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The capacitor on DC voltage - an energy store

Test:

Here is the circuit diagram for a better understanding:

Energy Stored on a Capacitor

Energy Stored on a Capacitor

Capacitor - Function and Symbol

Capacitor - Function and Symbol

At DC voltage, the capacitor acts as a charge accumulator. Essentially, the capacitor consists of two plates, which are electrically separated from each other - either by air or by an insulator (dielectric).

A characteristic value of the capacitor is the capacitance C. It describes the capacity of the capacitor to store a certain amount of charge Q on its plates at a certain voltage.

Q = C * V    or    C = Q / V

Colloquially expressed: "The larger the capacitor and the higher the voltage, the more charges find room on the capacitor plates".

Unit: [C] = Farad F = 1 C / V ("One Farad equals one Colomb per Volt")

Usual sizes:
Millifarad mF   =  10-3 F
Microfarad µF  = 10-6 F
Nanofarad nF  =  10-9 F
Picofarad pF   =  10-12 F

How to determine the capacity of a capacitor?

Plate distance: The smaller the plate distance, the more the charges on the opposite plate attract each other and the "more" charges therefore find "space" on the plates.

Capacitor - Plate distance and capacity

Capacitor - Plate distance and capacity

Plate area A: The larger the plate areas, the more loads can be stored on the plate.
Dielectric: Electric dipoles of the dielectric align themselves with the charges of the capacitor and "neutralize" them. Thus, more charges find place on the plates of the capacitor.

Capacitor - Dielectric and Capacity

Capacitor - Dielectric and Capacity


Charge- and Discharge Curve

Capacitor - Charge- and Discharge curve

Capacitor - Charge- and Discharge curve


Capacitor Charging Graph

Capacitor Charging Graph

Determine the time to charge or discharge a capacitor

As can be seen, the charge and discharge curves of a capacitor have a curvilinear shape, which can be described according to an e-function. Therewith, the capacitor would actually never be fully charged, a thing that of course does not make sense in practice.

In general, a capacitor charges and discharges more slowly the larger its capacity and the larger the resistor R in series. This is the basis for the so-called Time constant Ƭ (pronounced "Tau"):

Ƭ = R * C in seconds s

In practice, you would apply the following rule of thumb: The capacitor is fully charged or discharged after 5 Ƭ. The capacitor voltage has thus reached 0.99 of the supply voltage.

The level of the applied voltage has no influence on the charging time!

Always charge and discharge capacitors - especially larger ones - via a series resistor!


Charge and Discharge Equations

Capacitor to DC voltage– Charge and Discharge Equations

Capacitor to DC voltage– Charge and Discharge Equations


Exercise - Charge and Discharge Capacitor

The following parallel circuit is connected to a DC voltage of 100 V. How long does it take until both currents I1 and I2 are equal?

Capacitor to DC voltage– Charge and Discharge Equations - Exercise

Capacitor to DC voltage– Charge and Discharge Equations - Exercise

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