarity, a current flows through the capacitor in positive direction rising from zero to a peak value, and the voltage across the capacitor (in reverse polarity) drops from peak value to zero. This discharges the capacitor. So, at a 360° phase angle of the applied voltage signal (completion of one cycle of AC signal), the voltage across the capacitor has again dropped to zero, discharging the capacitor and the current through the capacitor has again raised to the peak value in a positive direction. The AC response of a capacitor can be illustrated through the following signal diagram:

The signal behavior of a capacitor can be summarized as follows:

1) A capacitor is meant to store charge temporarily in a circuit, which it returns to the circuit on discharging. The stored charge is returned in the form of a discharging current in the opposite direction of the charging current.

2) Whenever applied voltage to a capacitor in any direction increases, the capacitor charges. The current through it decreases exponentially, and the voltage across it rises exponentially until it equals the applied voltage. When charging, the voltage across the capacitor develops opposite to the applied voltage and current through it is always in the direction of applied voltage (and opposite to voltage developed across the capacitor).

3) Whenever applied voltage to a capacitor in any direction decreases, the capacitor discharges. The current through it increases exponentially and the voltage across it decreases exponentially until the capacitor is fully discharged or discharged to the lowest level depending upon the fall in the applied signal. When discharging, the voltage through the capacitor develops along the direction of the initially applied voltage and current through it is always in the opposite direction to initially applied voltage (charging voltage).

4) The current flows through the capacitor until the voltage applied to it is changing. Increasing voltage charges the capacitor and decreasing voltage discharges the capacitor. The voltage across the capacitor remains even if no current is flowing through it until it is discharged due to a decrease in applied voltage, or discharged through a resistor (or load), or by shorting.

5) In an AC circuit or in response to an AC signal, the current through the capacitor always leads voltage across it by 90°. The current through the capacitor depends upon not only capacitance and the rate of change of voltage but also the frequency of the applied signal.

6) The opposition to current by a capacitor (capacitive reactance) is inversely proportional to its capacitance as well as the frequency of the applied voltage. The higher the capacitance of a capacitor, the less is its capacitive reactance. Similarly, the higher the frequency of the applied voltage signal, the less is its capacitive reactance. For a constant DC signal, the capacitor acts as an open circuit after charging to a peak level. So, a capacitor can be used to block DC signals or DC components of electrical signals. Similarly, due to the frequency dependence of capacitive reactance, capacitors can be used to filter AC signal frequencies.

7) Since capacitors temporarily store charge, they are used in electrical memories.

In the next article, we will discuss different types of capacitors and their applications.

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