RC Capacitor Discharge Calculator

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

Calculation

RC Circuit Discharge

Calculate the discharge voltage of a capacitor in an RC circuit (low-pass filter) at a specific time. After 5τ, the capacitor is approximately 99.33% discharged.

Initial voltage (charging voltage)
Time after discharge begins
Result
Time Constant τ:
Discharge Voltage:
Discharge Current:

Discharge Curve

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


Formulas

Discharge Voltage
\[U_C = U_0 \cdot e^{-\frac{t}{\tau}}\]
Time Constant
\[\tau = R \cdot C\]
Discharge Current
\[I_R = \frac{U_C}{R}\]

Variable Legend

\(R\) Resistor (Ω)
\(C\) Capacitor (F)
\(\tau\) Time Constant (Sec)
\(t\) Discharge Time (Sec)
\(U_0\) Initial Voltage (V)
\(U_C\) Discharge Voltage (V)
\(I_R\) Discharge Current (A)
Discharge Times
  • After 1τ: 36.8% of the initial voltage
  • After 3τ: 5.0% of the initial voltage
  • After 5τ: 0.67% of the initial voltage

RC Circuit Discharge - Theory and Application

An RC circuit (also called an RC low-pass filter) consists of a resistor R and a capacitor C. During discharge, the current stored in the capacitor flows through the resistor, and the voltage decreases exponentially.

Discharge Behavior

Exponential Behavior

The discharge follows an exponential function. The voltage decreases continuously but theoretically never reaches zero.

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

The time constant determines the speed of discharge. After one time constant τ, the voltage has dropped to 36.8%.

\[\tau = R \times C\]

Practical Discharge Times

Time Remaining Voltage Discharged Practical Meaning
0.5τ 60.7% 39.3% Start of discharge
1τ 36.8% 63.2% One time constant
2τ 13.5% 86.5% Mostly discharged
3τ 5.0% 95.0% Practically discharged
5τ 0.67% 99.33% Fully discharged

Application Examples

Low-Pass Filter:
• Noise suppression
• Signal smoothing
• Anti-aliasing
• Audio filters
Timers:
• Delay circuits
• Pulse shapers
• Blinkers
• Reset circuits
Energy Storage:
• Buffer capacitors
• Flash devices
• Backup storage
• Voltage smoothing

Calculation Example

Example: Timing Circuit

Given: R = 100kΩ, C = 10µF, U₀ = 12V, t = 1s

Calculate Time Constant:

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

Discharge Voltage after 1s:

\[U_C = 12V \times e^{-\frac{1s}{1s}} = 12V \times 0{,}368 = 4{,}42V\]

✓ After one second, the voltage has dropped from 12V to 4.42V (63.2% discharged).

Important Notes
  • Discharge is a continuous process without abrupt changes
  • In practice, a capacitor is considered fully discharged after 5τ
  • The discharge current is highest at the beginning and decreases exponentially
  • The time constant τ is independent of the initial voltage
  • Temperature fluctuations can slightly change R and C


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  •