Electrical Power

1
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

2
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

3
Electrical Power

• P IV I2R V2/R

4
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
  I2(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 V2/R ? PR
  V2, or V 25V. Power lost is P IV 0.35W.

5
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)

6
Electrical Energy

• Electrical Energy is priced in kWh
• One kiloWatt 1000 Watts
• One kWh One kW for one hour

7
Electrical Energy

• Electrical Energy PowerTime 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

8
Electrical Energy

• Hand Generator

9
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?

10
Resistance of an object

• What would we expect it to depend on?
• (Resistance is the impedance to the flow of
  charge)

11
Resistance of an object

• What would we expect it to depend on?
• (Resistance is the impedance to the flow of
  charge)

L
A
12
Find Resistance of a material

• Depends on four factors
• R 8 Temp
• R 8 RHO (?) resitivity
• R 8 Length
• R 8 A-1 (cross-sectional Area)

13
Low resistance

• Short
• Fat
• cold

14
High Resistance

• Long
• Thin
• Hot

15
Series and Parallel Circuits
L
Series Single Path, high effective resistance
a
L
A
Parallel Multiple Paths, low effective
resistance
16
Resistivities at 20C Resistivities at 20C
Material Resistivity
Aluminum 2.82 108
Copper 1.72 108
Gold 2.44 108
Nichrome 150. 108
Silver 1.59 108
Tungsten 5.60 108
From Reference tables
17
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?

18
AWG gauge ConductorDiameter 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
19
(No Transcript)
20
Monthly Service Charge is 18 Monthly Service Charge is 18
Central Hudson Variable Costs Central Hudson Variable Costs 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

21
Monthly Charges Monthly Charges Monthly Charges (Includes the effect of Schedules 59, 91, 93)
6.00 Basic Charge, Basic Charge, plus
0.06850 0.06850 per Kwh for the first per Kwh for the first per Kwh for the first 600 Kwhs
0.07933 0.07933 per Kwh for the next per Kwh for the next per Kwh for the next 700 Kwhs
0.09260 0.09260 per Kwh for all additional Kwhs per Kwh for all additional Kwhs per Kwh for all additional Kwhs per Kwh for all additional Kwhs

Example - Example -                  
  If you used 1450 1450 Kwhs of electricity, your bill would be calculated like this Kwhs of electricity, your bill would be calculated like this Kwhs of electricity, your bill would be calculated like this Kwhs of electricity, your bill would be calculated like this Kwhs of electricity, your bill would be calculated like this Kwhs of electricity, your bill would be calculated like this  
  Basic Charge 6.00  
  0.06850 0.06850 x 600 Kwhs 41.100  
  0.07933 0.07933 x 700 Kwhs 55.531  
  0.09260 0.09260 x 150 Kwhs 13.890  
  Charge for 1450 1450 Kwhs 116.52 (franchise fees not included) (franchise fees not included)