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Electrical Power
• Power is the rate at which work is done or
energy is expended.
– Unit is Watt = Joule / second
– (James Watt worked on steam engines and launched
the industrial revolution)
• Power = Work / time
• Electrical Energy = Power * Time = VIt
Electrical Power
• Power is the rate at which a charge is
moved through a potential difference
• Power = Current * Voltage
= (Coulombs/sec) * (Joules / Coulomb)
= Joules / second
• Electrical Energy = Power * time = P *t
– J/sec * sec = Joules
Electrical Power
• P= IV = I2R = V2/R
Examples
• The power lines leading to a house typically
support 200A at 220V.
– How much power is the maximum available?
– If the wire leading to the house has a resistance of
0.014W, how much power is lost in the wiring?
– V/I = R = 1.1 Ohms. P = IV = 44kW in house. P =
I^2(0.014) = 560W in the wire leading to the house.
• The voltage in the neighborhood is typically
7200V. For the same 0.014W wire and
household power, how much power is lost in the
wire?
– P = 44000W, R = 0.014 Ohms. P = V^2/R  PR =
V^2, or V = 25V. Power lost is P = IV = 0.35W.
Electrical Energy
• Electrical Energy
– Follows the same conservation laws as all
other forms of energy
– Potential energy (charge at a high potential)
– Converts to kinetic energy (via a motor)
– Converts to thermal energy (via resistance)
Electrical Energy
• Electrical Energy is priced in kWh
– One kiloWatt = 1000 Watts
– One kWh = One kW for one hour
Electrical Energy
• Electrical Energy = Power*Time = Pt =VIt
• Electrical energy has units of Joules
• 3,600,000 Joules =
1000 Joules / sec * 3600 seconds =
1000 Watts * 1 hour = 1kiloWatt-hour =
1 kWh = $0.13
Electrical Energy
– Hand Generator
Examples
• Given a 60W light bulb in a 120V circuit, how much
current does it draw?
– What is its resistance?
– How many kWh does it consume in 8 hours?
– How much does this cost at $0.13/kWh?
• Given a stove with a burner having a 20W resistance
– How much power is developed with a 120V supply? How
much current?
– How much power is developed with a 240V supply? How
much current?
Resistance of an object
• What would we expect it to depend on?
• (Resistance is the impedance to the flow
of charge)
Resistance of an object
• What would we expect it to depend on?
• (Resistance is the impedance to the flow
of charge)
A
Find Resistance of a material
• Depends on four factors
– R ∞ Temp
– R ∞ RHO (ρ) resitivity
– R ∞ Length
– R ∞ A-1 (cross-sectional Area)
Low resistance
• Short
• Fat
• cold
High Resistance
• Long
• Thin
• Hot
Series and Parallel Circuits
a
A
Resistivities at 20°C
Material
Resistivity
Aluminum
2.82 × 10–8
Copper
1.72 × 10–8
Gold
2.44 × 10–8
Nichrome
150. × 10–8
Silver
1.59 × 10–8
Tungsten
5.60 × 10–8
From Reference tables
Examples
• Given a 100m silver wire with a 0.001m cross
sectional area, what is its resistance?
• Given a 100m nichrome wire with a 0.001m cross
sectional area, what is its resistance?
• What is the length of a piece of 16 gauge copper wire
with a resistance of 20 ohms?
AWG gauge
Conductor
Diameter mm
Ohms per 1000 ft.
Ohms per km
OOOO
11.684
0.049
0.16072
OOO
10.40384
0.0618
0.202704
OO
9.26592
0.0779
0.255512
0
8.25246
0.0983
0.322424
1
7.34822
0.1239
0.406392
2
6.54304
0.1563
0.512664
3
5.82676
0.197
0.64616
4
5.18922
0.2485
0.81508
5
4.62026
0.3133
1.027624
6
4.1148
0.3951
1.295928
7
3.66522
0.4982
1.634096
8
3.2639
0.6282
2.060496
9
2.90576
0.7921
2.598088
10
2.58826
0.9989
3.276392
11
2.30378
1.26
4.1328
12
2.05232
1.588
5.20864
13
1.8288
2.003
6.56984
14
1.62814
2.525
8.282
15
1.45034
3.184
10.44352
16
1.29032
4.016
13.17248
Monthly Service Charge is $18
Central Hudson Variable Costs
$0.047
$0.002
-$0.007
$0.004
$0.001
$0.003
$0.001
$0.004
$0.065
$0.014
Total
$0.134
Monthly Charges
–
$6.00
Basic Charge, plus
$0.06850 per Kwh for the first
600
$0.07933 per Kwh for the next
700
per Kwh for all additional
$0.09260 Kwhs
(Includes the
effect of
Schedules
59, 91, & 93)
Kwhs
Kwhs
Example If you
Kwhs of electricity, your bill would be calculated
used 1450 like this:
Basic
Charge
=
$6.00
$0.06850
x
600
Kwhs =
$41.100
$0.07933
$0.09260
x
x
700
150
Charge for 1450 Kwhs
Kwhs
Kwhs
=
=
=
$55.531
$13.890
(franchise fees not
$116.52included)