What is the Role of Capacitor in AC and DC Circuit?

What is the Role of Capacitor in AC and DC Circuit?

Role of Capacitor in AC Circuits:

In an AC circuit, capacitor reverses its charges as the current alternates and produces a lagging voltage (in other words, capacitor provides leading current in AC circuits and networks)

Role of Capacitor in DC Circuits:

In a DC Circuit, the capacitor once charged with the applied voltage acts as an open switch.

Let’s explain in detail, but we will go back to the basics of capacitor first to discuss the matter.

What is a Capacitor?

The capacitor is a two terminal electrical device used to store electrical energy in the form of electric field between the two plates. It is also known as a condenser and the SI unit of its capacitance measure is Farad “F”, where Farad is a large unit of capacitance, so they are using microfarads (µF) or nanofarads (nF) nowadays.

A capacitor is similar to a battery, as both stores electrical energy. A capacitor is a much simpler device that can’t produce new electrons, but stores them. Inside the capacitor the terminals connected with the two metal plates separated by dielectric material (such as waxed paper, mica, and ceramic), that separate the plates and allows them to hold opposite electrical charges maintaining electrical field.

Capacitors can be useful for storing charge and quickly discharging into the load. In a simple way, a capacitor also work as a small rechargeable battery. The electrical equivalent symbol of different types of capacitor is given below:

Now, we know the concept of the capacitor’s charging and its structure but, do you know what Capacitance is? the capacitance is the ability of a capacitor to stores the charge into it. There are some factors which affect the capacitance.

Plate’s Area

Gap between the plates

Permittivity of the insulating material

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A capacitor has wide range of applications in electronics, such as Energy Storage, Power Conditioning, Power factor correction, Oscillators and filtration.

In this tutorial we will explain you, how you can use a capacitor in an electronic circuit. There are three ways to connect a capacitor in an electronic circuit,

Capacitor in Series

Capacitor in Parallel

Capacitor in AC Circuits

Capacitor in DC Circuits

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How Capacitor Works?

Working and Construction of a Capacitor

Whenever voltage is applied across its terminals, (Also known as charging of a capacitor) current start to flow and continue to travel until the voltage across both the negative and positive (Anode and Cathode) plates become equal to the voltage of the source (Applied Voltage). These two plates are separated by a dielectric material (such as mica, paper, glass, etc. which are insulators), which is used to increase the capacitance of the capacitor.

When we connect a charged capacitor across a small load, it starts to supply the voltage (Stored energy) to that load until the capacitor fully discharges.

Capacitor comes in different shapes and their value is measured in farad (F). Capacitors are used in both AC and DC systems (We will discuss it below).

Capacitance (C):

Capacitance is the amount of electric charge moved in the condenser (Capacitor), when one volt power source is attached across its terminal.

Mathematically,

Capacitance Equation:

C=Q/V

Where,

C = Capacitance in Farads (F)

Q = Electrical Charge in Coulombs

V = Voltage in Volts

We will not go in detail because our basic purpose of this discussion is to explain the role and application/uses of capacitors in AC and DC systems. To understand this basic concept, we have to understand the basic types of capacitor related to our topic (as there are many types of capacitor and we will discuss capacitor types latter in another post because it is not related to the question).

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Capacitors in Series

How to Connect Capacitors in Series?

In series no capacitor is directly connected to the source. To connect them in series you need to join them end to end, as shown in the below image,

When you connect the capacitors in series the total capacitance is decreased. Hence, the connection is in series so the current through the capacitors will be equal. Also, the charge stored by plate of capacitor will be same because it is coming from the adjacent capacitor’s plate.

Hence,

I T = I 1 +I 2 +I 3 +…+I n

and

Q T = Q 1 +Q 2 +Q 3 +…+Q n

Now, for finding the value of capacitance of the above circuit, we will apply Kirchhoff’s Voltage Law (KVL), then we have

V T =V C1 +V C2 +V C3

As we know that, Q = CV

And V = Q/C

So,

(Q/ C T ) = (Q/ C 1 ) + (Q/ C 2 ) + (Q/ C 3 )

Hence,

1/C T = (1/C 1 ) + (1/C 2 ) + (1/C 3 )

For nth no. of capacitor connected in series,

For two capacitors in series, the formula will be

C T = (C1 x C2) / (C1 + C2)

Now, you can find the capacitance of the above circuit, by using the formula,

Here, C1 = 10uf and C2 = 4.7uF

So, C T = (10 x 4.7) / (10 + 4.7)

C T = 47 / 14.7

C T = 3.19uF

Capacitors in Parallel

How to Connect Capacitors in Parallel?

In parallel every capacitor is directly connected to the source, as you can see in the below image,

When you connect the capacitors in parallel the total capacitance is equal to the sum of all the capacitor’s capacitance. Because the top plate and bottom plate of all capacitor connected together, due to this the plate area is also increased.

The total current in the parallel circuit will be equal to the current across every capacitor.

By applying Kirchhoff’s law,

I T = I 1 + I 2 + I 3

Now, the current across the capacitor is expressed as,

I = C (dV /dt)

So,

By solving the above equation

C T = C 1 + C 2 + C 3

And, for nth no. of capacitor connected in series,

C T = C 1 + C 2 + C 3 + … + C n

Now, you can find the capacitance of the circuit, by using the above formula,

Here, C 1 = 10uf and C 2 = 1uF

So, C T = 10uF + 1uF

C T = 11uF

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Polar and Non-Polar Capacitor

Non Polar Capacitor: (Used in both AC and DC Systems)

The Non Polar capacitors can be used in both AC and DC systems. They can be connected to the power supply in any direction and their capacitance does not effect by the reversal of polarity.

Polar Capacitor: (Only used in DC Circuits and Systems)

This type of capacitor is sensitive about their polarity and can be only used in DC systems and networks. Polar Capacitors don’t work in the AC system, because of the reversal of polarity after each half cycle in AC supply.

Role of Capacitors in AC Circuits

The capacitor has lots of applications in AC systems and we will discuss few uses of capacitor in AC networks below.

Transformer less power supply:

Capacitors are used in transformer less power supplies. In such circuits, the capacitor is connected in series with the load because we know that the capacitor and inductor in pure form does not consume power. They just take power in one cycle and deliver it back in the other cycle to the load. In this case, it is used to reduce the voltage with less power wastage.

Split phase induction motors:

The capacitors are also used in induction motor to split a single phase supply into a two phase supply to produce a revolving magnetic field in the rotor to catch that field. This type of capacitor is mostly used in household water pumps, Fans, air conditioner and many devices which need at least two phases to work.

Power Factor Correction and Improvement:

There are lots of advantages of power factor improvement. In a three phase power systems, capacitor bank is used to supply reactive power to the load and hence improve the power factor of the system. Capacitor bank is installed after a precise calculation. Basically, it delivers the reactive power which was previously traveled from the power system, hence it reduces the losses and improves the efficiency of the system.

Capacitors in AC Circuits

How to Connect a Capacitor in AC Circuit?

In DC Circuit, the capacitor charges slowly, until the charging voltage of a capacitor is equal to the supply voltage. Also, in this condition the capacitor doesn’t allow the current to pass through it after it gets fully charged.

And, when you connect a capacitor across an AC source, it charges and discharges continuously, due to continuous change in the voltage levels. Capacitance in AC circuits is depends upon the frequency of the supplied input voltage. Also, if you see the phasor diagram of an ideal AC capacitor circuit you can observe that, current leads the voltage by 90⁰.

In AC capacitor circuit, current is directly proportional to the rate of change of supplied input voltage, which can be expressed as,

I = dQ /dt

I = C (dV / dt)

Now, we will calculate the capacitive reactance in AC circuit.

As we know that, I = dQ/dt and Q = CV

And, the AC input voltage in the above circuit will be expressed as,

V = V m Sin wt

So, I m = d(CV m Sin wt )/dt

I m = C*V m Cos wt *w (after differentiation)

I m = wC V m Sin (wt + π/2)

At, w =0, Sin (wt + π/2) = 1

Hence,

I m = wCV m

V m / I m = 1/wC (where, w = 2πf and V m / I m = X c )

Capacitive Reactance (X c ) =

Now, to calculate the capacitive reactance of the above circuit,

Xc = 1 / 2π(50)(10)

Xc = 3183.09 Ω

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Role of Capacitors in DC Circuits

Power conditioning:

In DC systems, capacitor is used as a filter (mostly). Its most common use is converting AC to DC power supply in rectification (such as bridge rectifier). When AC power is converted into fluctuating (with ripples i.e. not a steady state with the help of rectifier circuits) DC power (Pulsating DC) in order to smooth and filter out these ripples and fluctuation, DC Polar capacitor is used. Its value is calculated precisely and depends on the system voltage and the demand load current.

Decoupling Capacitor:

Decoupling capacitor is used, where we have to decouple the two electronics circuits. In other words, the noise generated by one circuit is grounded by decoupling capacitor and it does not affect the performance of other circuit.

Coupling Capacitor:

As we know that Capacitor blocks DC and allows AC to flow through it (we will discuss it in the next session that how does it happens). So it is used to separate AC and DC signals (also used in the filter circuits for the same purpose). Its value is calculated in such a way that its reactance is minimized on the basis of frequency, which we want to pass through it. Coupling Capacitor is also used in filters (ripple remover circuits like RC filters) to separate AC and DC signal and removes the ripples from pulsating DC supply voltage to convert it into pure AC voltage after rectification.

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