1. Natural Response of an RC Circuit
ECE 201 Circuit Theory I

2. Typical RC Circuit
ECE 201 Circuit Theory I

3. Circuit Conditions
Assume that the switch has been in position a for a very long time.
ECE 201 Circuit Theory I

4. The Capacitor is Charged to the Source Voltage Vg
The circuit now looks like
ECE 201 Circuit Theory I

5. Write the Node Voltage Equation
ECE 201 Circuit Theory I

6. Substituting back
ECE 201 Circuit Theory I

7. Plot of the Natural Response
ECE 201 Circuit Theory I

8. Current, Power, and Energy
ECE 201 Circuit Theory I

9. Summary of Procedure
Determine the initial voltage across the Capacitor.
Determine the Time Constant, τ.
Apply
ECE 201 Circuit Theory I