1. Kevin D. Donohue, University of Kentucky1 Energy Storage Elements Capacitance/Inductance and RC Op Amp Circuits

2. Kevin D. Donohue, University of Kentucky2 Energy Storage in Electric Circuits Analogous to a spring storing the energy used to compress it or a flywheel storing the energy used rotate it …  a capacitor can store energy in an electric field from the voltage used to move charge into it.  An inductor can store the energy in a magnetic field from the current used to create lines of flux around it. L +v(t)-+v(t)- i(t)i(t) C +v(t)-+v(t)- i(t)i(t)

3. Kevin D. Donohue, University of Kentucky3 Examples Solve for voltages, currents, charge, power, and energy in simple circuits containing inductors and capacitors.

4. Kevin D. Donohue, University of Kentucky4 Ideal and Practical Models  What happens if current changes instantaneously in an ideal inductor?  What happens if voltage changes instantaneously in a ideal capacitor?  What would be an equivalent model for an ideal inductor in a DC circuit?  What would be an equivalent model for an ideal capacitor in a DC circuit?

5. Kevin D. Donohue, University of Kentucky5 Ideal and Practical Models  A small amount of current leaks through the dielectric in an actual capacitor. A practical model can be constructed from 2 ideal lumped-parameter models  The coils used to construct an inductor may have a significant resistance component. A practical model can be constructed from 2 ideal lumped- parameter models C R leak L

6. Kevin D. Donohue, University of Kentucky6 Capacitor Combinations  Series capacitors can be combined according to the following formula:  Parallel capacitors can be combined according to the following formula: C1C1 C2C2 CNCN C eq C1C1 C2C2 CNCN   … …

7. Kevin D. Donohue, University of Kentucky7 Inductor Combinations  Series inductors can be combined according to the following formula:  Parallel inductors can be combined according to the following formula: L1L1 L2L2 LNLN L eq L1L1 L2L2 LNLN   … …

8. Kevin D. Donohue, University of Kentucky8 Examples Simplify circuits with series and parallel combinations of inductor and capacitors.

9. Kevin D. Donohue, University of Kentucky9 Application - Integrator Circuit Show that this circuit integrates the input signal v s (t) according to the equation below for time greater than 0: +vo(t)-+vo(t)- vs(t)vs(t) R C

10. Kevin D. Donohue, University of Kentucky10 Application - Differentiator Circuit Show that this circuit differentiates the input signal v s (t) according to the equation below: +vo(t)-+vo(t)- vs(t)vs(t) R C