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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
RC Circuit - charging capacitor Hover me! Get this illustration
RC Circuit - charging capacitor

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 \(t\).
Details about the formula
  • Summary: With this formula you can calculate the current at all times that flows into the capacitor during charging. Resistance and capacitance as well as charging current must be given.
  • This formula was added by FufaeV on .
  • This formula was updated by FufaeV on .