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 0.014, 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 0.014wire 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 20 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

L

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

L

A

L

Parallel: Multiple Paths, low effective resistance

Series: Single Path, high effective resistance

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 gaugeConductorDiameter 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 $18Central 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 –

(Includes the effect of

Schedules 59, 91, & 93)

$6.00 Basic Charge, plus

$0.06850 per Kwh for the first 600 Kwhs

$0.07933 per Kwh for the next 700 Kwhs

$0.09260per Kwh for all additional Kwhs

Example -                  

 

If you used 1450

Kwhs of electricity, your bill would be calculated like this:  

 

Basic Charge = $6.00  

  $0.06850 x 600 Kwhs = $41.100  

  $0.07933 x 700 Kwhs = $55.531  

  $0.09260 x 150 Kwhs = $13.890  

  Charge for 1450 Kwhs = $116.52 (franchise fees not included)