Transcript ElectricalCircuitsx

Electrical Circuits
ALESSANDRO VOLTA
(1745-1827)
POTENTIAL IN VOLTS,
CURRENT IN AMPS,
RESISTANCE IN OHMS!
ANDRE MARIE AMPERE
(1775-1836)
GEORG SIMON OHM
(1789-1854)
Sources of Voltage
Voltage, also
known as
“electromotive
force”, can be
create by
many sources
of energy
chemical
hydroelectric
nuclear
solar
wind
geothermal
biomass
ALLESANDRO VOLTA AND THE ELECTRIC BATTERY
A VOLTAGE SOURCE IS LIKE A WATER PUMP
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.
ION FLOW IN A FLOURESCENT BULB
SI
units
1 amp
1coulomb
1 second
Small microamp (μA) currents
flow through your body, but
larger amounts of current are
dangerous, even deadly.
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
Electrical Current
Potential difference creates an
electric field which induces
charge to flow in a circuit.
Moving electrons collide
with vibrating atoms, so they
zigzag in a random path,
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with a slow drift velocity. animation
The electric field travels at near the speed of light, but the drift
velocity is less than a millimeter per second! Electrons do not
race around a circuit.
Electrons flow in solid wire
circuits. Positive and
negative ions flow in
batteries (wet and dry cells),
and in gas-filled light bulbs.
Electrical Resistance
Resistance is a measurement of a material’s
ability to resist the flow of electrical charge.
1
1V
1A
ΔV
I R
V
1 volt
SI
1
ohm
R
units
1 amp
I
memory triangle
Resistivity depends on the nature of a material. Conductors
have low resistivity and insulators have high resistivity.
voltage
resistance 
current
Resistance depends on
the material’s type,
length, cross- section,
and temperature.
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resistance
codes
resistance
applet
Ohm’s Law
Electrical circuit versus a water circuit
When a device shows a linear relationship between
voltage and current, it is said to be “ohmic”
OHMIC
NONOHMIC
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animation
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animation
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 (R = ΔV/I)
 V 
2
P  I V  I (IR)
P

IV

PI R

 V
 R 
(V )2
P
R
Cost of Electrical Power
Example - Find the cost of a 1500 watt hair dryer run for
12 minutes, using the rate of $0.16 per kilowatt hour.
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cost  rate  energy
1 kW
website
power  1500 W  3
 1.5 kW
10 W
energy in kilowatt  hours (kW  h)
 1h 
time

12
min


  0.2 h
cost in dollars ($)
 60 min 
energy  power  time
time in hours (h)
 $ 
rate in dollars per kilowatt  hours 

 kW  h 
cost  0.16
$
kWh
 (1.5 kW)  (0.2 h)
cost  $0.048 or 4.8 cents!
Kirchhoff’s Rules
Rule #1 - The Loop Rule
A statement of
conservation of energy
The sum of the potential
differences (voltages) around
any closed loop in a circuit
must be zero
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
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  V1  V2  V3
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
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animation
ΔV1
ΔV
ΔV2
ΔV3
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  I 1  I2  I3
Combine the two equations:
I
I1
I2
I3



V V1 V2 V3
1
1
1
1



Req R1 R2 R3
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animation
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animation
ΔV
ΔV1
ΔV2
ΔV3
Equivalent Resistance
Holiday Lights
Series wiring was often used for Christmas tree lights from 1900-1940
Most sets had 8 bulbs sharing 120 volts, so 15 volts
each. But, when one bulb burns out they all go
out!
Parallel wiring became popular in the 50s and 60s
Each bulb has 120 volts and consumes ~10 watts
(like a night light). When one bulb burns out,
the rest stay on, but they use a lot of power usually 250 watts per strand - and they get hot!
Miniature lights became popular by the 1970s
Most are 50 bulbs in a series “set”, then a few
sets in parallel (up to 300), and use little power.
To avoid “one out, all out” modern miniature
bulbs use a “jumper” with insulation around
it. When the bulb burns out, the jumper wire
now has 120 volts across it, so the insulation
burns off. The circuit is now complete.
Now LED lights are popular and inexpensive
Light emitting diodes (LED) use very little
power, typically under 5 watts for 70 lights!
Applied Circuits
Parallel circuits are used for
Speakers in series or parallel
wiring 120 volt outlets.
• All devices plugged in get 120 volts
• Each is independent of the others
• As more devices are used, the total
resistance decreases and total
current increases.
• Most circuits are limited to 20 amps.
Batteries in series or parallel
Applied Circuits
What type of wiring scheme is used for these circuits?
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animation
Combination Circuits
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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 
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 12Ω equivalent
V  IR 12  3  36 v
Find voltage across 3Ω equivalent
V  IR  32  6 v
Find voltage across 2Ω resistor