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# Electrical Power

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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 = 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.

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 = 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

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 ∞ Temp • R ∞ RHO (ρ) resitivity • R ∞ Length • R ∞ 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. 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?