Series and parallel connection of capacitors and charging and discharging process

1. Connection method of capacitor

1. Parallel connection

The electrodes of two or more capacitors with the same polarity are connected together. The connection method of the access circuit is the parallel connection of the capacitors. The parallel connection of the two capacitors is as shown in the figure.

Capacitors in parallel

The total capacitance of parallel capacitors is equal to the sum of the parallel capacitances.

Capacitor parallel calculation formula

Capacitors connected in parallel are equivalent to increasing the facing area of ​​the capacitor plates, so the equivalent capacitance is always greater than the capacitance of any one of the capacitors.

2. Series connection

Connect the positive terminal of the next capacitor to the negative terminal of the previous capacitor, and connect the positive terminal of the first capacitor and the negative terminal of the last capacitor to the circuit. This connection is called a series connection. Two capacitors are connected in series as shown in the figure.

Capacitors in series

When capacitors are connected in series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of each capacitance.

Series capacitance calculation formula

When capacitors are connected in series, it is equivalent to increasing the distance between the capacitor plates, and the equivalent capacitance is smaller than the capacitance of any one capacitor. Capacitors in series can share the voltage of a circuit.

2. Charging and discharging of capacitors

1. Capacitor charging

In the circuit shown below, US is a constant voltage source, C is a capacitor with a large capacitance, S is a single-pole double-throw switch, and H is a light bulb. First close the switch S and contact 1, and the power supply charges the capacitor.

Capacitor charging experimental circuit

During the charging process, no charge directly passes through the dielectric inside the capacitor, but the electrons move directionally from the positive plate of the capacitor → light bulb → ammeter → positive electrode of the power supply → negative electrode of the power supply → negative plate of the capacitor, forming a current, as shown in the figure.

Capacitor charging diagram

The charging process is the initial stage of charging. The charging current is large and u rises quickly. As , the charging current gradually decreases and the rising speed of u slows down and approaches the power supply voltage E. The curve is shown in the figure.

Capacitor charging curve

It can be observed on the circuit that the light goes from bright to dark and finally goes out. The relevant formulas involved are as follows:

Charging time constant

Charging voltage

recharging current

The relationship between time constant and charging voltage is as follows.

τc--------Charging voltage Vc (v)

0----------0%

1τc------63.2%

2τc------86.5%

3τc------95%

4τc------98.2%

5τc------100%

2. Capacitor discharge

Close the switch S and contact 2, and the capacitor discharges the lamp H.

Capacitor discharge test circuit

It can be seen from the figure that during the discharge process of the capacitor, no charge passes through the internal dielectric of the capacitor.

Capacitor discharge diagram

The discharge process of the capacitor is the largest at the beginning, and then gradually decreases; the charge of the capacitor is the largest at the beginning of the discharge process, and then gradually decreases. When the charge decreases to zero, the discharge is completed, and the current decreases to zero. The curve is as follows.

Capacitor discharge curve

It can be observed on the circuit that the light goes from bright to dark and finally goes out. This phenomenon is common in daily life. For example, after you turn off the power of some electronic devices, the power indicator light on the device slowly goes out, which is a phenomenon of capacitor discharge. There are many power strips that can be seen. The relevant formulas involved in capacitor discharge are as follows:

Capacitor discharge time constant

capacitor discharge voltage

capacitor discharge current

3. Summary

When the capacitance value we want is not available on hand, we can get it by connecting capacitors in series and parallel. A characteristic of the capacitor can be obtained by charging and discharging the capacitor. The voltage across the capacitor cannot change suddenly. It doesn't matter if you can't remember the charging process of the capacitor, but you should remember the relationship between the time constant and the charging voltage and the characteristic that the voltage cannot change suddenly. These two points will be of great help when you design and analyze the circuit.