1. Lecture 15 Review: Capacitors Related educational materials:
Energy storage and dynamic systems
Basic time-varying signals
Capacitors
Related educational materials:
Chapter 6.3

2. Dynamic Systems
We now consider circuits containing energy storage elements
The circuits are dynamic systems
They are governed by differential equations
We need to be concerned with the input and output of the system as functions of time
The system output depends upon the state of the system at previous times

3. Basic Time-Varying Signals
Step functions
Exponential functions

4. Example: Sliding mass with friction

5. Do forced, natural response; input and output response plots
Time constant and effect of mass on time constant
Notes:
Mention transient, steady-state
Natural vs. forced response
Homogeneous vs. particular solution

6. Energy storage elements – capacitors
Capacitors store energy as an electric field
In general, constructed of two conductive elements separated by a non-conductive material

7. Capacitors Voltage-charge relation: Circuit symbol: Recall: So:
C is the capacitance
Units are Farads (F)

8. Capacitor voltage-current relations
Differential form:
Integral form:

9. Annotate previous slide to show initial voltage, define times on integral, sketchy derivation of integration of differential form to get integral form.

10. Important notes about capacitors
If voltage is constant, no current flows through the capacitor
If nothing in the circuit is changing with time, capacitors act as open circuits
Sudden changes in voltage require infinite current
The voltage across a capacitor must be a continuous function of time

11. Capacitor Power and Energy

12. Example
The voltage applied to the capacitor by the source is as shown. Plot the power absorbed by the capacitor and the energy stored in the capacitor as functions of time.

13. Example – continued

14. Example – continued

15. Series combinations of capacitors

16. Series combinations of capacitors
A series combination of capacitors can be represented as a single equivalent capacitance

17. Parallel combinations of capacitors

18. Parallel combinations of capacitors
A parallel combination of capacitors can be represented as a single equivalent capacitance

19. Example
Determine the equivalent capacitance, Ceq