Question

I2 N Helpful transformer equations: EMF1 effective For Homework, do (and write-up) all problems. If you are in doubt as to what the write-up should look like, see the file "Example - writing up homework problems" on Canvas. 1. A typical house has 100W lightbulbs, and has 10 of them on at any given time. The voltage from the wall is 115V. What is the resistance, R, of a house? There are 1000 houses in your neighborhood, all connected to the same voltage source at the same point. What is the combined resistance of your neighborhood? 2. 3. The power station burns a lot of coal, so it's smoky, and they want to put it a long way from your house... say, 60 miles (100km) away. The power cables (for reasons beyond the scope of this class - the buzzword is "skin depth") have a cross-sectional area of 1cm2. Copper has a resistance of 1.7e-8 2*m. What is the resistance of the power cable from the station to your neighborhood? 4. The power station puts out 115V, and the current runs through 100km of wires with resistance Rwire to your neighborhood, which has resistance Rhouses. (See image next page). Find formulae (and numbers) for Voltage at the wall socket in a house Power delivered to the houses Power lost in the wire from the station Fraction of power that got to the houses. a. b. c. d. IV 5. The power station puts out 115kV, and the current runs through 100km of wires with resistance Rwire to your neighborhood, which has resistance Rhouses. Just before going to the houses, the wires go into a transformer with turns ratio 1000:1, so the voltage is stepped down by a factor of 1000. (see image next page). Find formulae (and numbers) for Power delivered to the houses Power lost in the wire Fraction of power that got to the houses. a. b. c.

Answer 1

According to the above given question the solution follows as that (1) Ans: The total power of all bulbs rightarrow = 100 times 10 = 1000 watt where voltage v = 115 v, Current (i) = p/v - 1000/115 = 66.667 A rightarrow Resistance R = V/I = 115/66.667 = 1.785 ohm (2) Ans: The total resistance will be Parallel combination of resistance of 1000 houses. Then the resistance of house = -R Therefore rightarrow 1/R_= 1/R + 1/R + .... upto 1000 term. = 1000/R Therefore R_= R/1000 (3) Ans: The Length of cable (L) = 100 km rightarrow 100 times 10^3 m The cross Sectional area (A) = 1 cm^2 = 1 times 10^- 4 m^2 The Resistivity (S) = 1.7 times 10^- 8 ohm m Therefore the Resistance R = S L/A = 1.7 times 10^- 8 times 100 times 10^3/10^- 4 = 17 Ohm (4) Ans: The voltage of = 115 V The power deliver to house () = I^2