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Energy Storage Elements

Energy Storage Elements. Capacitance/Inductance and RC Op Amp Circuits . i ( t ). + v ( t ) -. C. i ( t ). + v ( t ) -. L. 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 …

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Energy Storage Elements

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

  2. i(t) + v(t) - C i(t) + v(t) - L 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. Kevin D. Donohue, University of Kentucky

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

  4. 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? Kevin D. Donohue, University of Kentucky

  5. 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 Rleak L Rleak Kevin D. Donohue, University of Kentucky

  6. Capacitor Combinations • Series capacitors can be combined according to the following formula: • Parallel capacitors can be combined according to the following formula: …  C1 C2 CN Ceq …  C1 C2 CN Ceq Kevin D. Donohue, University of Kentucky

  7. Inductor Combinations • Series inductors can be combined according to the following formula: • Parallel inductors can be combined according to the following formula: …  L1 L2 LN Leq …  L1 L2 LN Leq Kevin D. Donohue, University of Kentucky

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

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

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

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