Lecture B
Electrical circuits, power supplies and
passive circuit elements
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!)
Electrical Circuit – example
A
Voltage source –
provides power
to circuit
v(t)
t=0
Switch – modifies
path of charges
B
+-
Circuit elements
Perfect conductors
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)
Control Elements
• Examples:
• Switches and transistors (MOSFETs, BJTs)
• We will present only switches here – MOSFETs and BJTs
will be introduced in a later lecture
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
Switch operation
• Time t<0:
• Time t>0:
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
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
Voltage sources
• Independent voltage
sources provide a
specified voltage
• Regardless of the
current provided
• Can provide infinite
power!
• Ideal, independent
voltage source symbols:
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
Current sources
• Independent current
sources provide a
specified current
• Regardless of the
voltage provided
• Can provide infinite
power!
• Ideal, independent
current source symbol:
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
Common types of source signals
• Time-varying signals
• DC (Direct Current)
signals
• Constant with time
• AC (Alternating Current)
• Vary sinusoidally with
time
Passive Circuit Elements
• Examples:
• Resistors
• Capacitors
• Inductors
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.
Resistance
Resistors
• Circuit symbol:
• Voltage-current
relation (Ohm’s Law):
v( t )  R  i( t )
• R is the resistance
• Units are ohms ()
Resistance analogies
• Sliding mass with constant
velocity on surface with friction
• Pressure loss in horizontal
pipe
P1
Flow rate
P2
Mass’s
velocity, v(t)
Externally applied
force, F(t)
Mass, m
Surface with sliding
coefficient of friction, b
Pump
• Energy added by force
applied to mass
• Energy dissipated by friction
as heat
• Energy added by pump
• Energy dissipated by
friction in pipe
• 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
• 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.
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
Capacitors
• Circuit symbol:
• Voltage-current
relation:
dv( t )
i( t )  C
dt
• C is the capacitance
• Units are Farads (F)
• Capacitors can store
energy
Wc 
1 2
Cv
2
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
Capacitance analogies
• Stretched spring
• Energy added by force in spring
• Energy stored in spring:
1
Ws  C S F 2
2
• Pressurized accumulator
• Energy added by pressure change
• Energy stored by pressure change
1
W f  C f ( Pgas ) 2
2
• 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
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
• Demo: Simple electromagnet
Inductors
• Circuit symbol:
• Voltage-current
relation:
v( t )  L
• L is the inductance
• Units are Henries (H)
di( t )
dt
• Inductors can store
energy
WL 
1 2
Li
2
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
Inductor analogies
• Increasing velocity of sliding
mass (with no friction)
• Increased flow rate in fluid
system
• Applied force increases energy
applied to mass
• Energy stored in change of
velocity of mass:
• Applied pressure adds energy
• Energy stored in increased fluid
flow rate:
1
Wm  mv 2
2
Wf 
1
Lw 2
2
• Demo:
– Electromagnet to illustrate magnetic field
– Show practical inductors
– Analogies:
• Sliding mass
• Slug of moving fluid