transmission lines

Question

Suppose a company decides to ship 150 000 W over 2.0 Ω transmission lines at 560 V.
a) How much power is lost? (and.I = 143,498 W)


b) What is the efficiency of transmission?(ans. η = 4.3%)


c) Compare the power lost above to the power lost in question 1. Discuss which mode of power delivery (high voltage at low current OR low voltage at high current) is more efficient. Why?

Answer 1

The answers you were given don't quite make sense, so I suspect there's a typo or two.  That said, here's the general approach.

 

First, power equals current times voltage, P = I*E.  We can use this to calculate current.  Once we have current, we use Ohm's law (E = I*R) to find voltage drop across the wire, and then use P = I*E again to find power drop in the wire.

 

The last question is the important concept for you to grasp, that it's more efficient to transport power at high voltage (and low current).  This can also be seen if you substitute Ohm's law into the power formula to get P = I²R.

 

If you have any additional questions on this, let me know.

Answer 2

(a)

 

Start with

 

P = 150,000 W

 

Divide by line voltage to get current

 

I = P/V = 150,000/560 A ≅ 267.86 A

 

Power dissipated along the line is

 

ΔP = I²R = (267.86)²(2.0) W ≅ 143,498 W

 

(b)

 

Efficiency is

 

η = 100(P - ΔP)/P = 100(150,000 - 143,498)/150,000 ≅ 4.3% 

 

(c)

 

You want to minimize ΔP, so from

 

ΔP = I²R

 

you can conclude that low current is preferable to high current, but it also depends on the voltage:

 

ΔP = I²R = (P/V)²R = P²R / V²

 

So you will also want a high voltage to minimize the loss.  In short, you want a combination of low current with high voltage.