1. Electrical circuits, power supplies and passive circuit elements
Lecture B
Electrical circuits, power supplies and passive circuit elements

2. Electrical Circuits
We want to transfer electrical energy to perform a task
We want to supply energy to some load
Charged particles want to “move” when an emf applied
Apply emf and constrain the path of the charged particles
Force charged particles to supply energy to the load in order to do work (no path through load  no useful work done!)

3. Electrical Circuit – example

4. Types of Circuit Elements
Circuit components are generally classified as control elements, passive elements, and active elements
Control Elements – direct and modify the current (e.g. switches)
Passive Elements – total energy delivered to the element by the rest of the circuit is nonnegative (e.g. resistors, capacitors, inductors)
Active Elements – can provide energy to the circuit (e.g. batteries, generators)

5. Control Elements Examples: Switches and transistors (MOSFETs, BJTs)
We will present only switches here – MOSFETs and BJTs will be introduced in a later lecture

6. Control element example -- switches
Switches can be used to direct and control the flow of current
The switch can act as an insulator or a conductor

7. Switch operation
Time t<0:
Time t>0:

8. Power Supplies Power supplies provide a source of electrical power
The power source is typically a non-electrical process
Electro-mechanical sources: generators typically convert a rotational motion to electrical power by moving magnets relative to one another. The rotational motion is induced by mechanical means, such as flowing fluid through a turbine.
Chemical sources: batteries convert energy created by a chemical reaction to electrical energy
Piezoelectric materials produce a voltage when they are deformed
Solar cells convert light to electrical energy

9. Conceptual types of power supplies
Power supplies can be modeled in a number of ways:
Voltage, current sources
Independent, dependent sources
Ideal and non-ideal sources

10. Voltage sources
Independent voltage sources provide a specified voltage
Regardless of the current provided
Can provide infinite power!
Ideal, independent voltage source symbols:

11. Voltage sources – continued
Dependent voltage sources provide a voltage which is based on some other parameter in the system
Example dependent source symbol:
Often used as control elements

12. Current sources
Independent current sources provide a specified current
Regardless of the voltage provided
Can provide infinite power!
Ideal, independent current source symbol:

13. Current sources – continued
Dependent current sources provide a current which is based on some other parameter in the system
Example dependent source symbol:
Also often used as control elements

14. Common types of source signals
Time-varying signals
DC (Direct Current) signals
Constant with time
AC (Alternating Current)
Vary sinusoidally with time

15. Passive Circuit Elements
Examples:
Resistors
Capacitors
Inductors

16. Passive circuit elements - resistors
Resistance models the fact that energy is always lost during charge motion
Electrons moving through a material “collide” with the atoms composing the material
These collisions impede the motion of the electrons
Thus, a voltage potential difference is required for current to flow. This potential energy balances the energy lost in these collisions.

17. Resistance

18. Resistors Circuit symbol: R is the resistance
Units are ohms ()
Voltage-current relation (Ohm’s Law):

19. Resistance analogies
Sliding mass with constant velocity on surface with friction
Energy added by force applied to mass
Energy dissipated by friction as heat
Pressure loss in horizontal pipe
Energy added by pump
Energy dissipated by friction in pipe

20. Note that, in the two previous cases, none of the energy being supplied to the system is stored. The energy supplied by the force and by the pump are dissipated by the friction as heat. The kinetic and potential energies in the systems are not changing.
Resistance is purely and energy dissipation mechanism

21. Demos: Show types of resistors (power resistor, low power resistor)
Apply voltage to power resistor, measure current. Calculate power. Note that power resistor heats up as power dissipation increases.
Apply voltage to low power, high-resistance resistor. Calculate power dissipation.
Apply voltage to low power, low-resistance resistor. Calculate power dissipation, burn out resistor.

22. Passive circuit elements – capacitors
Capacitors store energy in the form of an electric field
Typically constructed of two conductive materials separated by a non-conductive (dielectric) material

23. Capacitors Circuit symbol: C is the capacitance
Units are Farads (F)
Voltage-current relation:
Capacitors can store energy

24. Capacitors Notes: Capacitors can store energy
The voltage-current relation is a differential equation
Capacitance limits rate of change of voltage
If the voltage is constant, the current is zero and the capacitor looks like an open-circuit

25. Capacitance analogies
Stretched spring
Energy added by force in spring
Energy stored in spring:
Pressurized accumulator
Energy added by pressure change
Energy stored by pressure change

26. Demos: Show types of capacitors, note sizes
Demo of energy storage with Bob Olsen’s super-capacitor/wheel device
Analogous systems:
Stretched spring
Toilet tank

27. Passive circuit elements - inductors
Inductors store energy in the form of a magnetic field
Often constructed by coiling a conductive wire around a ferrite core

28. Demo: Simple electromagnet

29. Inductors Circuit symbol: L is the inductance
Units are Henries (H)
Voltage-current relation:
Inductors can store energy

30. Inductors Notes: Inductors can store energy
The voltage-current relation is a differential equation
If the current is constant, the voltage difference is zero and the inductor looks like a perfect conductor

31. Inductor analogies
Increasing velocity of sliding mass (with no friction)
Applied force increases energy applied to mass
Energy stored in change of velocity of mass:
Increased flow rate in fluid system
Applied pressure adds energy
Energy stored in increased fluid flow rate:

32. Demo: Electromagnet to illustrate magnetic field
Show practical inductors
Analogies:
Sliding mass
Slug of moving fluid