1. Chapter 5: CAPACITANCE and INDUCTANCE
Capacitors
Inductors
Capacitor Inductor Combinations

2. Review So far, we have talked about two kinds of circuit elements:
Sources (independent and dependent)
active, can provide power to the circuit.
Resistors
passive, can only dissipate power.

3. Energy Storage Elements
Capacitors store energy in an electric field
Inductors store energy in a magnetic field
Capacitors and inductors are passive elements:
Can store energy supplied by circuit
Can return stored energy to circuit
Cannot supply more energy to circuit than is stored
Voltages and currents in a circuit with energy storage elements are solutions to linear, constant coefficient differential equations!

4. For Practical Solutions
Practicing engineers almost never solve the differential equations directly.
Instead, they use:
LaPlace transforms (covered in EEE 302)
AC steady-state analysis
These techniques covert the solution of differential equations into algebraic problems-circuit analysis.

5. Example Applications
Capacitors and inductors are used to build filters and amplifiers with desired frequency responses:
RF and IF amplifiers in a superhetrodyne receiver
Instrumentation amplifiers
Capacitors are used in A/D converters to hold a sampled signal until it can be converted into bits
Integrated circuits have layers of conductors (metal, silicon with impurities) with insulators (glass) between. This is a capacitor!
This capacitance is one of the limiting factors in processor speeds
This capacitance is used to create RAM’s

6. Capacitance
Capacitance occurs when two conductors (plates) are separated by a dielectric (insulator).
Charge on the two conductors creates an electric field that stores energy.
The voltage difference between the two conductors is proportional to the charge:
q = C v
The proportionality constant C is called capacitance.
Units of Farads (F) - C/V

7. Capacitors
i(t) + -
v(t)
The
rest of
the
circuit

8. Capacitors (cont’d)
Energy stored:

9. Example
i(t)
The
rest of
the
circuit +
0.2F
v(t) - t
i(t) 1A
-1A 1s 2s

10. Example (cont’d) t
v(t) 5V 1s 2s
wc(t)
2.5J 2s 1s t