Capacitors 2 conducting plates separated by an insulator (or dielectric) Connect to a voltage source, stores +q and –q on plates: q = Cv C = capacitance in F Symbol

Differentiate: Integrate: For DC signals, a capacitor is an open circuit. Power: Energy: Continuity of Energy: Voltage of a capacitor cannot “jump.” Ideal vs. Real Capacitors:

Example 1. Find the current through a 200-μF capacitor whose voltage is shown.

Example 2. Find the stored energy in each capacitor under dc conditions. Ans. 16 mJ, 128 mJ

Parallel Capacitors

Series Capacitors

Example 3. Find the voltage across each capacitor. Ans: 15V, 10V, 5 V

Inductors a coil of conducting wire L = inductance in H Symbol

v-i char:: Integrate: For DC signals, an inductor is a short circuit. Power: Energy: Continuity of Energy: Current in an inductor cannot “jump.” Ideal vs. practical Inductors:

Example 4. Under dc conditions, find iL and vC and stored energy. Ans. 2A, 10V,4J, 50J

Series and Parallel Inductors Inductors: L behaves like R Capacitors: C behaves like G Voltage and Current Divider Equations apply.

Example 5. Given: Find:

Passive Elements: Power and Energy

Compare with Mechanics Mass: Spring: Fluid Friction:

Electrical Mechanical Rotational q x θ i u ω v f τ C k κr R D Dr L M J (or I)