Originally Answered: Can someone explain this physics homework question?
The question is very badly worded. I believe it should be this (but I might be wrong!):
Power is transmitted between 2 high voltage cables over a distance of 80km.(so each cable is 80km long).
At the supply end, there is a voltage of 150kV between the ends of the cables.
The current through each cable is 300A.
Each cable has a resistance of 5x10^-5 ohms per metre.
Which statements are incorrect:
1) Each cable has a voltage of 1.2 kV between its ends.
2) 0.8% of a cable's output is being converted into heat in the cable
3) The heat generation inside a cable is 45*10^16J per second
4) The user gets an output voltage of 149 kV
The important point is that there are 4 different voltages here. Students often get confused by this and mix them up. Think of the 'circuit as a battery, 2 long wires, and a bulb.
The 'battery' supplies 150kV. Call this V1.
Due to the (small) resistance of each wire, there is a voltage drop from one end of a wire to the other end. Call this V2. Total voltage drop across both wires is 2V2 (think of the 2 wires as 2 resistors, each with a voltage V2 across it).
There is a voltage V3 across the bulb ('user')
V3 = V1 - 2V2.
The resistance of a single cable = length x resistance per metre = 80,000 x 5x10^-5 = 4Ω
The voltage drop between the ends of a cable (separated by 80km) is V = IR = 300x4=1200V=1.2kV.
So the 1st statement is correct.
The power into the cables from the supply = P=VI = 150,000 x 300 = 4.5x10^7 W =45MW
The heating power in ONE cable = P = VI = 1200 x 300 = 360000W = 0.36MW
The power output of the cable (at the user end) = 45 - 0.36 = 44.64MW
% of a cable's output is being converted into heat in the cable = (0.36/44.64) x 100 = 0.806%
The 2nd statement is correct (ignoring rounding)
Statement 3 is Incorrect. The heat generation in the cable is NOT 45x10^16W. It is 0.36MW (see above).
4) The user receives a voltage V3 - V1 - 2V2 = 150- 2x1.2 = 147.6kV
Statement 4 is Incorrect.
However, please note the question I answered is not quite the same question as your question - I may have misinterpreted your question.