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# Electrical circuits

## 1.

Electrical Circuits
ALESSANDRO VOLTA
(1745-1827)
ANDRE MARIE AMPERE
(1775-1836)
GEORG SIMON OHM
(1789-1854)

## 2.

Sources of Voltage (Energy)
Voltage, also
known as
“electromotive
force” can be
create by
many sources
of energy
solar
geothermal
wind
biomass
nuclear
hydroelectric
chemical
piezoelectric
ALLESANDRO VOLTA AND THE ELECTRIC BATTERY
A VOLTAGE SOURCE IS LIKE A WATER PUMP

## 3.

Electrical Current
Current is the rate of flow of charge through a conductor.
charge
current
time
I
q
t
Current flow is defined in the
direction of positive charge;
since electrons flow in wires,
current is opposite the flow of
electrons.
SI
units
1coulomb
1 amp
1 second
C
A
s
Small microamp ( A) currents
larger amounts of current are
CURRENT
EFFECT
0.0001 A
threshold of feeling
0.001 A
mild shock felt
0.005 A
shock is painful
0.015 A
muscle control is lost
0.100 A
death can occur

## 4.

Electrical Current
Potential difference creates an
electric field in a circuit. The
electric field induce charge to flow.
Moving electrons collide with
vibrating atoms, so they zigzag in
a random path, with a slow
click for
forward drift velocity.
animation
Although the electric field travels at near the speed of light, the
drift velocity of electrons is less than a millimeter per second.
Electrons do not race around a circuit!

## 5.

Electrical Resistance
Resistance is a measurement of a material’s ability to resist
the flow of electrical charge.
voltage
resistance
current
V
R
I
SI 1 ohm 1 volt
units
1 amp
Resistivity depends on the nature of a material. Conductors
have low resistivity and insulators have high resistivity.
Resistance depends on
the material’s type,
length, cross- section,
and temperature.
click for
resistance
codes
resistance
applet
V
A

## 6.

Alternating versus Direct Current
Thomas Edison brought direct current
to the masses. Nikola Tesla proved
alternating current to be more efficient.
Alternating current (ac) switches the
direction of the current back and forth
at 60 times per second (60 Hertz).
DIRECT CURRENT
North America uses ac for its power
grid because it was safer and more
reliable when infrastructure began.
Batteries provide direct current (to
increase battery life).
Most devices use direct current so a
transformer converts ac to dc often at
lower voltage.
Direct energy conversion devices like
light bulbs, heaters, can run off ac or dc
ALTERNATING CURRENT
click for animation

## 7.

Ohm’s Law
Electrical circuit versus a water circuit
click for
animation
click for
animation
slope = 1/R
voltage
OHMIC
cu
rr
en
t
cu
rr
en
t
cu
rr
en
t
When a device shows a linear relationship between
voltage and current, it is said to be “ohmic”
slope = 1/R
voltage
NONOHMIC
slope = 1/R
voltage
ONE-WAY (DIODE)

## 8.

Energy, Power, and Cost in Circuits
POWER LAW
power
energy charge voltage
current voltage
time
time
P I V
Combine Power Law with Resistance equation
P I V I(IR)
P I R
2
V
P I V
V
R
( V )2
P
R
Cost of Electrical Power
energy power time
Example - Find the cost of a 1500 watt hair dryer run for
12 minutes, using the rate of \$0.10 per kilowatt hour.
cost rate energy
energy in kilowatt hours (kW h)
cost in dollars (\$)
time in hours (h)
\$
rate in dollars per kilowatt hours
kW h
1 kW
1.5 kW
10 3 W
1h
time 12 min
0.2 h
60 min
power 1500 W
cost 0.10
\$
kW h
(1.5 kW) (0.2 h)
cost \$0.03 or 3 cents!

## 9.

Kirchoff’s Rules
Rule #1 - The Loop Rule
A statement of
conservation of energy
-4 v
The sum of the potential
differences (voltages) around
any closed loop in a circuit
must be zero
-2 v
example
+12 v
Rule #2 - The Junction Rule
A statement of
conservation of charge
The current entering a
junction in a circuit equals the
current leaving the junction
2A
10 A
3A
5A
example
-6 v

## 10.

Series Circuits
A series circuit has only one pathway around the circuit
Rule # 1 means that the voltage
across all resistors in series must
add up to the source voltage
V
V11
V22
V33
Rule # 2 means that the current
through all resistors in series
must equal the source current
I I1 I2 I3
Combine the two equations:
V V1 V2 V3
I
I1
I2
I3
Req R1 R2 R3
click for
animation

## 11.

Series Christmas Tree Lights
Series wiring was often used for Christmas tree lights
One bulb burns out, they all go out!
Who’s to say which one burned out!
Modern bulbs use a “jumper” wire.
This wire has insulation around it.
When the bulb burns out, the
jumper now has 120 volts across it.
The voltage produces a spark, and
the insulation burns off. The circuit
is now complete, with the one bulb
not lit but easily replaced.

## 12.

Parallel Circuits
A parallel circuit has multiple pathways around the circuit
Rule # 1 means that the voltage
across all resistors in parallel
must equal the source voltage
V V1 V2 V3
Rule # 2 means that the current
through all resistors in parallel
must add up to the source current
I I1 I2 I3
Combine the two equations:
I
I1
I2
I3
V V1 V2 V3
1
1
1
1
Req R1 R2 R3
click for
animation
click for
animation

## 13.

click for
animation
Combination Circuits
click for
animation
A combination circuit must be simplified into groups of series and
parallel resistors, and then the equivalent for each group is then found.
Req 10 2 12
1
1 1
= +
Req = 3
Req 12 4
Req =1+2 +3 + 4 =10

## 14.

Combination Circuits
The total current in the combination circuit is determined and used to
work “backwards” to find other branch currents and resistor voltages.
V
120 v
I
12 A
Req 10
Find current through circuit
I V / R 36 /12 3 A
Find current through 12 equivalent
V IR 12 3 36 v
Find voltage across 3 equivalent
V IR 3 2 6 v
Find voltage across 2 resistor