capacitor symbol || capacitor for ac

Capacitor is an electrical device that store energy in the form of charge i.e. it oppose  the sudden change in voltage. Let's discuss about "capacitor symbol || capacitor for ac". Generally, it is two conducting surface (known as plates) which is separated by the insulating material. The insulating material used on capacitor are air, mica, paper, ceramic etc. These insulating material are also called dielectric. These dielectric medium will help to separate two parallel conductor and energy is stored between these two parallel conductor (i.e. charge store between these conductors).

Capacitor symbol

Capacitor symbol is given by:-

The above figure is the symbol of capacitor which is used in the circuit. Two parallel conducting plates may be square, circular or rectangular, cylindrical or spherical in shape in the capacitor and store energy between them. 

The stored charge on the capacitor is directly proportional to potential different across it. i.e.

    Q ∝ V

∵ Q = CV

Where C is proportionality constant which is also know as capacitance. Capacitance of a capacitor is the the ability to store charge. The SI unit of capacitance of capacitor is Farad and denoted by F. The energy stored in the capacitor is given by:-

E = CV² / 2

    = QV / 2

For parallel plate capacitor, capacitance is given below

C = A∈ / d

Where, A = cross-section area of conductor

             d = distance between the plates

             ∈ = permittivity of the medium

For air medium, Cair = ∈₀ A / d

And for other medium,

Cmedium = ∈r∈₀ A / d

    = ∈r Cair

Here, ∈r = relative permittivity of medium

The deformation of molecule structure of dielectric material is called polarization which is done by electric field. If electric field intensity is increased, the amount of polarization also increased. If it exceeds the limit, destructive current will flow and that maximum amount of electric field intensity ( limit value ) is known as dielectric strength.

Capacitor can be categorized into 2 types. They are :- a. Non-polarized capacitor b. Polarized capacitor

The capacitor which need not to connected in proper orientation is non-polarized capacitor. Like mica, paper, ceramic, polyester, polystyrene etc. are non-polarized capacitor. We can connect these capacitor in any orientation, and no any problem are occurred for these while connecting any orientation. The capacitor which need to connected in proper orientation is polarized capacitor like electrolytic capacitor, tantalum capacitor etc. If this capacitor is not connected in proper polarity, it will malfunction.

The value of capacitance of capacitor with conducting slab is given by:-

C = ∈₀ A / (d - t)

Also, the value of capacitance of capacitor with dielectric slab is given by:-

C = ∈₀ A / [d - t (1 - 1 / ∈r) ]

where t = thickness of slab

Energy stored is the amount of energy that is stored in the parallel plates. This energy in the capacitor is given by,

U = qV / 2

    = q² / 2C

    = CV² / 2

Also, For energy density,

u = U / Ad

    = (1/2)(∈₀ A /d) x (Ed)² x (1 / Ad)

    = ∈₀ E² / 2

Application of capacitor 

1. It is used to block DC current. [ Since parallel plates are separated by dielectric material i.e. no direct connection to flow current but in AC, polarity changes alternatively which makes capacitor charging and discharging continuously. So AC current will pass ]

2. In AC power system, it can be used to improve power factor by providing capacitive power which will compensate inductive power.

3. It is used in resonance circuit such as radio tuning.

4. It can be used in low pass filter and high pass filter of frequency.

5. It can be used as stator by phase shifting in single phase induction motor.

Capacitor for AC

As we have already discuss in application, it is used in AC system for improving power factor, stator etc. Single phase induction motor are not self staring so capacitor is added in that for starting like celling fan in our house is connected with capacitor for starting. To improve power factor, the best way is adding capacitor in the circuit. There are different method for it but generally parallel connection of capacitor bank is more popular.

Change of current in RC DC circuit

Let us consider, a DC voltage having a cell of voltage V, inductor of inductance L, resistor of resistance R and switch. As we know capacitor acts as voltage opposing device.

1. Rise of voltage

When switch is turn on, current will flow in the circuit from battery and charge is store on capacitor. There is going to sudden change in voltage but it is oppose by capacitor i.e. it allow exponentially increase in voltage which is given by,

    v = V (1 – e^-t/RC)

    v = V (1 – e^{-t/ τ})

where τ = RC

Also, q = Q (1 – e^-t/RC)

     q = Q (1 – e^{-t/ τ})

If t = τ then,

    v = V (1 - e^-1) = 0.632 V

    q = 0.632 Q

1. Decay of voltage

When switch is turn off, current will stop to flow in the circuit from battery but the charge store in the capacitor is flow in the circuit i.e. voltage will sudden goes decrease at that case but due to presence of capacitor, it allow exponentially decrease in voltage which is given by,

     v = V e^-t/RC

     v = V e^{-t / τ} = 0.37 V

Also,

    q = 0.37 Q