1. LCR circuit R V0 L I(t)=0 for t<0 V(t) C + trial solution2 R + V0 1 L
I(t)=0 for t<0
V(t) C
trial solution
characteristic equation
general solution

2. LCR circuit – initial conditions+ R L V0 C
I(t)
Initial conditions I(0), ?
No energy stored

3. LCR circuit
overdamped solution

4. LCR circuit
critically damped solution

5. LCR circuit t
underdamped (oscillatory) solution

6. LCR circuit overdamped solution β is real critically damped solution
underdamped (oscillatory) solution

7. LCR circuit overdamped solution critically damped solution
underdamped (oscillatory) solution

8. CP2 September 2003

9. This way up

10. This way up

11. This way up

12. This way up

13. LCR circuit overdamped solution critically damped solution
underdamped (oscillatory) solution