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🆕What is a Capacitor — Charge and Discharge of a Capacitor

What is a Capacitor

Most radio components can be divided into two groups passive and active . And the capacitor must be attributed to the first group of passive components. In theory, any capacitor can be represented as two plates separated by an insulator.

They are characterized by capacity. The unit of capacitance is the farad (F), defined as one coulomb per volt (1 C/V).

Capacitors are widely used in radio electronics.

In electronic circuits, they are used to block DC and pass AC. 

In analog filter networks, they are used to smooth the output of power supplies. In resonant circuits, they are used to tune radio receivers to given frequencies.

Capacitor charge and discharge

In order to charge the capacitor, it is necessary to connect it to the DC circuit. On fig. 1 shows a circuit for charging a capacitor. Capacitor C is connected to the terminals of the generator. Using the key, you can close or open the circuit. Let us consider in detail the process of charging a capacitor. 

The generator has internal resistance. When the key is closed, the capacitor will charge up to a voltage between the plates equal to e. d.s. generator: Uc \u003d E.

In this case, the plate connected to the positive terminal of the generator receives a positive charge (+q), and the second plate receives an equal negative charge (-q).

The amount of charge q is directly proportional to the capacitance of the capacitor C and the voltage on its plates: q = CUc


Fig. 1. Capacitor charge circuit 

In order for the capacitor plates to be charged, it is necessary that one of them gain and the other lose a certain amount of electrons.

The transfer of electrons from one plate to another is carried out along the external circuit by the electromotive force of the generator, and the process of moving charges along the circuit is nothing more than an electric current called the  charging capacitive current  Izar. 

The charging current in the circuit usually flows in thousandths of a second until the voltage across the capacitor reaches a value equal to e. d.s. generator.

The graph of the increase in voltage on the capacitor plates during its charging is shown in Fig. 2a, from which it can be seen that the voltage Uc gradually increases, first rapidly, and then more and more slowly, until it becomes equal to e. d.s. generator E. After that, the voltage across the capacitor remains unchanged.


Rice. 2. Graphs of voltage and current when charging a capacitor

While the capacitor is charging, a charging current flows through the circuit. Charging current graph is shown in fig. 2b. At the initial moment, the charging current has the largest value, because the voltage on the capacitor is still zero, and according to Ohm’s law iozar \u003d E / Ri, since all e. d.s. generator is applied to the resistance Ri.

As the capacitor is charged, i.e., the voltage on it increases, for the charging current it decreases. When there is already tension on the capacitor, the voltage drop across the resistance will be equal to the difference between e. d.s. generator and the voltage on the capacitor, i.e. equal to E — U s. Therefore izar = (E-Uс)/Ri

From this it can be seen that with an increase in Uс, izar decreases and at Uс = E, the charging current becomes equal to zero.

Read more about Ohm’s law here: Ohm’s law for a circuit section

The duration of the process of charging the capacitor depends on two quantities: 

1) from the internal resistance of the generator Ri, 

2) from the capacitance of the capacitor C. 

On fig. 2 shows graphs of smart currents for a capacitor with a capacity of 10 microfarads: curve 1 corresponds to the process of charging from a generator with e. d.s. Е = 100 V and with internal resistance Ri = 10 Ohm, curve 2 corresponds to the process of charging from a generator with the same e. d.s., but with lower internal resistance: Ri = 5 ohms. 

From a comparison of these curves, it can be seen that with a lower internal resistance of the generator, the current strength at the initial moment is greater, and therefore the charging process is faster.


Rice. 3. Graphs of charging currents at different resistances

On fig. 3 compares the graphs of charging currents when charging from the same generator with e. d.s. E = 100 V and internal resistance Ri = 10 ohm of two capacitors of different capacities: 10 μF (curve 1) and 20 μF (curve 2). 

The value of the initial charging current iozar \u003d E / Ri \u003d 100/10 \u003d 10 A is the same for both capacitors, but since a larger capacitor accumulates more electricity, its charging current must take longer, and the charging process is longer.


Rice. 4. Graphs of charging currents for different capacities

Capacitor Discharge

Disconnect the charged capacitor from the generator and attach resistance to its plates. 

There is a voltage Uc on the capacitor plates, therefore, a current will flow in a closed electrical circuit, called the discharge capacitive current idis. 

Current flows from the positive side of the capacitor through the resistor to the negative side. This corresponds to the transition of excess electrons from the negative to the positive, where they are lacking. The process of frames of a row occurs until the potentials of both plates are equal, i.e., the potential difference between them becomes equal to zero: Uc=0. 

On fig. 4, a shows a graph of a decrease in the voltage across the capacitor during a discharge from Uco = 100 V to zero, and the voltage decreases first quickly and then more slowly. 

On fig. 4b shows a graph of the change in the discharge current. The strength of the discharge current depends on the value of the resistance R and, according to Ohm’s law, idis = Uc/R


Rice. 5. Graphs of voltage and currents during the discharge of the capacitor

At the initial moment, when the voltage on the capacitor plates is the largest, the discharge current is also the largest, and with a decrease in Uc during the discharge, the discharge current also decreases. When Uc=0, the discharge current stops. 

The duration of the discharge depends on: 

1) from the capacitance of the capacitor C 

2) on the value of the resistance R, to which the capacitor is discharged. 

The greater the resistance R, the slower the discharge will occur. This is due to the fact that with a large resistance, the discharge current is small and the amount of charge on the capacitor plates decreases slowly. 

This can be shown on the graphs of the discharge current of the same capacitor, having a capacity of 10 microfarads and charged to a voltage of 100 V, at two different resistance values ​​(Fig. 5): curve 1 — at R = 40 Ohm, iopen = Uco/R = 100/40 = 2.5 A and curve 2 — at 20 Ohm iopen = 100/20 = 5 A.


Rice. 6. Graphs of discharge currents at different resistances

The discharge is slower also when the capacitance of the capacitor is large. It turns out this is because with a larger capacitance, there is more electricity on the capacitor plates (more charge) and it will take a longer period of time for the charge to drain.

This is clearly shown by the graphs of the discharge currents for two capacitors with a different capacitance, charged to the same voltage of 100 V and discharging to a resistance R = 40 Ohm (Fig. 6: curve 1 — for a capacitor with a capacity of 10 microfarads and curve 2 — for a capacitor with a capacity of 20 microfarad).


Rice. 7. Graphs of discharge currents for different capacities

From the considered processes, we can conclude that in a circuit with a capacitor, the current passes only at the moments of charge and discharge, when the voltage on the plates changes.

This is explained by the fact that when the voltage changes, the magnitude of the charge on the plates changes, and this requires the movement of charges along the circuit, i.e., an electric current must pass through the circuit. A charged capacitor does not pass direct current, since the dielectric between its plates opens the circuit. 

Capacitor energy 

In the process of charging, the capacitor stores energy, receiving it from the generator. When a capacitor is discharged, all the energy of the electric field is converted into thermal energy, that is, it goes to heat the resistance through which the capacitor is discharged.

The greater the capacitance of the capacitor and the voltage on its plates, the greater will be the energy of the electric field of the capacitor. The amount of energy possessed by a capacitor with a capacitance C, charged to a voltage U, is: W \u003d Wc \u003d CU 2 / 2

Example.  Capacitor C=10 microfarads is charged to voltage Uv=500 V. It is necessary to determine the energy that will be released in the form of heat at the resistance through which the capacitor is discharged.

Solution.  When discharging, all the energy stored by the capacitor will turn into heat. Therefore, W \u003d Wc \u003d CU 2 / 2 \u003d (10 x 10 -6  x 500) / 2 \u003d 1.25 j.

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