Current During Charging and Discharging of a Capacitor

The capacitor is an electronic device that is used for storing the energy in the form of electrical charge, which can come into use when needed in the future for supplying the energy or charge after the source of power is detached from it. It is used in various types of appliances, just like computers, radios, televisions, etc., including these capacitors.

Moreover, it provides impermanent storage of energy as well in the circuits, and this energy can be supplied whenever needed. In addition, the property that lets the capacitor store the energy is called capacitance.

Discussion of Principles

A capacitor comprises two conductors that are separated with a small distance. Moreover, when the conductors are linked to a charging device such as a battery, the charge gets shifted from one conductor to the other until the dissimilarity in potential amid the conductors because of their equal but opposite charge becomes equivalent to the potential difference between the charging device’s terminals.

However, the quantity of charge collected on each conductor is directly proportional with the voltage, as well as the constant of proportionality is called capacitance. In addition, it is algebraically written as = – Q = CΔV. The charge ‘C’ is measured in units of coulomb i.e. (C), the voltage ΔV in volts (V), as well as the capacitance ‘C’ in units of farads (F). Moreover, the capacitors are devices, whereas, the capacitance is a property of a device.

Charging and Discharging of Capacitor Derivation

The charging, as well as the discharging of the capacitors, is essential as it is the capability for controlling as well as predicting the rate of charging or discharging of the capacitor which makes it useful in the electronic timing circuits. It occurs when the voltage is put across the capacitor and the potential can’t increase to the value applied immediately. However, since the charge with the terminal gets accumulated to its maximum value, it tends to resist the addition of further charge addition.

Therefore, the following are the factors on which the rate of charging or discharging of a capacitor depends:

• The capacitance of the capacitor.
• The resistance of the circuit with the help of which it is charged or is discharged.

When we pour a liquid into a vessel, the level of the liquid keeps increasing. In the same way, when we provide a charge to the conductor, the potential it has keeps on increasing. Therefore:

Charge “Q” ∝ Potential “V”

Or

Q = CV…(1)

Now, ‘C’ is a constant of the proportionality as well as is known as the conductor’s capacitance or capacity.

From equation…(1):

C = Q/V…(2)

The conductor’s capacitance is, therefore, defined as the proportion of the charge it has to the potential of the conductor.

The value of ‘C’ depends on the following factors:

• The size as well as the shape of the conductor.
• The nature of the medium around the conductor.
• The location of the adjacent charges.

It does not, however, depend on the conductor’s material. Furthermore, let ‘V’ = 1, consequently, from Equation (1):

Q = C or C = Q

Therefore, the capacitance of the conductor is numerically equivalent to the quantity or amount of the charge needed to increase its potential with the help of unity. Moreover, capacitance’s cgs unit is known as an esu of the capacitance or a stat farad i.e. st F.

Here,

1 stat farad = 1 stat coulomb/1 stat volt

The capacitance of a conductor is then referred to as 1 stat farad, if its potential increases with 1 stat volt, when a charge of 1 stat coulomb is provided to it. Moreover, the SI unit of the capacitance is known as a farad i.e. F.

From equation…(2):

1 farad ‘F’ = 1 coulomb ‘C’/1 volt ‘V’

Charging of a Capacitor

Let’s take a capacitor ‘C’ in sequence including a resistor ‘R’ making an RC charging circuit and is linked across a supply of the DC battery ‘Vs’ through a switch.

Now, at a particular time given ‘t’ = 0, the switch turns on as well as the capacitor gets charged completely. These are the starting situations of the circuit, therefore, at ‘t’ = 0, i = 0, as well as q = 0. At this time, when the switch is turned off, the time starts with ‘t’ = 0 and the current starts flowing in the capacitor through the resistor as well as the charge starts accumulating over the capacitor.

As the voltage in the starting across the capacitor is ‘0’ i.e. Vc = 0 at ‘t’ = 0, the capacitor is in the condition of short circuit conflicted only through the resistor i.e. ‘R’. Furthermore, now using Kirchhoff’s law of voltage i.e. KVL, the voltage drops surrounding the circuit are given as:

As a result, the current flowing inside the circuit is known as the charging current and is determined with the use of Ohm’s law, since ‘i’ = Vs/R.

Then,

Vs – Ri(t) – Vc(t) = 0

Plates of a capacitive device begin to charge as the voltage across them increases. In order for a capacitor to reach 63% of its full power potential, it takes one round to charge it one time constant (tau).

Capacitors continue to charge, reducing the voltage differential between them. Also, the circuit current is reduced. 

Despite the fact that the capacitor is charging, the voltage difference between Vs and Vc is decreasing. As a result, the circuit current also decreases. A completely charged capacitor is one that has t = ∞, I = 0, q = Q = CV, where the condition is larger than 5T. After an infinite amount of time, the charging current becomes null. Vc = Vs is now the supply voltage across the capacitor, making it a totally open circuit.

A capacitor’s charge-up time (1T) is denoted by the symbol RC (time constant merely defines a rate of charge, where R is in and C is in Farads).

The voltage across a capacitor (Vc) may be calculated at any stage in the charging process using the equation Vc = Q/C, which tells us that the voltage V is tied to the charge on a capacitor.

 Vc=Vs(1-e-t/RC)

 Where:

 The voltage across the capacitor is Vc.

 The supply voltage is Vs.

 The amount of time since the supply voltage was applied is t.

 The time constant is RC.

 Similar to the 4-time Constants charging circuit, the capacitor in this RC charging circuit is now almost completely charged after a period of time (4T). The voltage across the capacitor is around 98% of its maximum value, which is 0.98Vs (volts per second). At this 4T stage, capacitors’ transient periods are over. When the voltage across the capacitor (Vc) equals the source voltage (Vs), the capacitor is considered to have completely charged after 5T (Vs). As soon as the capacitor is completely charged, the circuit is shut off. The Steady-State Period begins after 5T.

Discharging a capacitor 

The charge contained in a capacitor is released when the capacitor is discharged. Let’s look at an example of a capacitor that has been discharged.

In series with a resistor of resistance R ohms, we connect a charged capacitor with capacitance C farad. Then, as demonstrated, we short circuit this series combination by turning on the push switch releasing a capacitor.

The capacitor begins to discharge as soon as it is short-circuited.

Assume that the capacitor has a voltage of V volts when fully charged. The circuit’s discharge current would be − V / R ampere as soon as the capacitor is short-circuited.

However, after the circuit is switched on at t = +0, the current through it is:

i= Cdv/dt

The faster the charging and discharging rate of the Capacitor, the smaller the Resistance or Capacitance, the smaller the Time Constant, and vice versa. Almost all electrical devices contain capacitors. They can be used as a power source. A discharging and charging of a capacitor example is a capacitor in a photoflash unit that stores energy and releases it swiftly during the flash.

Conclusion

A capacitor is termed as a device that is passive in nature as well as collects the energy in the electric field and sends back the energy to the circuit every single time needed. Moreover, no current flows with the help of the dielectric at the time of discharging or charging period. However, the leakage current is an exception in this case.