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AC Electricity
Getting Power to Our Homes
• Let’s power our homes with DC power
– DC means direct current: just like what batteries deliver
• But want power plants far from home
– and ability to “ship” electricity across states
• So power lines are long
– resistance no longer negligible
Power Dissipated in an Electricity Distribution System
• Estimate resistance of power lines: say 0.001 Ohms per meter, times 200 km = 0.001 W/m ´ 2´105 m = 20 Ohms
• We can figure out the current required by a single bulb using P = VI so I = P/V = 120 Watts/12 Volts = 10 Amps (!)
• Power in transmission line is P = I2R = 102 ´ 20 = 2,000 Watts!!
• “Efficiency” is e = 120 Watts/4120 Watts = 0.3%!!!
• What could we change in order to do better?
The Tradeoff
• The thing that kills us most is the high current through the (fixed resistance) transmission lines
• Need less current
– it’s that square in I2R that has the most dramatic effect
• But our appliance needs a certain amount of power
– P = VI so less current demands higher voltage
• Solution is high voltage transmission
– Repeating the above calculation with 12,000 Volts delivered to the house draws only
I = 120 Watts/12 kV = 0.01 Amps for one bulb, giving
P = I2R = (0.01)220 = 20´10-4 Watts, so
P = 0.002 Watts of power dissipated in transmission line
Efficiency in this case is e = 120 Watts/120.004 = 99.996%
DANGER!
• But having high voltage in each household is a recipe for disaster
– sparks every time you plug something in
– risk of fire
– not cat-friendly
• Need a way to step-up/step-down voltage at will
– can’t do this with DC, so go to AC
Why is AC the solution?
• AC, or alternating current, is necessary to carry out the transformation
• To understand why, we need to know something about the relationship between electric current and magnetic fields
• Any current-carrying wire has a circulating magnetic field around it: