Power needed to light NYC? (Circuits! Please help.) Hi there. I have a question from my physics lab. We're supposed to write a paper about the war of currents between Edison and Tesla/Westinghouse, and part of this involves estimating "the magnitude of the design problem." The actual question is as follows. 1. The problem statement, all variables and given/known data "What was the magnitude of the design problem. Estimate the power required to light the city of New York at that time [about 1900], the miles of wire required, the batteries required, the hydroelectric power required,...[.]" I suspect that this is mainly a matter of getting the right order of magnitude, as much of the information I would need to get a precise number is simply not findable, at least that I can see. I talked to several of the other lab groups from the class, and they couldn't find relevant information, either. Here is the information I could find, and some assumptions I was told it was okay to make (if they seem way off, I would vastly appreciate correction): - Population of NYC in 1900: 3,437,202 - Assumption: 2 light bulbs per person. - Assumption: Light bulb used was the Edison-Mazda cage filament lamp, which required 110-120 V (I used an average of 115 V) and 500 W. - Assumption: Wires used were solid copper, cylindrical, with a diameter of 1 cm. - Electrical resistivity of copper: 1.68 x 10^-8 ohm-meters. - Land area of NYC: 303.3 mi^2. - One city block: 0.25 mi^2. - Assumption: 10 buildings per city block. - Assumption: 1 mile of wire per building in 1900. Question 1. Is there a better way to estimate the miles of wire used? 2. My work so far I apologize in advance for the non-prettiness of my equations. 3,437,202 people * 2 light bulbs/person = 6,874,404 light bulbs. 500 W/bulb * 6,874,404 bulbs = 3.44*10^9 W required. 6,874,404 bulbs * 115 V/bulb = 7.91*10^8 V. P = Vi. i = P/V = 500 W/115 V = 4.35 A/bulb. 4.35 A/bulb * 6,874,404 bulbs = 2.989*10^7 A. 303.3 mi^2 / 0.25 mi^2 = 1.47*10^6 city blocks in New York city, which means 1.47*10^7 miles of wire using the assumptions above. Resistance of all this wire = R = rho(Cu) * (L/A) = 1.68*10^-8 ohm-meters * (2.37*10^10 m wire/(pi*(0.05 m)^2)) = 5.06*10^4 ohms. Power lost in the wire = (i^2)*R = (2.989*10^7 A)^2 * 5.06*10^4 ohms = 4.52*10^19 W. Question 2. Why is my power lost in the wire so much higher than the power required to light the light bulbs? I asked my prof; he said I might be using the wrong equation. He said that I might want to consider: P = Vi = (i^2)*R = (i^2)*(R(load)+R(line)). He then provided two other equations, but I don't understand what they mean or how he got them: P(lost) = P/(1+(P(load)/P(line)))) = P+(R(line)/(R(load)+R(line))). Question 3. Can someone point me to a good resource for finding out what electrical load is? Wikipedia said that the circuit connected to the output terminal is the load (which - I don't understand how that description differs from the entire circuit); my textbook, as far as I can see, didn't cover it. Should I assume that the light bulbs are the load? Question 4. My physics lecture prof suggested that I consider the branching of all the light bulbs in parallel, and said that I might assume that the wire branches 5 or 6 times from the power plant to the individual light bulb. How would I apply this? Question 5. Am I just making this a billion times more complicated than it should be? Should I just put down "42" as the answer? Any insight would be very much appreciated. Thank you for your time and attention.