Power Loss with and without Transformers

[titaniumpen]

Homework Statement

65 kW is to arrive at a town over two 0.100 ohm lines. Estimate how much power is saved if the voltage is stepped up from 120 V to 1200 V and then down again, rather than simply transmitting at 120V.


2. The attempt at a solution
First I want to find the power lost in each line. Since the power is delivered over two lines, the power over each line is half of the total.

P = VI
65000/2 = 120I
I = 271 A

So for the total power lost in the two lines,
P = (I^2)*R*2
P = 14670 W

Now I want to find the power lost if the voltage is 1200V. The same procedures apply.

65*10^3/2 = 1200I
I = 27.1 A

P = (I^2)R*2
P = 146.7 W

Difference between the two values of "wasted" power = 14500 W

That's my answer. But the textbook gave me an answer of around 54000 W. I looked at its steps. I don't know if they are wrong. The book first finds the delivered current by the equation 65000 W = 120 I

Then it finds the power wasted by the 2(I^2)R. Is that double counting?

 

[collinsmark]

First I want to find the power lost in each line. Since the power is delivered over two lines, the power over each line is half of the total.

That's the error, there. It takes at least two wires to complete the circuit. If either one of the wires went down, no current would flow through the other wire, and no power would be delivered to the town.

Remember, a circuit requires a closed loop. Current flows in a circle. From the power station, through one wire to the town, and back to the power station through the other wire. Each wire caries the same current as the other, just in the opposite direction.

The first step is to find to find out how much current is flowing through the circle (circuit). Since the problem statement said the power flowing to the town is P, the current flowing through the circuit (and thus each wire) must be P/V.

 

[titaniumpen]

I was looking at it a few hours ago, and I realized that you have to interpret the two wires as a series circuit. Then you told me that the second wire is the return path. Now everything makes sense. :D

 

[HarshChandola]

Transformer in SMPS help!

Hi there everybody, I'm new here, I m currently working on a project and i need to know few things, could some one please give me reasons that why do we have transformers in SMPS?
Thank You

 

[Antiphon]

Hi there everybody, I'm new here, I m currently working on a project and i need to know few things, could some one please give me reasons that why do we have transformers in SMPS?
Thank You

This is a new thread (mods?) but the short answer is when you need 1) galvanic isolation for safety reasons or 2) when the conversion ratio for the SMPS is very high and would lead to large inefficiencies by requiring very large or very small duty cycles in the SMPS.

If you want to take a 400V bus and buck-regulate it down to 1V, you will need magnetic transformers or face a 400:1 duty cycle and horrid efficiency.