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Level 3
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.

# Formula: Charging capacitor Capacitor current   Charging current   Capacitance   Resistance   Time

$$I(t) ~=~ I_0 \, \mathrm{e}^{-\frac{t}{R\,C}}$$ $$I(t) ~=~ I_0 \, \mathrm{e}^{-\frac{t}{R\,C}}$$ $$I_0 ~=~ I(t) \, \mathrm{e}^{\frac{t}{R\,C}}$$ $$C ~=~ - \frac{ t }{ \ln\left( \frac{I(t)}{I_0} \right) \, R }$$ $$R ~=~ - \frac{ t }{ \ln\left( \frac{I(t)}{I_0} \right) \, C }$$ $$t ~=~ - \ln\left( \frac{I(t)}{I_0} \right) \, R \, C$$ Rearrange formula

## Capacitor current

$$I(t)$$
Unit $$\text{A}$$
Capacitor current is the electric current that flows into the plate of the capacitor and thus builds up a voltage on the capacitor. This capacitor current decreases exponentially with time during the charging process, while the capacitor voltage $$U(t)$$ increases exponentially.

## Charging current

$$I_0$$
Unit $$\text{A}$$
Charging current is the initial current that flows into the capacitor plate at time $$t = 0$$. Its value is given by the applied source voltage.

## Capacitance

$$C$$
Unit $$\text{F}$$
Electrical capacitance is a characteristic quantity of the capacitor and tells how many charges must be brought onto the capacitor to charge the capacitor to the voltage $$1 \, \text{V}$$.

## Resistance

$$R$$
Unit $$\Omega$$
Resistor with resistance $$R$$ connected in series with the capacitor. The resistor has an influence on how fast the capacitor can charge.

## Time

$$t$$
Unit $$\text{s}$$
After the source voltage $$U_0$$ is applied (switch is closed), the capacitor starts to charge. The charging current starts to flow through the circuit and decays over time $$t$$.