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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 20:38:01

These online calculators computes various parameters for charging and discharging the capacitor with the resistor. Formulae used for calculations are below the calculators.

##### Discharging the Capacitor with the Resistor

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

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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