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Capacitor in Direct Current Circuit

These online calculators computes various parameters for charging and discharging the capacitor with the resistor
Timur2012-07-08 15:39:56
These online calculators computes various parameters for charging and discharging the capacitor with the resistor. Formulae used for calculations are below the calculators.
Charging the Capacitor with a ResistorCreative Commons Attribution/Share-Alike License 3.0 (Unported)
0.12345678901234567890
 Time Constant, milliseconds:
 5 Time Constants (99.2% charged), milliseconds:
 Initial Current, Amperes:
 Maximum Power Dissipation, Watts:
 Capacitor Voltage, Volts:
 Capacitor Charge, microCoulombs:
 Capacitor Energy, milliJoules:
 Power Supply Work, milliJoules:

Discharging the Capacitor with the ResistorCreative Commons Attribution/Share-Alike License 3.0 (Unported)
0.12345678901234567890
 Initial Capacitor Energy, milliJoules:
 Initial Capacitor Charge, microCoulombs:
 Time Constant, milliseconds:
 Initial Current, Amperes:
 Maximum Power Dissipation, Watts:
 Final Capacitor Charge, microCoulombs:
 Final Capacitor Energy, milliJoules:
 Final Capacitor Voltage, Volts:

Below is the picture of electrical circuit for charging the capacitor with the power supply unit.
capacitor.jpg

After switch K is closed, direct current starts charging the capacitor.
According to Ohms law, the sum of capacitor and resistor voltages is equal to power supply voltage.
\epsilon=IR+\frac{q}{C}
The capacitor charge and current depend on time. At the initial moment, there is no charge at the capacitor, thus, current is maximum, as well as power dissipation on the resistor.
I=\frac{\epsilon}{R}, P=I^2R
During charging, capacitor voltage changing according to the following equation
V(t)=\epsilon(1-e^{-\frac{t}{RC}})
where tau
\tau=RC
is called Time Constant. Since charging is infinite process, usually, a capacitor is considered to be fully charged after 5 time constants. After 5 time constants, the capacitor will be charged to 99.2% of the supply voltage.
Capacitor Charge
Q=CV
Capacitor Energy
W=\frac{Q^2}{2C}
Work of Power Supply
A=Q\epsilon

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