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 = I 2 R = V 2 /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 , 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  wire and household power, how much power is lost in the wire? –P = 44000W, R = Ohms. P = V^2/R  PR = V^2, or V = 25V. Power lost is P = IV = 0.35W.

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 MaterialResistivity Aluminum2.82 × 10–8 Copper1.72 × 10–8 Gold2.44 × 10–8 Nichrome150. × 10–8 Silver1.59 × 10–8 Tungsten5.60 × 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 OOO OO

Monthly Service Charge is $18 Central Hudson Variable Costs $0.047 $ $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) $6.00Basic Charge,plus $ per Kwh for the first600Kwhs $ per Kwh for the next700Kwhs $ per Kwh for all additional Kwhs Example - If you used1450 Kwhs of electricity, your bill would be calculated like this: Basic Charge=$6.00 $ x600Kwhs=$ $ x700Kwhs=$ $ x150Kwhs=$ Charge for1450Kwhs=$ (franchise fees not included)