RC Capacitor Charging Calculator

Calculate the charging voltage of an RC circuit at a specific time

Calculation

RC Circuit Charging

Calculate the charging voltage of a capacitor in an RC circuit (low-pass filter) at a specific time. After 5τ, the capacitor is approximately 99.33% charged. After 1τ, the charging voltage reaches about 63.2% of the input voltage.

Input voltage (applied voltage)
Time after charging begins
Result
Time Constant τ:
Charging Voltage:
Charging Current:

Charging Curve

Hover over the chart to read the charging voltages at different times.



Formulas

Charging Voltage
\[U_C = U_0 \cdot \left(1 - e^{-\frac{t}{\tau}}\right)\]
Time Constant
\[\tau = R \cdot C\]
Charging Current
\[I_R = \frac{U_0 - U_C}{R}\]

Variable Legend

\(R\) Resistor (Ω)
\(C\) Capacitor (F)
\(\tau\) Time Constant (Sec)
\(t\) Charging Time (Sec)
\(U_0\) Input Voltage (V)
\(U_C\) Charging Voltage (V)
\(I_R\) Charging Current (A)
Charging Times
  • After 1τ: 63.2% of the input voltage
  • After 3τ: 95.0% of the input voltage
  • After 5τ: 99.33% of the input voltage

RC Circuit Charging - Theory and Application

An RC circuit (also called an RC low-pass filter) consists of a resistor R and a capacitor C. During charging, the capacitor is charged through the resistor, and the voltage rises exponentially until it reaches the input voltage.

Charging Behavior

Exponential Behavior

The charging follows an inverse exponential function. The voltage rises continuously and asymptotically approaches the input voltage.

\[U_C(t) = U_0 \cdot \left(1 - e^{-\frac{t}{\tau}}\right)\]
Time Constant τ

The time constant determines the speed of charging. After one time constant τ, the voltage has risen to 63.2%.

\[\tau = R \times C\]

Practical Charging Times

Time Charging Voltage Charged Practical Meaning
0.5τ 39.3% 39.3% Start of charging
1τ 63.2% 63.2% One time constant
2τ 86.5% 86.5% Mostly charged
3τ 95.0% 95.0% Practically charged
5τ 99.33% 99.33% Fully charged

Application Examples

Low-Pass Filter:
• Signal smoothing
• Noise suppression
• Anti-aliasing
• Bandwidth limitation
Time Delay:
• Delay circuits
• Soft-start
• Debouncing circuits
• Timing generators
Voltage Smoothing:
• Smoothing capacitors
• Power supplies
• Voltage regulators
• Buffer circuits

Calculation Example

Example: Delay Circuit

Given: R = 100kΩ, C = 10µF, U₀ = 5V, t = 1s

Calculate Time Constant:

\[\tau = R \times C = 100k\Omega \times 10\mu F = 1s\]

Charging Voltage after 1s:

\[U_C = 5V \times (1 - e^{-\frac{1s}{1s}}) = 5V \times 0{,}632 = 3{,}16V\]

✓ After one second, the voltage has risen from 0V to 3.16V (63.2% of 5V).

Charging Current Behavior

Initial Charging Current

At the start of charging (t = 0), the capacitor is uncharged (UC = 0V). The initial current is therefore at its maximum:

\[I_0 = \frac{U_0}{R}\]
Current Behavior

The charging current decreases exponentially as the voltage difference between the input voltage and the capacitor voltage decreases:

\[I(t) = \frac{U_0}{R} \cdot e^{-\frac{t}{\tau}}\]
Important Notes
  • Charging is a continuous process without abrupt changes
  • In practice, a capacitor is considered fully charged after 5τ
  • The charging current is highest at the beginning and decreases exponentially
  • The time constant τ is independent of the input voltage
  • Temperature fluctuations can slightly change R and C
  • The charging current is limited by the resistor R

Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?


Capacitor functions

Series connection with capacitors  •  Series connection with 2 capacitors  •  Reactance Xc of a capacitor  •  Time constant of an R/C circuit  •  Capacitor charging voltage  •  Capacitor discharge voltage  •  R/C for the charging voltage  •  Series circuit R/C  •  Parallel circuit R/C  •  Low pass-filter R/C  •  High pass-filter R/C  •  Integrator R/C  •  Differentiator R/C  •  Cutoff-frequency R,C  •  R and C for a given impedance  •