Attempt at worked power loss example

[GreyArea]

I’m trying to work through an exercise, you’ll probably recognise it.  We’re trying to supply 10E10 power at 115V through a cable with resistance 0.05u? per foot.  Calculate the power loss per foot.

OK, so our good friend P=IV gets rearranged to I=P/V so I get 869E6 Amps (869MA).

Next we’ll calculate the power loss on the foot of cable;

I now have the current and the resistance so let’s calculate the Vdrop;

Vdrop=IR = 869MA x 0.05u?  = 869E6x.05E-6 = 43.45V

So what’s the power loss?  Well, I can now do P=IV on the loss of 43.45V so;

Ploss= 869MA x 43.45 = 37GW!!   This is bigger than the power we started out with, so does this mean that we’re losing more power than we start with?

To calculate Vdrop, I’m multiplying the current by a much smaller number so obviously I’ll get a fractional result, I think the mistake I’m then making is that I’m now taking that result and multiplying it by the same starting current as it’s >1 of course I’m going to get a bigger result.

I think my answer must be wrong because later questions are asking me to calculate how long the cable would need to be before the power is completely lost.  I just don’t know where I’ve gone wrong in my thinking.

[Chalcogenide]

10E10 = 1E11 = 100GW, and 37GW/100GW is almost equal to 43.5V/115V, so it all works out fine, although the numbers in this exercise are very far away from any realism.

[keethrax]

10E10 = 1E11 = 100GW, and 37GW/100GW is almost equal to 43.5V/115V, so it all works out fine, although the numbers in this exercise are very far away from any realism.

Well, he didn't make up the numbers... it's straight out of the Art of Electronics for one, and probably ends up elsewhere as well. The whole point of the exercise is why the power grid isn't  (Low Voltage) DC. Parenthetical note to head of the "What about HVDC transmission lines?" question.

Hey GreyArea: Are you looking at one of the new (3rd) edition books, or an older one? Just curious if the exercise made the transition into the new book.

EDIT: Addressed question to wrong person
EDIT 2: Fixed typo