Introduction to Electrical Engineering - Basic vocational knowledge (Institut für Berufliche Entwicklung, 213 p.)
 6. Electrical Field
 6.2. Capacity
 6.2.1. Capacity and Capacitor 6.2.2. Behaviour of a Capacitor in a Direct Current Circuit 6.2.3. Types of Capacitors

### 6.2.2. Behaviour of a Capacitor in a Direct Current Circuit

An uncharged capacitor is connected to a direct voltage source according to Fig. 6.9. (switch position 1).

Fig. 6.9. Circuit for charging and discharging a capacitor

The terminal voltage of the uncharged capacitor is 0. In order that, between the plates of the capacitor, the voltage can be applied to which it is connected, the capacitor must be charged. This means that a charging current must flow at the instant of switching on. The intensity of the current at the instant of switching on is determined by the large difference between charging voltage and terminal voltage of the capacitor and the resistance. With increasing charge of the capacitor, the voltage of it increases and will reach the value of the charging voltage when the process of charging is finished. With increasing charge, the voltage difference between charging voltage and terminal voltage of the capacitor also drops and, consequently, the charging current also drops. At the end of charging, the voltage difference and the charging current are 0. A direct current is no longer allowed to flow now. This is also due to the design of the capacitor because a dielectric (insulating material) is between its two connections.

When the capacitor is now discharged via a resistor according to Fig. 6.9. (switch position 2), at the first instant of discharge, a discharge current must flow which is only limited by the resistance. Since, due to the discharge, the terminal voltage of the capacitor drops, the discharge current must also drop in the course of time. After complete discharge, the terminal voltage and the discharge current have dropped to 0. The course taken by current and voltage during charging and discharging is shown in Fig. 6.10. Charging commences at time t1 and discharging at time t2. It is evident that charging and discharging currents suddenly reach their maximum value at the beginning of the charging or discharging process and then they reach the value of 0 after some time. Both in charging and in discharging, the voltage changes its value only slowly. There are no sudden voltage changes in capacitors.

Fig. 6.10. Behaviour or current and voltage during the charging and discharging of a capacitor tein = ton · taus = toff

Since the peak value of the discharge current is limited only by the discharge resistance, a capacitor should not be discharged via s short circuit. If this would occur, however, at the first instant of discharge, an extremely high current would flow for a short time which might cause the destruction of the capacitor or a fusing of the shorting bridge. As a capacitor retains its charge for some time after charging without external discharge, particular caution is necessary when working at installations containing capacitors. After disconnection from the mains, the fact that the capacitors are completely discharged must be checked or discharge via a resistor must be effected. In many installations, a discharge resistance is incorporated in order to avoid dangers to man.

During discharging, a capacitor acts as an electrical energy source (during a certain time, its terminal voltage drives a current). The energy stored in a capacitor is written as

W = C/2 · U2

(6.7.)

where:

 W energy C capacity U voltage

The energy that can be stored in a capacitor is relatively small. It is of advantage however, that it is available as a short-time energy release. Advantage of this effect is taken in a photoflash device and in some spot-welding equipment.

Example 6.2.

Which energy is stored in a capacitor of 47 µF charged up to 100 V?

Given:

U = 100 V
C = 47 µF

To be found:

W

Solution:

W = C/2 · U2
W = 23.5 · 10-6 (A·· s)/V · 104 V2
W = 0.235 Ws
W = 235 mWs

The energy stored in the capacitor is 235 mWs.