R/C for given charging voltage

Calculation of R or C for a given charging voltage at a specific time

Calculate R/C for charging voltage

RC Charging Process

On this page you can calculate the values of a capacitor or resistor that are required to achieve a specific charging voltage on a capacitor at a given time.

Results
Resistor:
Capacitor:

RC Charging Process

RC Charging Circuit
Legend
R = Resistor [Ω]
C = Capacitor [F]
τ = Time constant [s]
t = Charging time [s]
U = Applied voltage [V]
UC = Capacitor charging voltage [V]
Calculation formulas
Capacitor: \[C = \frac{t \cdot (-1)}{R \cdot \ln\left(1-\frac{U_C}{U}\right)}\]
Resistor: \[R = \frac{t \cdot (-1)}{C \cdot \ln\left(1-\frac{U_C}{U}\right)}\]
Charging Process
  • Exponential function: UC(t) = U(1 - e-t/τ)
  • Time constant: τ = RC
  • 63% after τ: After one time constant
  • 99% after 5τ: Practically fully charged

RC Charging Process - Theory and Applications

The Capacitor Charging Process

When charging a capacitor through a resistor, the voltage across the capacitor follows an exponential function. The charging speed is determined by the time constant τ = RC. These calculations make it possible to determine the required component values for a desired charging voltage at a specific time.

Mathematical Foundations

Charging voltage over time
\[U_C(t) = U \cdot \left(1 - e^{-\frac{t}{\tau}}\right)\]

Exponential function of the charging process with Ω = RC

Rearrangement for R and C
\[\frac{U_C}{U} = 1 - e^{-\frac{t}{\tau}}\]

Normalized form for component calculation

Time Constant and Charging Behavior

After 1τ (63%)
\[U_C = 0.632 \cdot U\]

After one time constant the capacitor is 63% charged.

After 3τ (95%)
\[U_C = 0.950 \cdot U\]

After three time constants practically fully charged.

After 5τ (99%)
\[U_C = 0.993 \cdot U\]

After five time constants full charge is reached.

Practical Applications

Timing Circuits:
• Timer circuits
• Delay circuits
• Oscillators
• Pulse generators
Power Supply:
• Buffer capacitors
• Soft-start circuits
• Voltage regulators
• Backup systems
Signal Processing:
• Sample-and-hold
• Integrator circuits
• ADC inputs
• Analog filters

Calculation Examples

Example 1: Calculate resistor

Given: C = 10µF, U = 12V, UC = 8V, t = 10ms

\[R = \frac{0.01 \cdot (-1)}{10 \times 10^{-6} \cdot \ln(1-8/12)} = 918Ω\]

Result: The required resistor is approximately 918Ω.

Example 2: Calculate capacitor

Given: R = 1kΩ, U = 5V, UC = 3V, t = 1ms

\[C = \frac{0.001 \cdot (-1)}{1000 \cdot \ln(1-3/5)} = 1.1µF\]

Result: The required capacitance is approximately 1.1µF.

Design Considerations

Important Design Aspects
  • Time constant: τ = RC determines the charging speed
  • Voltage rating: Capacitor must be rated for operating voltage
  • Leakage current: Real capacitors have parasitic resistances
  • Tolerances: Component variations affect timing behavior
  • Temperature influence: Capacitance and resistance are temperature dependent
  • ESR: Equivalent series resistance affects behavior

Discharge Process

Capacitor Discharge
\[U_C(t) = U_0 \cdot e^{-\frac{t}{\tau}}\]

During discharge, the voltage follows a falling exponential function. After one time constant, 37% of the initial voltage remains.

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