Solution to the RC Circuit Differential Equation
This page presents the mathematical solution to the differential equation derived on the previous page, providing insights into the charge condensateur formule capacitorchargingformula.
The solution process involves:
- Identifying the general form of the solution
- Determining the particular solution based on initial conditions
- Combining the general and particular solutions
Example: The general solution takes the form:
Uct = Ae^−t/RC + E
Where A is a constant determined by initial conditions.
For a capacitor initially uncharged Uc=0att=0, the complete solution is:
Uct = E1−e(−t/RC)
Highlight: This equation describes the voltage across the capacitor as it charges over time.
Key observations:
- The capacitor voltage approaches the source voltage E as time increases
- The temps de charge condensateur formule capacitorchargingtimeformula is characterized by the time constant τ = RC
Definition: The time constant τ represents the time it takes for the capacitor to reach approximately 63% of its final voltage.
This solution is fundamental for understanding the circuit RC équation différentielle RCcircuitdifferentialequation and its applications.
